Skip to content

Manipulator Control

Manipulator control closes a loop on joint position, on end-effector pose, or on contact force. Which of the three a flight system closes determines what tasks it can attempt, and the choice has always been made against processor budget rather than against control theory.

The corpus separates into five families by what the loop is closed on. Resolved motion rate control computes joint rates from a commanded end-effector velocity through the manipulator Jacobian, and is the 1969 origin of Cartesian arm control [13]. Redundancy resolution adds a null-space term to the pseudoinverse solution so that a seven-joint arm can serve a secondary goal, such as keeping the nearest point of the arm away from an obstacle, with the end-effector trajectory unchanged; the founding result is a graphics simulation with an exact world model, not a sensed one [16]. Khatib moved collision avoidance from the planner into the servo loop as a potential field, and states that local minima can trap the robot in a cluttered scene [15]. Force and impedance control closes the loop on contact: adaptive compliance control enforces a target interaction dynamics between reference position and contact force with no force setpoint, and is simulation only [21]. Joint and Cartesian impedance control with adaptive friction compensation has been run on one finger of the DLR-HIT II hand, a laboratory result on one prototype [22]. Free-floating base control, treated in a later section, adds the reaction of the arm on its carrier to every one of these.

Flown planetary arms use the first family and a position-based form of the fourth. The remaining three are ground-tested or simulated for space use. Reviews that organize the free-floating literature are available [18][28], as is a short compilation of published arm specifications from the Canadarm series to the Mars Exploration Rover deployment device [29].

The flown Mars arm lineage and its open-loop contact scheme

Section titled “The flown Mars arm lineage and its open-loop contact scheme”

The flown Mars arms are one family. The Mars Pathfinder deployment mechanism, the Mars Surveyor 2001 4 degree of freedom arm, the Mars Exploration Rovers’ 5 degree of freedom instrument deployment device, the Phoenix arm, the Mars Science Laboratory arm, InSight’s 4 degree of freedom arm refurbished from Mars Surveyor 2001, Perseverance’s 5 degree of freedom robotic arm and the 3 degree of freedom sample handling arm all descend from a common flight software lineage: InSight’s builds on Phoenix’s, which builds on the principles of the Mars Pathfinder onboard software [1]. That software is deliberately simple and predictable because of the power, compute and communication constraints, and it achieves straight-line Cartesian motion by breaking a task into via points, solving the inverse kinematics at each and interpolating between them in joint space [1].

None of them ran a continuous force loop. Enforced deflection, the heritage way of loading a target, is an open-loop joint-space command: the arm is driven past contact by the displacement its compliance model says will produce the wanted wrench [1]. It works because the target does not move and the only regulated quantity is a static preload. Continuous in-contact force control is one of three capabilities the Mars Sample Return sample transfer system would have introduced for the first time in planetary exploration [1].

Perseverance’s docking sequence is the same algorithm applied to a mating task. Iterative Force Control holds the arm still, reads the 6 degree of freedom force torque sensor, computes the Cartesian motion the pose-dependent compliance matrix says will produce the missing force, converts it to joint commands, executes, and reads again, terminating on a deadband around the goal or on a parameterized iteration limit [4]. The compliance matrices are computed analytically per link and tool and tuned by kinematic calibration with laser metrology. The arm applies several hundred newtons to surface targets and over 700 N into the dock [4].

Placement accuracy, not force, is the quantity reported from flight. The Mars Exploration Rover deployment device placed instruments with a stated repeatability of about 1 mm and 1 degree, given as an operations summary without a supporting measurement campaign [24]. For Curiosity the arm error budget predicted misses of 26.2 mm total and 23.2 mm lateral against requirements of 20 mm and 15 mm; after calibration the estimate was 14.0 mm and 12.7 mm, and laser tracker verification on Earth showed under 5 mm [25]. On Mars, a drill hole on sol 180 landed within about 2 to 3 mm of the target picked in an image, one measurement on one hole [26]. Phoenix reported more than 150 sols of arm operation, 53 dig sequences and 18 sample deliveries, with hardness reported as motion-impeded events and no force or placement figures quantified [27].

Perseverance’s arm force torque sensor must measure loads on the order of plus or minus 800 N and 200 Nm while the sensor swings through 100 degrees Celsius over a Martian day, and it is calibrated to three overlapping load ranges by one two-stage least squares fit that absorbs offset, scaling and thermal error introduced when the sensor was integrated into the arm [2]:

RangeForce rangeMoment rangeAbsolute accuracy, forceAbsolute accuracy, momentRelative accuracy, forceRelative accuracy, moment
Precision500 N125 Nm43 N11 Nm29 N7.5 Nm
Nominal800 N200 Nm65 N16 Nm45 N11 Nm
Extended1800 N600 Nm150 N50 Nm105 N35 Nm

Source: [2], Table 1. Accuracies are 3 sigma residual error; relative accuracy applies after taring the sensor, which is how operations use it. A single calibration satisfies all three ranges, and the technique supports re-calibration from Earth while the rover is on Mars.

The alternatives were compared directly. Across a wrist force torque sensor, joint torque sensors, link strain gauges, motor current sensors and flexibility modeling on a 5 degree of freedom laboratory arm, the six-axis wrist sensor was the most accurate, the most repeatable and the only one independent of arm configuration, and also the most complex [3]. Motor current sensing held average error under 5 N in the direction of the applied load across the whole range, but showed up to 15 N of crosstalk in directions where no force was applied, and shares the configuration dependence of the joint and link techniques. Link strain gauges gave about 1 N average error below 20 N, about 5 N at 40 N and about 20 N at 60 N. Three of the five techniques need strain gauges, which had never flown on a landed mission [3]. Flexibility modeling is an estimator rather than a sensor, and was the only one of the five that had actually been used on another planet’s surface [3].

Continuous force control, and what the flight computer does to it

Section titled “Continuous force control, and what the flight computer does to it”

Mars Sample Return’s sample transfer system is the first planetary application that needs it, because the task is peg-in-hole rather than press-and-hold: a returnable sample tube assembly has to be inserted into a sleeve in the orbiting sample, and the orbiting sample’s lid has to be guided into its chamfer, which means regulating lateral force and torque while moving axially, and still producing smooth preload and unload transitions in other configurations [1]. The Perseverance sensor that would measure it is accurate to 45 N in force and 11 Nm in moment after taring, at nominal range [2].

The wrench itself is estimated from five sets of paired strain gauges bonded to opposing sides of five rectangular beams carrying the whole load path, compensated against unstrained gauges for thermal drift, with four of the five sets multiplied through a calibration matrix; because that compensation is imperfect a reading is only treated as valid within a 15 minute drift timeout, which is what bounds how long an insertion may take [1]. Two control forms are carried: force regulation, a PID loop closed on up to all six wrench axes to a setpoint, and hybrid motion, the same regulation on the lateral axes while the tool frame force Z axis follows a trapezoidal velocity profile, which is what an insertion or extraction uses [1]. An earlier design iteration emulated a mechanical remote center of compliance in software, a technique called active compliance, and it was dropped as needlessly complex and too dependent on passive compliance modeling. Enforced deflection survives as an open-loop joint-space command.

The flight computer shapes the implementation. On the Sample Retrieval Lander’s RAD750, the baseline trajectory must be pre-planned as a series of via points that force control then deviates from, and Jacobian matrices are cached at each via point rather than recomputed, which makes them only locally accurate: commanding a lateral control twist produces a tool pose error that grows with the distance from the cached via point [1]. A more capable computer would compute the displacement online. The response is to bound how far force regulation may deviate from the baseline trajectory, and to buy misalignment back by proprioceptive probing, a series of light contacts inside the chamfer that refine the relative position of the end effector, the same trick as a touch off in machining. The requirement on the most stressing case, inserting the glove assembly into an orbiting sample sleeve, is to keep force at the tube tip below 15 N and moment below 2.25 Nm while accommodating 3.5 mm and 79 mrad of misalignment, with 6 dB gain and 30 degree phase stability margins on every wrench control axis, and to go from free space to fully seated within 15 minutes [1].

Validation was split between simulation and hardware because the flight arm was years away. Actuator models were built at three levels, a linear time invariant frequency domain model from which gain and phase margins were drawn, the same model in the time domain, and a non-linear time domain simulation adding Stribeck friction, current and velocity limiting and backlash; seven actuator simulations were then assembled into an arm model with non-linear contact dynamics [1]. The hardware was the Bradbury testbed, seven actuators of the same morphology as the sample transfer arm, and the Clark testbed, one spare actuator from each of the three Bradbury motor families so that single degree of freedom motor dynamics could be explored with the kinematics abstracted away.

The heritage the campaign inherits from is a wrist sensor and an iteration loop, not a servo [2][4].

Robonaut 2 is the one space manipulator whose loop structure is stated [5]. Four nested loops, current, velocity, torque and impedance, run at 5 kHz on the embedded motor drivers, while the centralized RoboDyn controller computes kinematics, dynamics and trajectory generation at about 50 Hz; the non-elastic wrist and finger joints run at about 500 Hz to keep hand motion smooth [5]. The embedded loops are configured at startup with pre-tuned gains and limits, except the impedance loop, which takes stiffness and damping updates from RoboDyn in real time, derived from each joint’s effective inertia and a user-specified natural frequency and damping ratio. Gravity and inertial compensation come from recursive Newton-Euler and composite rigid body computations. Parameter changes are blended rather than stepped, to avoid torque jumps, and the trajectory monitor stops motion gracefully when position error times gain would exceed the joint torque limit [5]. Reported degradation from running the centralized loop at 50 Hz was not noticeable [5].

The stiffness and damping are set from a natural frequency and damping ratio per joint, so the same joint can be stiff or soft on command. In a climbing demonstration the base leg was held at 20 rad/s natural frequency, damping ratio 1.2 and a 100 Nm torque limit while the reaching leg started stiff and was then softened to 0.5 rad/s, damping ratio 1.5 and a 20 Nm limit [5]. Roll joints have very low effective inertia, which drives the computed damping very small, and small construction and sensor calibration discrepancies then make the joint swing, so a per-joint minimum damping is enforced [5].

No control loop rate, processor, clock or memory figure is published for the Space Station Remote Manipulator System, for Dextre, or for the Mars 2020 arm.

An arm on a free-flying base pushes the base. ETS-VII flew a 2 m, six degree of freedom, roughly 140 kg arm on a 2550 kg satellite with principal inertias of 6200, 3540 and 7090 kg m squared, so the coupling is measurable [7].

Two control formulations were flown. The Generalized Jacobian Matrix maps joint rates to inertial-frame hand motion with the base reaction included, allowing resolved motion-rate control in inertial space on a free-floating base with the attitude control system off [7]. In flight, a 200 mm straight-line inertial path at 10 mm/s held hand pitch at -22.8 degrees while the base pitched 0.6 degrees under the reaction moment. Reaction Null-Space control instead selects joint motions lying in the null space of the inertia coupling matrix, which produce zero net reaction; for a non-redundant six degree of freedom arm with hand orientation constrained, three degrees of freedom remain for reactionless motion. Measured induced momentum for a reactionless path was small against a conventional spline path over the same endpoints, base attitude disturbance stayed under 0.5 degrees, and recovery time after the motion was near zero against a non-negligible wait for the conventional case [7].

The same null-space formulation applies when the base is flexible rather than free, with structural vibration replacing rigid-body attitude change as the quantity suppressed [8]. The published caution is numerical: the pseudoinverse is ill-conditioned near rank-deficient configurations, and because the pseudoinverse distribution is not integrable the coupling momentum drifts in configuration space, which joint damping arrests after a transient.

Free-floating operation has a time limit that is not a control limit. Gravity gradient torque drifts the base attitude more than one degree over several minutes at 550 km, and beyond one degree of pointing error the high-bandwidth relay link is lost [7].

A free-floating arm also carries singularities that no kinematic analysis will find. Their existence and location are functions of the mass and inertia distribution of the whole system, spacecraft included, rather than of the linkage, so a change of payload moves them and a calibration does not survive it [11]. At such a configuration the end effector can move in one inertial direction only, whatever the joints are commanded to do: resolved rate and resolved acceleration laws that invert the Jacobian fail outright, and transposed-Jacobian and pseudoinverse laws follow the available direction and settle at the wrong point. In the worked planar example, a 40 kg base with 4 and 3 kg links of 0.5 m is dynamically singular at joint angles of -65 and -11.41 degrees, and a transposed-Jacobian controller commanded from (2, 0) to (1.5, 1.5) m reaches that configuration in about 5 s and never leaves it [11]. Two design levers remove the problem: raising system inertia, in whose limit only the kinematic singularities remain, or, in the planar case, mounting the arm at the system center of mass.

That is also where the standard adaptive control results stop. The dynamics of a free-flying base cannot be written linearly in the dynamic parameters, because the coupling term in the inertia matrix cannot be factored into parameter-bearing and parameter-free parts while the base inertia block is time varying, and every adaptive scheme that presupposes linear parameterization is therefore inapplicable [12]. The consequence for a servicer is set by the base-to-arm mass and inertia ratio: in simulation of a planar two-link arm with 50 kg, 2.5 m links, a PD law converges at a ratio of 10 and diverges at a ratio of 2 while a model-based law still converges, and a space station used as a manipulator base has been put as low as 3. Both results are analysis and simulation with rigid links and no joint friction, and both hold only where the generalized Jacobian keeps full rank, which is the condition a dynamic singularity violates.

Free-floating control has a theory line independent of the ETS-VII flights. The generalized Jacobian was derived for an uncontrolled base from momentum conservation, in simulation only [14]. Fixed-base algorithms transfer to a free-floating arm given measured base attitude and avoidance of dynamic singularities, shown with a transposed-Jacobian law on a planar example [17]. Velocity-level redundancy resolution for a free-flying redundant arm has been derived without any numerical example [32]. Reactionless manipulation was flown on ETS-VII on 30 September 1999, with the evidence a single telemetry figure read off a plot [19]. Contact between two free-floating bodies is handled by choosing a virtual mass the chaser’s impedance-controlled hand presents to avoid pushing a non-cooperative target away; the verification used two fixed-base arms, so base reaction was not physically present [20]. A dual-arm combined impedance and PD law for tumbling target capture exists only as a planar co-simulation [23].

Compliant capture and contact tasks under delay

Section titled “Compliant capture and contact tasks under delay”

Capture of the free-flying target began with the hand about 400 mm from the grapple fixture against a target drifting at 10 mm/s, running reactionless motion with attitude control on for the coarse phase and switching to Generalized Jacobian visual servoing with attitude control off once hand position error fell below 100 mm [7]. The staged strategy reached the 100 mm switch point in roughly 50 s and captured at roughly 150 s while holding base attitude within 0.5 degrees, against a conventional approach that took longer, exceeded one degree of attitude excursion, and finished close to the arm’s reach limit.

Contact tasks were also run with the human in the loop across a 6 to 7 second round-trip delay, closing a direct bilateral coupling with kinesthetic force feedback so that the delay sits inside the force loop [9]. A slope-tracing task and an 18 mm peg-in-hole insertion with 0.4 mm clearance were completed with no visual feedback, at a hand speed limited to 2.0 mm/s. That work is covered under time-delayed teleoperation, and the vehicle itself under ETS-VII.

Dextre exists because about 250 orbital replacement units on the Space Station are designated for robotic servicing, and inserting one into its alignment guides without jamming requires 2 mm motion resolution and programmable force-moment accommodation on the arms [6]. Its two arms are identical 7-joint manipulators with about 3.3 m straight-arm reach and 600 kg payload capacity, sharing the joint sequence and therefore the kinematic equations of the 17.6 m, 7-joint Space Station Remote Manipulator System that positions Dextre at the worksite. Each arm carries a six-axis force-moment sensor at the wrist and an ORU and tool changeout mechanism at the tip, containing a parallel jaw gripper compatible with standard H and micro fixtures, an extendable 7/16 inch socket drive, a camera with a two-stop zoom lens, two lights and an extendable umbilical carrying power, data and video [6].

The dual-arm configuration is a consequence of stiffness, not of dexterity. While one arm extracts or inserts an ORU, the other grips a stabilization H-fixture near the worksite; because only a single ORU storage location is available, the arms then swap roles, the first storing the failed unit on the carrier while the second installs the replacement [6]. Changeout times, insertion clearances and alignment tolerances are not published [6].

Perseverance’s bit exchange is the planetary equivalent and is timed: about 20 minutes to deposit a bit and about 25 minutes to retrieve one, of which about 2 minutes is the docking [4].

Section titled “Force accommodation on orbital arms, and force feedback across a link”

Dextre’s force moment accommodation was measured on a single-arm ground testbed with three Shuttle arm astronauts. Inserting a converter ORU from worst-case misalignment without accommodation took 5 to over 15 minutes at peak contact forces of 190 to 220 N and Cooper-Harper ratings of 6 to 9; with it active the same operators finished in 2.0 to 2.5 minutes at 16 to 19 N and rated every run 1 [31]. The stability condition is that the arm force loop bandwidth stays below the gripper servo bandwidth. The testbed is not the flight dual arm.

On the Space Station, the KONTUR-2 joystick closed a bilateral loop to ground robots over S-band with 20 to 30 ms measured round trip delay and a 1000 Hz local loop [30]. Time Domain Passivity Control held the same gains over a 65 ms internet link, positional accuracy degraded in microgravity and was partly recovered by joystick damping, and the findings are qualitative and not tabulated [30].

Contact tasks fail on the force loop, not the position loop. Perseverance docking is protected by monitoring the motors at 64 Hz for current, stalls, shorts, temperature, position discrepancy and joint limits, by faulting if a contact switch is pressed before contact is expected, by constraining measured preload to the target plus a margin, by holding lateral forces and moments inside deadbands, by checking dock rotation against softstops more conservative than the hardstops, and by a per-phase iteration limit [4]. Thermal testing found a limit-cycling condition during docking that was fixed by changing the algorithm [4].

Arm flight software without force control fails differently. The InSight Instrument Deployment Arm’s standard response to any fault is to stop all motors and heaters, announce the fault to spacecraft fault protection and in telemetry, mark itself safed, and accept only recovery commands, which blocks any further sequenced motion; recoverable events instead run a specific expansion, such as powering off on a motor overheat, waiting for the temperature to drop, and resuming, with an interruption depth limit past which the software safes itself [10]. Monitored conditions include overcurrent, stalls, short circuits, over and under temperature, encoder to resolver mismatch, joint limit violations, Cartesian unreachability, timeout, and arm motion impeded by hard regolith.

Operational safety of a flown arm now includes the carrier. Curiosity’s Slip Risk Assessment Process decides whether a parked rover may put its arm on the ground. It ran 1258 times through sol 4307 with a 93.6 percent go rate, falling to 71.4 percent above 25 degrees of tilt, and half of the 58 no-go outcomes were a perched wheel [33]. Six significant parked slip events are known across the four NASA Mars rovers, with no hardware damage, and the slip likelihood remains expert judgment [33]. This is flight data on arm safety, not on arm control law.

Ground testbeds for the next arms are the second family. Bradbury, the 7 degree of freedom, 2.3 m, 98 kg Mars Sample Return development arm, matches the flight arm kinematics with commercial actuators and must preload up to 350 N axially to extract a sample tube; the paper reports no placement accuracy or stiffness [34]. OWLAT at JPL pairs a 7 degree of freedom arm with a Stewart-platform lander to test Ocean Worlds sampling autonomy against simulant [39]. COLDArm, a 4 degree of freedom, 2 m arm with a 40 N tip force, runs without survival heaters near 100 K in ground tests at technology readiness level 6; the source is a program briefing, not a report [35].

Vision-guided capture is the third family, demonstrated on the ground only. An adaptive visual servoing architecture with fault-tolerant pose registration captured a tumbling mockup in four hardware-in-the-loop runs, with an average position error of 2.4 cm against a 4 cm gripper envelope and 5.8 mm/s relative velocity at capture, using a 1000 Hz control loop [36]. A survey classifies the visual servoing literature by recognition, approach and contact phase and gives no performance figures [38]. A survey of orbital servicing arms inventories the air-bearing and hardware-in-the-loop facilities where such controllers are tested [37].

Learning-based control is at the simulation stage. A data-assisted port-Hamiltonian law for a free-floating arm reduced end-effector attitude error by 77.5 percent against a model-based baseline for 16 percent more control effort, on one planar 2 degree of freedom simulation [40]. Causal-curiosity reinforcement learning to classify the mass and friction of an unknown object has been run only in a PyBullet simulation of one cube [42].

Robot-agnostic alignment, which needs only end-effector and target pose, was tested on two MoonBot limbs in a sand testbed at JAXA. The continuous variant aligned in 57.86 s (standard deviation 8.23 s) against 92.90 s for the stepped variant, with three trials per condition and pose from external motion capture [41].

No flown planetary arm has run continuous force control; the Mars Sample Return design is validated on testbeds and in simulation [1]. Flight placement figures rest on operations summaries and single measurements [24][26]. The ETS-VII reactionless result is one flight with no repeat trials [19], and the free-floating adaptive, singularity and capture results are analysis or simulation with rigid links [12][23]. Dextre accommodation was tested on a ground arm, not in orbit [31]. KONTUR-2 reports performance qualitatively [30]. No loop rate or processor figure is published for the Space Station arms or the Mars 2020 arm. Learning-based and agnostic alignment controllers are simulation or small-sample sand-testbed results [40][41][42]. Vision-guided capture rests on four runs [36].

References

  1. Dolci, M., Bowkett, J., Bailey, P., Boettcher, A., Kim, J., Rogers, P., Pham, T.-H., Chavez Clemente, D., Shatts, J., Townsend, J., Twu, P. and Collins, C. (2025). Robotics Capabilities Development for Mars Sample Return Transfer Activities . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{dolci2025robotics,
      title = {Robotics Capabilities Development for Mars Sample Return Transfer Activities},
      author = {Dolci, Marco and Bowkett, Joseph and Bailey, Philip and Boettcher, Anna and Kim, Junggon and Rogers, Preston and Pham, Tu-Hoa and Chavez Clemente, Daniel and Shatts, Jennifer and Townsend, Julie and Twu, Philip and Collins, Curtis},
      booktitle = {IEEE Aerospace Conference},
      pages = {1-25},
      address = {Big Sky, Montana},
      year = {2025},
      doi = {10.1109/aero63441.2025.11068463},
      abstract = {The planned NASA-European Space Agency (ESA) Mars Sample Return campaign aims to be the first set of missions to bring Martian samples back to Earth, where thousands of scientists would make groundbreaking discoveries that could redefine our understanding of the Red Planet and perhaps even the origins of life on Earth. A crucial component of the circa 2023 baseline design for the missions was the transfer of sample tubes from the Martian surface to the ascent vehicle, which requires a highly dexterous robotic arm and sophisticated control strategies. Development and testing of the control algorithms were underway at NASA's Jet Propulsion Laboratory on advanced R&D testbeds, while the ESA is responsible for delivering the flight robotic arm. To meet the complex requirements for transferring the sample tubes, we propose an abstract layer consisting of three important robotics capabilities, each to be implemented for the first time in planetary exploration. 1. 7-DoF Manipulation: This capability focuses on managing the kinematics of the 7-DoF robotic arm. It includes the development of algorithms for forward and inverse kinematics, joint redundancy management, kinematic calibration, deflection compensation, target-to-pose selection, trajectory generation, and control strategies for single-joint, multi-joint, Cartesian motions, and free-space closed-loop control. 2. Robotics Vision: This capability pertains to a monocular vision system mounted on the robotic arm's end-effector with an additional redundant camera. These cameras are essential for localizing the Mars 2020 rover (M2020) tube-retrieval station, the SRL OS, identifying tubes on the Martian surface, and estimating the robotic arm's pose to ensure successful interactions with the station. 3. In-Contact Manipulation: This capability addresses the robot's interaction with its external environment. It involves load estimation using a 6-DoF force-torque sensor, force regulation (standard load-wrench control to a setpoint), and hybrid motion (force regulation orthogonal to a baseline velocity). This paper documents for posterity the infusion of these robotics capabilities, including the requirements, analysis, and testing processes that would have been necessary to ensure the success of the circa 2023 SRL Sample Transfer System design.}
    }
  2. Schaler, E. W., Wisnowski, J., Iwashita, Y., Edlund, J. A., Sly, J. H., Raff, W., Kriechbaum, K. L., Frost, M. A., McCormick, R. L. and Townsend, J. A. (2021). Two-Stage Calibration of a 6-Axis Force-Torque Sensor for Robust Operation in the Mars 2020 Robot Arm . Advanced Robotics. Source
    BibTeX
    @article{schaler2021calibration,
      title = {Two-Stage Calibration of a 6-Axis Force-Torque Sensor for Robust Operation in the Mars 2020 Robot Arm},
      author = {Schaler, Ethan W. and Wisnowski, James and Iwashita, Yumi and Edlund, Jeffrey A. and Sly, Jacqueline H. and Raff, William and Kriechbaum, Kristopher L. and Frost, Matthew A. and McCormick, Ryan L. and Townsend, Julie A.},
      journal = {Advanced Robotics},
      year = {2021},
      doi = {10.48577/jpl.wbf9x6},
      abstract = {A main objective of the Mars 2020 rover mission (Perseverance) is to collect and preserve samples of rock and soil from the Martian surface. To accomplish this task, the Perseverance Rover carries a Sampling and Caching Subsystem outfitted with Coring Drill mounted on a 5 degree-of-freedom (DOF) robotic arm. Safe operation of the Robotic Arm and its tools relies on force feedback, provided by a custom Force-Torque Sensor (FTS) which is positioned to sense end-effector external loads. This work describes the methods and algorithms used in the calibration of the Robotic Arm FTS to achieve the required force-feedback accuracy over all expected Mars and Earth operating environments. Data collection strategies, standalone versus system-integrated sensor findings, and results of validation exercises in Earth-ambient and Mars-like environments are included.}
    }
  3. Helmick, D., Okon, A. and DiCicco, M. (2006). A Comparison of Force Sensing Techniques for Planetary Manipulation . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{helmick2006comparison,
      title = {A Comparison of Force Sensing Techniques for Planetary Manipulation},
      author = {Helmick, Daniel and Okon, Avi and DiCicco, Matt},
      booktitle = {IEEE Aerospace Conference},
      pages = {1-14},
      address = {Big Sky, Montana},
      year = {2006},
      doi = {10.1109/aero.2006.1655724},
      abstract = {Five techniques for sensing forces with a manipulator are compared analytically and experimentally. The techniques compared are: a six-axis wrist force/torque sensor, joint torque sensors, link strain gauges, motor current sensors, and flexibility modeling. The accuracy and repeatability of each technique is quantified and compared. The relative complexity and the impact on flight design of each technique are also compared. The results presented can be used in a trade study for missions requiring manipulator force sensing capabilities}
    }
  4. Brooks, S., Townsend, J., Collins, C., Carsten, J., Frost, M., Reid, J., Robinson, M. and Warner, A. (2022). Docking the Mars 2020 Perseverance Robotic Arm . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{brooks2022docking,
      title = {Docking the Mars 2020 Perseverance Robotic Arm},
      author = {Brooks, Sawyer and Townsend, Julie and Collins, Curtis and Carsten, Joseph and Frost, Matthew and Reid, Jason and Robinson, Matthew and Warner, Antonia},
      booktitle = {IEEE Aerospace Conference},
      pages = {1-12},
      address = {Big Sky, Montana},
      year = {2022},
      doi = {10.1109/aero53065.2022.9843517}
    }
  5. Badger, J. M., Hulse, A. M., Taylor, R. C., Curtis, A. W., Gooding, D. R. and Thackston, A. (2014). Model-based Robotic Dynamic Motion Control for the Robonaut 2 Humanoid Robot . IEEE-RAS International Conference on Humanoid Robots, 20140000410. Source
    BibTeX
    @inproceedings{badger2014model,
      title = {Model-based Robotic Dynamic Motion Control for the Robonaut 2 Humanoid Robot},
      author = {Badger, Julia M. and Hulse, Aaron M. and Taylor, Ross C. and Curtis, Andrew W. and Gooding, Dustin R. and Thackston, Allison},
      booktitle = {IEEE-RAS International Conference on Humanoid Robots},
      number = {20140000410},
      pages = {62-67},
      institution = {NASA},
      year = {2014},
      doi = {10.1109/humanoids.2013.7029956},
      abstract = {Robonaut 2 (R2), an upper-body dexterous humanoid robot, has been undergoing experimental trials on board the International Space Station (ISS) for more than a year. R2 will soon be upgraded with two climbing appendages, or legs, as well as a new integrated model-based control system. This control system satisfies two important requirements; first, that the robot can allow humans to enter its workspace during operation and second, that the robot can move its large inertia with enough precision to attach to handrails and seat track while climbing around the ISS. This is achieved by a novel control architecture that features a joint-level embedded impedance control law which is tightly interfaced with a kinematic and dynamic coordinated control system that resides on centralized processors. This paper presents the integrated control algorithm as well as several test results that illustrate R2's safety features and performance.}
    }
  6. Stieber, M. E., Hunter, D. G. and Abramovici, A. (1999). Overview of the Mobile Servicing System for the International Space Station . International Symposium on Artificial Intelligence, Robotics and Automation in Space. Source
    BibTeX
    @inproceedings{stieber1999overview,
      title = {Overview of the Mobile Servicing System for the International Space Station},
      author = {Stieber, M. E. and Hunter, D. G. and Abramovici, A.},
      booktitle = {International Symposium on Artificial Intelligence, Robotics and Automation in Space},
      address = {ESTEC, Noordwijk},
      year = {1999},
      url = {http://robotics.estec.esa.int/i-SAIRAS/isairas1999/s02-01.pdf}
    }
  7. Yoshida, K. (2003). Engineering Test Satellite VII Flight Experiments for Space Robot Dynamics and Control: Theories on Laboratory Test Beds Ten Years Ago, Now in Orbit . The International Journal of Robotics Research, 5. Source
    BibTeX
    @article{yoshida2003engineering,
      title = {Engineering Test Satellite VII Flight Experiments for Space Robot Dynamics and Control: Theories on Laboratory Test Beds Ten Years Ago, Now in Orbit},
      author = {Yoshida, Kazuya},
      journal = {The International Journal of Robotics Research},
      volume = {22},
      number = {5},
      pages = {321--335},
      year = {2003},
      doi = {10.1177/0278364903022005003},
      abstract = {The Engineering Test Satellite VII (ETS-VII), an unmanned spacecraft equipped with a 2-m long, six-degree-of-freedom manipulator arm, was developed and launched by the National Space Development Agency of Japan (NASDA). ETS-VII has successfully carried out a variety of on-board experiments with its manipulator arm, and these key technologies are essential for an orbital free-flying robot. These results will provide a solid basis for future satellite servicing missions. This paper highlights manipulator control utilizing the concepts of the generalized Jacobian matrix and the reaction null-space. These concepts have been proposed and discussed for the past ten years using laboratory test beds, and their practical application has now been demonstrated in orbit.}
    }
  8. Nenchev, D. N., Yoshida, K., Vichitkulsawat, P. and Uchiyama, M. (1999). Reaction Null-Space Control of Flexible Structure Mounted Manipulator Systems . IEEE Transactions on Robotics and Automation, 6. Source
    BibTeX
    @article{nenchev1999reaction,
      title = {Reaction Null-Space Control of Flexible Structure Mounted Manipulator Systems},
      author = {Nenchev, Dragomir N. and Yoshida, Kazuya and Vichitkulsawat, P. and Uchiyama, Masaru},
      journal = {IEEE Transactions on Robotics and Automation},
      volume = {15},
      number = {6},
      pages = {1011--1023},
      year = {1999},
      doi = {10.1109/70.817666},
      abstract = {A composite control law for end-effector path tracking with a flexible structure mounted manipulator system is proposed, such that no disturbances on the flexible base are induced. The control law is based on the reaction null-space concept introduced earlier to tackle dynamic interaction problems of free-floating robots, or moving base robots in general. The control law is called composite since it ensures base vibration suppression control as well, although independently of the reactionless motion control subtask. The requirement of task independence is essential to avoid the appearance of complex dynamics expressions in the control law, such as nonlinear velocity-dependent coupling terms and dependencies of inertias on the elastic coordinates. We present experimental data from computer simulations and the experimental test bed TREP developed at Tohoku university. The experimental data is shown to agree well with theory.}
    }
  9. Imaida, T., Yokokohji, Y., Doi, T., Oda, M. and Yoshikawa, T. (2003). Ground-Space Teleoperation of a Robot Arm Mounted on Engineering Test Satellite No. VII by Direct Bilateral Coupling under a Long Time Delay Condition . Journal of the Robotics Society of Japan, 3. Source
    BibTeX
    @article{imaida2003groundb,
      title = {Ground-Space Teleoperation of a Robot Arm Mounted on Engineering Test Satellite No. VII by Direct Bilateral Coupling under a Long Time Delay Condition},
      author = {Imaida, Takashi and Yokokohji, Yasuyoshi and Doi, Toshitsugu and Oda, Mitsushige and Yoshikawa, Tsuneo},
      journal = {Journal of the Robotics Society of Japan},
      volume = {21},
      number = {3},
      pages = {309--320},
      year = {2003},
      doi = {10.7210/jrsj.21.309},
      abstract = {A bilateral teleoperation experiment with Engineering Test Satellite No.VII (ETS-VII) was conducted on November 22, 1999. Round-trip time for communication between the NASDA ground station and ETS-VII was approximately six to seven seconds. We constructed a bilateral teleoperator that is stable even under such a long time delay. Several experiments, such as slope tracing task and peg-in-hole task, were carried out. Task performance was compared between bilateral mode and unilateral mode with force telemetry data visually displayed on a screen. All tasks were possible by bilateral control without any visual information. Experimental results showed that kinesthetic force feedback to the operator is helpful even under such long time delay and improves the performance of the task.}
    }
  10. Ali, K. S. (2021). InSight Mars Lander Instrument Deployment Arm Flight Software . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{ali2021insight,
      title = {InSight Mars Lander Instrument Deployment Arm Flight Software},
      author = {Ali, Khaled S.},
      booktitle = {IEEE Aerospace Conference},
      pages = {1-11},
      address = {Big Sky, Montana},
      year = {2021},
      doi = {10.1109/aero50100.2021.9438296},
      abstract = {The Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) lander landed on Mars on November 26, 2018 and continues to investigate the internal structure of the planet two years later. The Instrument Deployment Arm (IDA), a robotic arm on the lander, was used to deploy the science instrument payloads from the lander deck to the surface of Mars and to take images of the lander and the surrounding environment. This was the first precision deployment and release by a robotic arm on another planet. After deploying the instruments, the IDA has been used for instrument commissioning, scientific data gathering, and to assist with troubleshooting one of the science instruments. This paper provides a high-level summary of the flight software that controls the IDA. The paper provides an overview of the IDA software interfaces, task structure, command handling strategy, motion specification, motion planning, motor control, grapple control, fault protection, and telemetry.}
    }
  11. Papadopoulos, E. and Dubowsky, S. (1993). Dynamic Singularities in Free-Floating Space Manipulators . ASME Journal of Dynamic Systems, Measurement and Control, 1. Source
    BibTeX
    @article{papadopoulos1993singularities,
      title = {Dynamic Singularities in Free-Floating Space Manipulators},
      author = {Papadopoulos, Evangelos and Dubowsky, Steven},
      journal = {ASME Journal of Dynamic Systems, Measurement and Control},
      volume = {115},
      number = {1},
      pages = {44--52},
      year = {1993},
      doi = {10.1007/978-1-4615-3588-1_4},
      abstract = {Dynamic Singularities are shown for free-floating space manipulator systems where the spacecraft moves in response to manipulator motions without compensation from its attitude control system. At a dynamic singularity the manipulator is unable to move its end-effector in some inertial direction; thus dynamic singularities must be considered in the design, planning, and control of free-floating space manipulator systems. The existence and location of dynamic singularities cannot be predicted solely from the manipulator kinematic structure because they are functions of the dynamic properties of the system, unlike the singularities for fixed-base manipulators. Also analyzed are the implications of dynamic singularities to the nature of the system’s workspace.}
    }
  12. Xu, Y. and Shum, H.-Y. (1991). Dynamic Control of a Space Robot System with No Thrust Jets Controlled Base . Robotics Institute, Carnegie Mellon University, CMU-RI-TR-91-33. Source
    BibTeX
    @techreport{xu1991dynamic,
      title = {Dynamic Control of a Space Robot System with No Thrust Jets Controlled Base},
      author = {Xu, Yangsheng and Shum, Heung-Yeung},
      number = {CMU-RI-TR-91-33},
      institution = {Robotics Institute, Carnegie Mellon University},
      year = {1991},
      url = {https://www.ri.cmu.edu/pub_files/pub3/xu_yangsheng_1991_4/xu_yangsheng_1991_4.pdf}
    }
  13. Whitney, D. E. (1969). Resolved Motion Rate Control of Manipulators and Human Prostheses . IEEE Transactions on Man-Machine Systems. Source
    BibTeX
    @article{whitney1969resolved,
      title = {Resolved Motion Rate Control of Manipulators and Human Prostheses},
      author = {Whitney, D. E.},
      journal = {IEEE Transactions on Man-Machine Systems},
      volume = {10},
      pages = {47-53},
      year = {1969},
      doi = {10.1109/tmms.1969.299896},
      abstract = {The kinematics of remote manipulators and human prostheses is analyzed for the purpose of deriving resolved motion rate control. That is, the operator is enabled to call for the desired hand motion directly along axes relevant to the task environment. The approach suggests solutions to problems of coordination, motion under task constraints, and appreciation of forces encountered by the controlled hand.}
    }
  14. Umetani, Y. and Yoshida, K. (1989). Resolved Motion Rate Control of Space Manipulators With Generalized Jacobian Matrix . IEEE Transactions on Robotics and Automation, 3. Source
    BibTeX
    @article{umetani1989resolved,
      title = {Resolved Motion Rate Control of Space Manipulators With Generalized {J}acobian Matrix},
      author = {Umetani, Yoji and Yoshida, Kazuya},
      journal = {IEEE Transactions on Robotics and Automation},
      volume = {5},
      number = {3},
      pages = {303--314},
      year = {1989},
      doi = {10.1109/70.34766},
      abstract = {The authors establish a control method for space manipulators taking dynamical interaction between the manipulator arm and the base satellite into account. The kinematics of free-flying multibody systems is investigated by introducing the momentum conservation law into the formulation and a novel Jacobian matrix in generalized form for space robotic arms is derived. The authors develop a control method for space manipulators based on the resolved motion control concept. The proposed method is widely applicable in solving not only free-flying manipulation problems but also attitude-control problems. The validity of the method is demonstrated by computer simulations with a realistic model of a robot satellite.>}
    }
  15. Khatib, O. (1986). Real-Time Obstacle Avoidance for Manipulators and Mobile Robots . Earth and Space Science, 1. Source
    BibTeX
    @article{khatib1986real,
      title = {Real-Time Obstacle Avoidance for Manipulators and Mobile Robots},
      author = {Khatib, Oussama},
      journal = {Earth and Space Science},
      volume = {5},
      number = {1},
      pages = {90-98},
      publisher = {SAGE Publications},
      year = {1986},
      doi = {10.1177/027836498600500106},
      abstract = {This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an upper speed limit. The artificial potential field ap proach has been extended to collision avoidance for all ma nipulator links. In addition, a joint space artificial potential field is used to satisfy the manipulator internal joint con straints. This method has been implemented in the COSMOS system for a PUMA 560 robot. Real-time collision avoidance demonstrations on moving obstacles have been performed by using visual sensing.}
    }
  16. Maciejewski, A. A. and Klein, C. A. (1985). Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments . The International Journal of Robotics Research, 3. Source
    BibTeX
    @article{maciejewski1985obstacle,
      title = {Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments},
      author = {Maciejewski, Anthony A. and Klein, Charles A.},
      journal = {The International Journal of Robotics Research},
      volume = {4},
      number = {3},
      pages = {109-117},
      publisher = {SAGE Publications},
      year = {1985},
      doi = {10.1177/027836498500400308},
      abstract = {The vast majority of work to date concerned with obstacle avoidance for manipulators has dealt with task descriptions in the form ofpick-and-place movements. The added flexibil ity in motion control for manipulators possessing redundant degrees offreedom permits the consideration of obstacle avoidance in the context of a specified end-effector trajectory as the task description. Such a task definition is a more accurate model for such tasks as spray painting or arc weld ing. The approach presented here is to determine the re quired joint angle rates for the manipulator under the con straints of multiple goals, the primary goal described by the specified end-effector trajectory and secondary goals describ ing the obstacle avoidance criteria. The decomposition of the solution into a particular and a homogeneous component effectively illustrates the priority of the multiple goals that is exact end-effector control with redundant degrees of freedom maximizing the distance to obstacles. An efficient numerical implementation of the technique permits sufficiently fast cycle times to deal with dynamic environments.}
    }
  17. Papadopoulos, E. and Dubowsky, S. (1991). On the Nature of Control Algorithms for Free-Floating Space Manipulators . IEEE Transactions on Robotics and Automation, 6. Source
    BibTeX
    @article{papadopoulos1991nature,
      title = {On the Nature of Control Algorithms for Free-Floating Space Manipulators},
      author = {Papadopoulos, Evangelos and Dubowsky, Steven},
      journal = {IEEE Transactions on Robotics and Automation},
      volume = {7},
      number = {6},
      pages = {750--758},
      year = {1991},
      doi = {10.1109/70.105384},
      abstract = {It is suggested that nearly any control algorithm that can be used for fixed-based manipulators also can be employed in the control of free-floating space manipulator systems, with the additional conditions of estimating or measuring a spacecraft's orientation and of avoiding dynamic singularities. This result is based on the structural similarities between the kinematic and dynamic equations for the same manipulator but with a fixed base. Barycenters are used to formulate the kinematic and dynamic equations of free-floating space manipulators. A control algorithm for a space manipulator system is designed to demonstrate the value of the analysis.>}
    }
  18. Dubowsky, S. and Papadopoulos, E. (1993). The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems . IEEE Transactions on Robotics and Automation, 5. Source
    BibTeX
    @article{dubowsky1993kinematics,
      title = {The Kinematics, Dynamics, and Control of Free-Flying and Free-Floating Space Robotic Systems},
      author = {Dubowsky, Steven and Papadopoulos, Evangelos},
      journal = {IEEE Transactions on Robotics and Automation},
      volume = {9},
      number = {5},
      pages = {531--543},
      year = {1993},
      doi = {10.1109/70.258046}
    }
  19. Yoshida, K., Hashizume, K. and Abiko, S. (2001). Zero Reaction Maneuver: Flight Validation with ETS-VII Space Robot and Extension to Kinematically Redundant Arm . IEEE International Conference on Robotics and Automation. Source
    BibTeX
    @inproceedings{yoshida2001zero,
      title = {Zero Reaction Maneuver: Flight Validation with ETS-VII Space Robot and Extension to Kinematically Redundant Arm},
      author = {Yoshida, Kazuya and Hashizume, Kenichi and Abiko, Satoko},
      booktitle = {IEEE International Conference on Robotics and Automation},
      volume = {1},
      pages = {441--446},
      year = {2001},
      doi = {10.1109/robot.2001.932590},
      abstract = {Presents the experimental results and post-flight analysis of reaction null-space based reactionless manipulation, or zero reaction maneuver (ZRM). The concept has been developed with an insight into the motion dynamics of free-flying multibody systems and its practical availability is clearly demonstrated with ETS-VII, a Japanese space robot. The ZRM is proven particularly useful for removing the velocity limit of manipulation due to the reaction constraint and the time loss due to waiting for the attitude recovery. The existence of the ZRM is very limited for a 6 DOF manipulator arm mounted on a free-flying base, but it is discussed how more operational freedom is obtained with a kinematically redundant arm.}
    }
  20. Yoshida, K., Nakanishi, H., Ueno, H., Inaba, N., Nishimaki, T. and Oda, M. (2004). Dynamics, control and impedance matching for robotic capture of a non-cooperative satellite . Advanced Robotics, 2. Source
    BibTeX
    @article{yoshida2004dynamics,
      title = {Dynamics, control and impedance matching for robotic capture of a non-cooperative satellite},
      author = {Yoshida, Kazuya and Nakanishi, Hiroki and Ueno, Hiroshi and Inaba, Noriyasu and Nishimaki, Takeshi and Oda, Mitsushige},
      journal = {Advanced Robotics},
      volume = {18},
      number = {2},
      pages = {175-198},
      publisher = {Informa UK Limited},
      year = {2004},
      doi = {10.1163/156855304322758015},
      abstract = {In this paper, the contact motion between rigid bodies floating in space is formulated and dynamic conditions are investigated in order to capture a non-cooperative target. As for the theoretical investigation, the definition of the virtual mass is recalled to model the inertial property of a space robot for the case of no joint control. By selecting the posture, the virtual mass can be altered, but its variation may be minor. Then the impedance control is introduced to realize a wide range of impedance characteristics. Impedance matching is discussed for the case in which the hand of an impedance-controlled robot approached and collided with a passive target. The specific inertia property, referred to as Virtual-mass for Impedance Matching, is defined as an equivalent virtual mass of the hand that yields impedance matching with a target floating in space. Experiments are carried out using two robot manipulators as a motion simulator of chaser and target. Through the experiments, the concept of the impedance matching is verified and satellite capture is demonstrated using the strategy that an impedance controlled probe is inserted into the thruster nozzle cone of the target. Whether the impedance matching gives a criteria if the target is pushed away by the probe is investigated.}
    }
  21. Seraji, H. (1994). Adaptive Compliance Control: An Approach to Implicit Force Control in Compliant Motion . Minerals. Source
    BibTeX
    @inproceedings{seraji1994adaptive,
      title = {Adaptive Compliance Control: An Approach to Implicit Force Control in Compliant Motion},
      author = {Seraji, Homayoun},
      booktitle = {Minerals},
      pages = {2705-2712},
      publisher = {JPL Open Repository},
      year = {1994},
      doi = {10.1109/robot.1994.350927},
      abstract = {This paper addresses the problem of controlling a manipulator in compliant motion while in contact with an environment having an unknown stiffness. Admittance control is used as an explicit force control scheme in which a force setpoint is specified and is tracked by the force compensator. Two adaptive PID and PI force compensators are proposed. The compensators ensure robust tracking of step force setpoints and rejection of constant disturbances. Since the environmental stiffness can typically vary by several orders of magnitude, compensator adaptation is used to ensure a stable and uniform system performance. Dynamic simulation results for a 7 DOF Robotics Research arm are presented to demonstrate the efficacy of the proposed admittance control scheme in executing contact tasks.>}
    }
  22. Chen, Z., Lii, N. Y., Wimböck, T., Fan, S. and Liu, H. (2011). Experimental Evaluation of Cartesian and Joint Impedance Control with Adaptive Friction Compensation for the Dexterous Robot Hand DLR-HIT II . International Journal of Humanoid Robotics, 4. Source
    BibTeX
    @article{chen2011experimental,
      title = {Experimental Evaluation of Cartesian and Joint Impedance Control with Adaptive Friction Compensation for the Dexterous Robot Hand DLR-HIT II},
      author = {Chen, Zhaopeng and Lii, Neal Y. and Wimböck, Thomas and Fan, Shaowei and Liu, Hong},
      journal = {International Journal of Humanoid Robotics},
      volume = {8},
      number = {4},
      pages = {649--671},
      publisher = {World Scientific},
      year = {2011},
      url = {https://elib.dlr.de/80479/1/S0219843611002605.pdf}
    }
  23. Stolfi, A., Gasbarri, P. and Sabatini, M. (2017). A combined impedance-PD approach for controlling a dual-arm space manipulator in the capture of a non-cooperative target . Acta Astronautica. Source
    BibTeX
    @article{stolfi2017combined,
      title = {A combined impedance-PD approach for controlling a dual-arm space manipulator in the capture of a non-cooperative target},
      author = {Stolfi, A. and Gasbarri, P. and Sabatini, M.},
      journal = {Acta Astronautica},
      volume = {139},
      pages = {243-253},
      publisher = {Elsevier BV},
      year = {2017},
      doi = {10.1016/j.actaastro.2017.07.014}
    }
  24. Trebi-Ollennu, A., Leger, P. C., Baumgartner, E. T. and Bonitz, R. G. (2005). Robotic arm in-situ operations for the Mars Exploration Rovers Surface mission . IEEE International Conference on Systems, Man and Cybernetics. Source
    BibTeX
    @inproceedings{trebiollennu2005robotic,
      title = {Robotic arm in-situ operations for the Mars Exploration Rovers Surface mission},
      author = {Trebi-Ollennu, Ashitey and Leger, P. Chris and Baumgartner, Eric T. and Bonitz, Robert G.},
      booktitle = {IEEE International Conference on Systems, Man and Cybernetics},
      volume = {2},
      pages = {1799-1806},
      publisher = {IEEE},
      year = {2005},
      doi = {10.1109/icsmc.2005.1571409},
      abstract = {This paper describes the operations of the 5 degree-of-freedom instrument deployment device (IDD), a dexterous robotic manipulator on the Mars Exploration Rovers, spirit and opportunity. The unprecedented flawless operations of the IDD enabled precise and reliable placement of at least 3 in situ instruments in sequential order on a designated target position on Martian rock/soil any time during the Martian diurnal cycle (day or night). These placements demonstrated a repeatability of /spl sim/1 mm in position and /spl sim/1 degree in orientation. This operations breakthrough is underappreciated, but it alone enabled the scientist to characterize a wide range of rocks and soils in a timely manner in the hunt for geological clues that revealed that the planet was once rich in water. In this paper we describe the IDD planning and command sequence generation process used to place and hold in situ instruments directly against rock and soil targets of interest within the IDD work volume.}
    }
  25. Collins, C. L. and Robinson, M. L. (2013). Accuracy analysis and validation of the Mars Science Laboratory (MSL) robotic arm . Mechanisms and Robotics Conference. Source
    BibTeX
    @inproceedings{collins2013accuracy,
      title = {Accuracy analysis and validation of the Mars Science Laboratory (MSL) robotic arm},
      author = {Collins, Curtis L. and Robinson, Matthew L.},
      booktitle = {Mechanisms and Robotics Conference},
      publisher = {American Society of Mechanical Engineers},
      year = {2013},
      doi = {10.1115/detc2013-13034},
      abstract = {The Mars Science Laboratory (MSL) Curiosity Rover is currently exploring the surface of Mars with a suite of tools and instruments mounted to the end of a five degree-of-freedom robotic arm. To verify and meet a set of end-to-end system level accuracy requirements, a detailed positioning uncertainty model of the arm was developed and exercised over the arm operational workspace. Error sources at each link in the arm kinematic chain were estimated and their effects propagated to the tool frames. A rigorous test and measurement program was developed and implemented to collect data to characterize and calibrate the kinematic and stiffness parameters of the arm. Numerous absolute and relative accuracy and repeatability requirements were validated with a combination of analysis and test data extrapolated to the Mars gravity and thermal environment. Initial results of arm accuracy and repeatability on Mars demonstrate the effectiveness of the modeling and test program as the rover continues to explore the foothills of Mount Sharp.}
    }
  26. Robinson, M., Collins, C., Leger, P., Carsten, J., Tompkins, V., Hartman, F. and Yen, J. (2013). In-Situ Operations and Planning for the Mars Science Laboratory Robotic Arm: The First 200 Sols . IEEE International Conference on Systems, Man and Cybernetics. Source
    BibTeX
    @inproceedings{robinson2013situ,
      title = {In-Situ Operations and Planning for the Mars Science Laboratory Robotic Arm: The First 200 Sols},
      author = {Robinson, Matthew and Collins, Curtis and Leger, Paul and Carsten, Joseph and Tompkins, Vandana and Hartman, Frank and Yen, Jeng},
      booktitle = {IEEE International Conference on Systems, Man and Cybernetics},
      volume = {tbd},
      pages = {153-158},
      year = {2013},
      doi = {10.1109/sysose.2013.6575259},
      abstract = {The Robotic Arm (RA) has operated for more than 200 Martian solar days (or sols) since the Mars Science Laboratory rover touched down in Gale Crater on August 5, 2012. During the first seven months on Mars the robotic arm has performed multiple contact science sols including the positioning of the Alpha Particle X-Ray Spectrometer (APXS) and/or Mars Hand Lens Imager (MAHLI) with respect to rocks or loose regolith targets. The RA has supported sample acquisition using both the scoop and drill, sample processing with CHIMRA (Collection and Handling for In- Situ Martian Rock Analysis), and delivery of sample portions to the observation tray, and the SAM (Sample Analysis at Mars) and CHEMIN (Chemistry and Mineralogy) science instruments. This paper describes the planning and execution of robotic arm activities during surface operations, and reviews robotic arm performance results from Mars to date.}
    }
  27. Bonitz, R., Shiraishi, L., Robinson, M., Carsten, J., Volpe, R., Trebi-Ollennu, A., Arvidson, R. E., Chu, P. C., Wilson, J. J. and Davis, K. R. (2009). The Phoenix Mars Lander Robotic Arm . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{bonitz2009phoenix,
      title = {The Phoenix Mars Lander Robotic Arm},
      author = {Bonitz, Robert and Shiraishi, Lori and Robinson, Matthew and Carsten, Joseph and Volpe, Richard and Trebi-Ollennu, Ashitey and Arvidson, Raymond E. and Chu, P. C. and Wilson, J. J. and Davis, K. R.},
      booktitle = {IEEE Aerospace Conference},
      pages = {1-12},
      organization = {Jet Propulsion Laboratory, California Institute of Technology},
      address = {Big Sky, Montana},
      year = {2009},
      doi = {10.1109/aero.2009.4839306},
      abstract = {The Phoenix Mars Lander Robotic Arm (RA) has operated for 149 sols since the Lander touched down on the north polar region of Mars on May 25, 2008. During its mission it has dug numerous trenches in the Martian regolith, acquired samples of Martian dry and icy soil, and delivered them to the Thermal Evolved Gas Analyzer (TEGA) and the Microscopy, Electrochemistry, and Conductivity Analyzer (MECA). The RA inserted the Thermal and Electrical Conductivity Probe (TECP) into the Martian regolith and positioned it at various heights above the surface for relative humidity measurements. The RA was used to point the Robotic Arm Camera to take images of the surface, trenches, samples within the scoop, and other objects of scientific interest within its workspace. Data from the RA sensors during trenching, scraping, and trench cave-in experiments have been used to infer mechanical properties of the Martian soil. This paper describes the design and operations of the RA as a critical component of the Phoenix Mars Lander necessary to achieve the scientific goals of the mission.}
    }
  28. Flores-Abad, A., Ma, O., Pham, K. and Ulrich, S. (2014). A review of space robotics technologies for on-orbit servicing . Progress in Aerospace Sciences. Source
    BibTeX
    @article{floresabad2014review,
      title = {A review of space robotics technologies for on-orbit servicing},
      author = {Flores-Abad, Angel and Ma, Ou and Pham, Khanh and Ulrich, Steve},
      journal = {Progress in Aerospace Sciences},
      volume = {68},
      pages = {1-26},
      publisher = {Elsevier BV},
      year = {2014},
      doi = {10.1016/j.paerosci.2014.03.002}
    }
  29. Won, D., So, B.-R. and Kim, H.-D. (2022). A Survey of Space Robotic Manipulator . Journal of Space Technology and Applications, 4. Source
    BibTeX
    @article{won2022survey,
      title = {A Survey of Space Robotic Manipulator},
      author = {Won, Daehee and So, Byung-Rok and Kim, Hae-Dong},
      journal = {Journal of Space Technology and Applications},
      volume = {2},
      number = {4},
      pages = {257--267},
      year = {2022},
      doi = {10.52912/jsta.2022.2.4.257},
      abstract = {In the 1970s, space robotics was used to attach a robotic manipulator to the first planetary exploration satellite of the Soviet Union. Since then, it has been developed to use various on-orbit services such as space debris removal, parts replacement/repairing, refueling, orbit changing, and construction of a space station in Earth orbit. In planetary exploration projects such as the Moon and Mars, various space robotic manipulators are being designed and developed to be used in the collection of samples and building bases on Mars. Recently, the use of various space robotic manipulators to perform missions in the Earth orbit or on the planet has been increasing. Countries with state-of-the-art space technology plan and implement new space-related projects. In this article, we would like to introduce the technology development trends and functions of space robot manipulators that have been used in various space challenge projects in advanced space technology countries.}
    }
  30. Artigas, J., Riecke, C., Weber, B., Stelzer, M., Balachandran, R., Schaetzle, S., Bayer, R., Steinmetz, B.-M., Vogel, J., Brunner, B., Albu-Schäffer, A., Guk, M., Zaborovskyi, V., Kondratiev, A., Muliukha, V., Silinenko, A. and Shmakov, O. (2016). Force-Feedback Teleoperation of On-Ground Robots from the International Space Station in the Frame of the KONTUR-2 Experiment . International Symposium on Artificial Intelligence, Robotics and Automation in Space. Source
    BibTeX
    @inproceedings{artigas2016force,
      title = {Force-Feedback Teleoperation of On-Ground Robots from the International Space Station in the Frame of the KONTUR-2 Experiment},
      author = {Artigas, Jordi and Riecke, Cornelia and Weber, Bernhard and Stelzer, Martin and Balachandran, Ribin and Schaetzle, Simon and Bayer, Ralph and Steinmetz, Bernhard-Michael and Vogel, Jörg and Brunner, Bernhard and Albu-Schäffer, Alin and Guk, M. and Zaborovskyi, V. and Kondratiev, A. and Muliukha, V. and Silinenko, A. and Shmakov, O.},
      booktitle = {International Symposium on Artificial Intelligence, Robotics and Automation in Space},
      pages = {1166-1173},
      year = {2016},
      doi = {10.1109/icra.2016.7487246},
      abstract = {This paper presents a new robot controller for space telerobotics missions specially designed to meet the requirements of KONTUR-2, a German & Russian telerobotics mission that addressed scientific and technological questions for future planetary explorations. In KONTUR-2, Earth and ISS have been used as a test-bed to evaluate and demonstrate a new technology for real-time telemanipulation from space. During the August 2015' experiments campaign, a cosmonaut teleoperated a robot manipulator located in Germany, using a force-feedback joystick from the Russian segment of the International Space Station (ISS). The focus of the paper is on the design and performance of the bilateral controller between ISS joystick and Earth robot. The controller is based on a 4-Channels architecture in which stability is guaranteed through passivity and the Time Delay Power Network (TDPN) concept. We show how the proposed approach successfully fulfills mission requirements, specially those related to system operation through space links and internet channels, involving time delays and data losses of different nature.}
    }
  31. Mukherji, R., Rey, D. A., Stieber, M. and Lymer, J. (2001). Special Purpose Dexterous Manipulator (SPDM) Advanced Control Features and Development Test Results . International Symposium on Artificial Intelligence, Robotics and Automation in Space. Source
    BibTeX
    @inproceedings{mukherji2001special,
      title = {Special Purpose Dexterous Manipulator (SPDM) Advanced Control Features and Development Test Results},
      author = {Mukherji, R. and Rey, D. A. and Stieber, M. and Lymer, John},
      booktitle = {International Symposium on Artificial Intelligence, Robotics and Automation in Space},
      address = {St-Hubert, Quebec},
      year = {2001},
      url = {https://roboshare.esa.int/i-SAIRAS/isairas2001/papers/Paper_AM104.pdf}
    }
  32. Nenchev, D. N., Umetani, Y. and Yoshida, K. (1992). Analysis of a redundant free-flying spacecraft/manipulator system . IEEE Transactions on Robotics and Automation, 1. Source
    BibTeX
    @article{nenchev1992analysis,
      title = {Analysis of a redundant free-flying spacecraft/manipulator system},
      author = {Nenchev, Dragomir N. and Umetani, Yoji and Yoshida, Kazuya},
      journal = {IEEE Transactions on Robotics and Automation},
      volume = {8},
      number = {1},
      pages = {1-6},
      publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
      year = {1992},
      doi = {10.1109/70.127234},
      abstract = {An analysis of the momentum conservation equations of a redundant free-flying spacecraft/manipulator system acting in a zero-gravity environment is presented. In order to follow a predefined end-effector path, the inverse kinematics at velocity level is considered. The redundancy is solved alternatively in terms of pseudoinverses and null-space components of the manipulator inertia matrix, the manipulator Jacobian matrix, and the generalized Jacobian matrix. A general manipulation task is defined as end-effector continuous path tracking with simultaneous attitude control of the spacecraft. Three subtasks of the general task are considered. The case of manipulator motions that yield no spacecraft attitude disturbance is analyzed in more detail and a special 'fixed-attitude-restricted' (FAR) Jacobian is defined. Through singular-value decomposition of this Jacobian, corresponding FAR dexterity measures (FAR manipulability and FAR condition number) are derived.>}
    }
  33. Curtis, A. (2025). 14 Rover-years of Slip Risk Assessment for Robotic Arm Safety . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{curtis2025rover,
      title = {14 Rover-years of Slip Risk Assessment for Robotic Arm Safety},
      author = {Curtis, Aaron},
      booktitle = {IEEE Aerospace Conference},
      publisher = {JPL Open Repository},
      year = {2025},
      doi = {10.48577/jpl.bfiydz},
      abstract = {Science return from the Curiosity and Perseverance Mars rovers, like Spirit and Opportunity before them, depends in large part on “contact science” activities in which instruments on a turret mounted on a robotic arm are placed near, on, or into the ground surface. When planning arm operations, rover teams are responsible for ensuring that torques and forces on arm joints and links will not exceed design specifications during contact science. This necessarily includes consideration of likelihood and consequence of rover movement due to wheel slip or settling. Simulation tools and practices for protecting Curiosity’s arm were initially presented at this conference by [1], centered on the Slip Risk Assessment Process (SRAP). During the 12 years of operating Curiosity, SRAP and related arm safety procedures were gradually improved, and subsequently adapted for use on Perseverance operations.Herein, we summarize those improvements and adaptations and then examine the use of SRAP and related procedures since their inception. We present data addressing questions including: How often do arm safety concerns preclude arm contact science? When contact science is precluded, what are the primary scenarios of concern? What is SRAP’s impact on the planning timeline? How do predicted wheel slip likelihoods compare with observed slip event frequency? In discussing these questions, we aim to consider how the Curiosity and Perseverance arm safety paradigm might be further optimized to maximize science return while maintaining hardware safety. We also aim to provide lessons that may be of use to planetary missions conducting terrain-contact science, including upcoming Lunar missions.}
    }
  34. Schoelen, D., Arnold, R., Dolci, M. and Wehage, K. (2024). Development Robotic Arm System Testbed for the Mars Sample Return Campaign . IEEE Aerospace Conference. Source
    BibTeX
    @inproceedings{schoelen2024development,
      title = {Development Robotic Arm System Testbed for the Mars Sample Return Campaign},
      author = {Schoelen, Dane and Arnold, Richard and Dolci, Marco and Wehage, Kristopher},
      booktitle = {IEEE Aerospace Conference},
      publisher = {JPL Open Repository},
      year = {2024},
      doi = {10.48577/jpl.sz5uf4},
      abstract = {The NASA-ESA led Mars Sample Return campaign will be the first to deliver samples from another planet to thousands of scientists worldwide who will rewrite textbooks with their discoveries. A critical step in the campaign is the transfer of sample tubes from the surface of Mars to the ascent vehicle which will require a highly dexterous robotic arm and advanced control strategies. Development and testing of the control algorithms is being carried out at NASA’s Jet Propulsion Laboratory on R&D testbeds while the flight robotic arm is under development by the ESA. The algorithm testing requires a seven degree of freedom robotic arm testbed closely resembling the kinematic configuration of the flight design which utilizes comparable mechanical components and avionics. The actuators of the testbed were designed around off the shelf drivetrain and sensor components which resemble the operation and performance of their flight counterparts, without the added complexity and expense of extreme radiation, vibration and thermal robustness. The cable harnessing is largely off the shelf and is integrated into a cable management system commonly used on industrial robots which is cheaper, easier to install and modify than a custom ribbon cable solution. Each actuator was tested on the benchtop for performance characterization and qualification of load capability. The integrated robotic arm was kinematically calibrated using vision-based metrology and applied load test cases. This paper describes the design, construction, and commissioning of this testbed, dubbed Bradbury, which meets the needs of the sample handling algorithm testing campaign while remaining relatively inexpensive and efficient to construct and reconfigure.}
    }
  35. Mccormick, R. (2024). COLDArm: A Cryogenic Capable Robotic Arm System for the Moon . Root. doi.org/10.48577/jpl.oyxw4y
    BibTeX
    @misc{mccormick2024coldarm,
      title = {COLDArm: A Cryogenic Capable Robotic Arm System for the Moon},
      author = {Mccormick, Ryan},
      journal = {Root},
      year = {2024},
      doi = {10.48577/jpl.oyxw4y},
      abstract = {No abstract available.}
    }
  36. Aghili, F. (2024). Adaptive Visual Servoing for On-Orbit Servicing. Source
    BibTeX
    @article{aghili2024badaptive,
      title = {Adaptive Visual Servoing for On-Orbit Servicing},
      author = {Aghili, Farhad},
      year = {2024},
      url = {https://arxiv.org/abs/2409.05295v1}
    }
  37. Alizadeh, A. and Zhu, Z. H. (2024). A comprehensive survey of space robotic manipulators for on-orbit servicing . Frontiers in Robotics and AI. Source
    BibTeX
    @article{alizadeh2024comprehensive,
      title = {A comprehensive survey of space robotic manipulators for on-orbit servicing},
      author = {Alizadeh, Ali and Zhu, Zheng H.},
      journal = {Frontiers in Robotics and AI},
      volume = {11},
      pages = {1470950},
      year = {2024},
      doi = {10.3389/frobt.2024.1470950},
      abstract = {On-Orbit Servicing (OOS) robots are transforming space exploration by enabling vital maintenance and repair of spacecraft directly in space. However, achieving precise and safe manipulation in microgravity necessitates overcoming significant challenges. This survey delves into four crucial areas essential for successful OOS manipulation: object state estimation, motion planning, and feedback control. Techniques from traditional vision to advanced X-ray and neural network methods are explored for object state estimation. Strategies for fuel-optimized trajectories, docking maneuvers, and collision avoidance are examined in motion planning. The survey also explores control methods for various scenarios, including cooperative manipulation and handling uncertainties, in feedback control. Additionally, this survey examines how Machine learning techniques can further propel OOS robots towards more complex and delicate tasks in space.}
    }
  38. Amaya-Mejía, L. M., Ghita, M., Dentler, J., Olivares-Mendez, M. and Martinez, C. (2024). Visual Servoing for Robotic On-Orbit Servicing: A Survey . International Conference on Space Robotics. Source
    BibTeX
    @inproceedings{amayamejia2024bvisual,
      title = {Visual Servoing for Robotic On-Orbit Servicing: A Survey},
      author = {Amaya-Mejía, Lina María and Ghita, Mohamed and Dentler, Jan and Olivares-Mendez, Miguel and Martinez, Carol},
      booktitle = {International Conference on Space Robotics},
      year = {2024},
      url = {https://arxiv.org/abs/2409.02324v1}
    }
  39. Tevere, E. (2024). OWLAT: The Evolution of an Advanced Lander-Manipulator Testbed for Enabling Autonomy Development for Ocean Worlds Missions . AIAA AVIATION Forum and ASCEND. Source
    BibTeX
    @inproceedings{tevere2024owlat,
      title = {OWLAT: The Evolution of an Advanced Lander-Manipulator Testbed for Enabling Autonomy Development for Ocean Worlds Missions},
      author = {Tevere, Erica},
      booktitle = {AIAA AVIATION Forum and ASCEND},
      year = {2024},
      doi = {10.2514/6.2024-4916},
      abstract = {NASA has developed platforms for evaluating autonomy technologies for lander-based robotic sampling missions to Ocean Worlds. Mission concepts that propose operations at a further distance from Earth and under constrained resources will rely more heavily on robust autonomy capabilities for mission operations. The Ocean World Lander Autonomy Testbed (OWLAT) was built in an effort to bridge the gap between autonomous technologies emerging from academia and industry, and the specific demands of lander-style mission operations. OWLAT provides a facility for testing technologies against the authentic challenges of autonomous operations in low-gravity environments. Purposefully designed to limit the implementation overhead, the testbed provides telemetry logging from the system and an adaptable interface for commanding by leveraging an open-source middle-ware suite. This paper presents the capabilities of the OWLAT testbed, a review of deployments of autonomous technologies on the testbed, and lessons learned from developing a high-fidelity, versatile testbed that facilitates the advancement of technology readiness level (TRL) for preconfigured autonomous operation solutions.}
    }
  40. Eslami, M. and Babazadeh, M. (2025). Learning-Based Data-Assisted Port-Hamiltonian Control for Free-Floating Space Manipulators . arXiv. Source
    BibTeX
    @article{eslami2025blearning,
      title = {Learning-Based Data-Assisted Port-Hamiltonian Control for Free-Floating Space Manipulators},
      author = {Eslami, Mostafa and Babazadeh, Maryam},
      journal = {arXiv},
      year = {2025},
      doi = {10.48550/arxiv.2509.09563},
      abstract = {A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A robust, model-based controller combined with a high-gain decentralized integrator establishes large robustness margins and strict time-scale separation, ensuring that subsequent learning cannot destabilize the primary dynamics. Learning, selected for its generalizability, is then applied to capture complex, unmodeled effects, despite inherent delay and transient error during adaptation. Formal Lyapunov analysis with explicit stability bounds guarantees convergence under bounded learning errors. The structured design confines learning to the simplest part of the dynamics, enhancing data efficiency while preserving physical interpretability. The approach is generic, with a free-floating space manipulator orientation control task, including integrated null-space collision avoidance, serving as a case study to demonstrate robust tracking performance and applicability to broader robotic domains.}
    }
  41. Karimov, S., Neppel, E., Santra, S., Uno, K. and Yoshida, K. (2025). An Agnostic End-Effector Alignment Controller for Robust Assembly of Modular Space Robots . International Conference on Space Robotics. Source
    BibTeX
    @inproceedings{karimov2025agnostic,
      title = {An Agnostic End-Effector Alignment Controller for Robust Assembly of Modular Space Robots},
      author = {Karimov, Shamistan and Neppel, Elian and Santra, Shreya and Uno, Kentaro and Yoshida, Kazuya},
      booktitle = {International Conference on Space Robotics},
      pages = {511-516},
      year = {2025},
      doi = {10.1109/isparo66239.2025.11437339},
      abstract = {Modular robots offer re-configurability and fault tolerance essential for lunar missions, but require controllers that adapt safely to real-world disturbances. We build on our previous hardware-agnostic actuator synchronization in Motion Stack to develop a new controller enforcing adaptive velocity bounds via a dynamic hypersphere clamp. Using only real-time end-effector and target pose measurements, the controller adjusts its translational and rotational speed limits to ensure smooth, stable alignment without abrupt motions. We implemented two variants - a discrete, step-based version and a continuous, velocity-based version - and tested them on two MoonBot limbs in JAXA’s lunar environment simulator. Field trials demonstrate that the step-based variant produces highly predictable, low-wobble motions, while the continuous variant converges more quickly and maintains millimeter-level positional accuracy, and both remain robust across limbs with differing mechanical imperfections and sensing noise (e.g., backlash and flex). These results highlight the flexibility and robustness of our robot-agnostic framework for autonomous self-assembly and reconfiguration under harsh conditions.}
    }
  42. McDonnell, C. J., Arana‐Catania, M. and Upadhyay, S. (2024). Autonomous Robotic Arm Manipulation for Planetary Missions using Causal Machine Learning . arXiv. Source
    BibTeX
    @article{mcdonnell2024autonomous,
      title = {Autonomous Robotic Arm Manipulation for Planetary Missions using Causal Machine Learning},
      author = {McDonnell, Cheryl J. and Arana‐Catania, Miguel and Upadhyay, Saurabh},
      journal = {arXiv},
      year = {2024},
      doi = {10.48550/arxiv.2403.00470},
      abstract = {Autonomous robotic arm manipulators have the potential to make planetary exploration and in-situ resource utilization missions more time efficient and productive, as the manipulator can handle the objects itself and perform goal-specific actions. We train a manipulator to autonomously study objects of which it has no prior knowledge, such as planetary rocks. This is achieved using causal machine learning in a simulated planetary environment. Here, the manipulator interacts with objects, and classifies them based on differing causal factors. These are parameters, such as mass or friction coefficient, that causally determine the outcomes of its interactions. Through reinforcement learning, the manipulator learns to interact in ways that reveal the underlying causal factors. We show that this method works even without any prior knowledge of the objects, or any previously-collected training data. We carry out the training in planetary exploration conditions, with realistic manipulator models.}
    }