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 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.

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].

What the force sensor costs to trust

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]:

Range	Force range	Moment range	Absolute accuracy, force	Absolute accuracy, moment	Relative accuracy, force	Relative accuracy, moment
Precision	500 N	125 Nm	43 N	11 Nm	29 N	7.5 Nm
Nominal	800 N	200 Nm	65 N	16 Nm	45 N	11 Nm
Extended	1800 N	600 Nm	150 N	50 Nm	105 N	35 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.

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. 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].

Control rates, where they are published

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. 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.

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.

Reaction on a free-flying base

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.

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.

Tool changeout

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.

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].

Failure modes

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.

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.