Slip Estimation and Terramechanics

Slip is the difference between the motion the wheels commanded and the motion the vehicle made. It is not directly observable: wheel encoders assume no slip by construction, and double integration of accelerometer output on a Mars rover is too noisy to recover position directly [2]. Every flown slip measurement therefore comes from visual odometry [2][1].

Definitions used in flight

Curiosity computes two fractions onboard [2]:

• Wheel slip fraction: the sum of the linear distances of all six visual-odometry-corrected wheel positions from their idealized no-slip positions, divided by the summed wheel path lengths since the previous visual odometry update. Defined for all basic motions including turns in place.
• Rover slip fraction: the Euclidean distance between the idealized and corrected positions of the rover origin, at the turning center between the middle wheels, divided by the no-slip path length of that origin since the previous update. Undefined during turns in place.

A wheel slip fraction of 0.0 means the rover reached its estimated no-slip position; 1.0 means a straight arc was commanded and visual odometry measured no motion at all [2]. No wheel slip fraction is computed for arcs shorter than 0.35 m, because a small absolute slip over a short arc produces a large fraction and would trip the excessive-slip drive fault [3].

The MER slip record this is built on

Both Mars Exploration Rovers measured slip only through NavCam imagery and visual odometry software, and the recorded extremes were 100 percent slip on the first attempt to exit Eagle Crater, 99.9 percent while stuck in the Purgatory ripple, and 125 percent during one climb in the Columbia Hills [7]. On sol 520 a commanded 0.6 m forward step with 10 to 11 degrees of roll produced 0.12 m of downslope slide, 20 percent slip, measured by tracking 80 features between two images.

Measured slip in flight

Quantity	Value	Vehicle and period
Average rover slip	6.24 percent	Curiosity to sol 2488 [2]
Average wheel slip	8.44 percent	Curiosity to sol 2488 [2]
Average of maximum rover slip per sol	16.69 percent	Curiosity to sol 2488 [2]
Maximum rover and wheel slip	98.70 percent	Curiosity, sol 2087 [2]
Maximum measured slip	125 percent	Spirit, sol 206, climbing a slope over 25 degrees [1]
Slip while embedded	98.9 to 99.5 percent	Opportunity, sols 463 to 483 [1]
Slip driving upslope on soil	about 40 percent	terrestrial test rover [5]

Slip above 100 percent means net motion opposite to the commanded direction, which is what a rover sliding downslope while its wheels turn uphill produces [1]. Opportunity’s Purgatory ripple embedding produced about 1 mm of motion against 2 m commanded on one step, and 50 m of wheel rotation had produced about 2 m of track.

Slip as a fault threshold

Slip only became a safety system once it was measurable. MER responded to the sol 339 event, in which a 40 cm arc produced under 20 cm of progress and therefore more than 50 percent slip, by making Slip Check a standard mode: blind segments capped at an initial 5 m, each followed by a 20 cm drive step with visual odometry to confirm the vehicle can still move [1]. Driving with visual odometry running continuously capped the rate at about 10 m/h, so Slip Check bought a bound on embedding depth rather than continuous knowledge.

Curiosity carries the same logic as a configurable fault: a slow limit with a persistence count, so that exceeding it on a set number of contiguous updates faults the drive [2]. Five Curiosity drives to sol 2488 were stopped by visual odometry failures, and the sol 672 partial embedding was stopped by VO Auto during a backwards drive. The operational consequence of the sol 672 event and of the sol 710 discovery that performance in polygonally-rippled sand at Hidden Valley was insufficient was a permanent shift toward slower VO Full driving, which reacts fastest to unexpected slip.

Slip prediction from imagery

Predicting slip before driving onto the terrain requires a mapping from appearance to behavior. The learned approach takes stereo geometry and appearance for a map cell, uses the rover’s own measured slip when it later traverses that cell as the training label, and fits the relationship so that slip at a future location can be predicted from a distance [6]. The argument for learning rather than modeling is that it replaces mechanical modeling of the vehicle and terrain, and that the same algorithm transfers to a different vehicle by retraining.

Measured performance sets the limit of the approach. Over 2000 test frames not intersecting the training set, average slip prediction error was about 21 percent; with the terrain type known perfectly the error falls to about 11 percent, so terrain misclassification carries most of the error, and it occurs mainly between visually similar terrains such as dust-covered surfaces [5]. The residual is comparable to the measurement error of slip itself [6].

The system built around it is Terrain Adaptive Navigation: goodness maps and terrain triage, terrain classification, remote slip prediction, D* path planning over a slip-augmented cost map, high-fidelity traversability analysis by kinematic and dynamic forward simulation of the rover along a candidate path, and slip-compensated path following [5]. The path follower compares visual odometry against vehicle kinematics, which gives motion without slippage, to estimate the slip and compensate for it during execution. Terrain triage runs the traversability check twice, once to decide whether slip prediction is needed for a cell at all and once after, because slip prediction is expensive.

Sensing range limits where prediction can be applied. Range error at 50 m is 2.5 m for MER NavCams, 0.60 m for MSL NavCams, and 0.20 m for MSL Pancams at maximum zoom, assuming 0.25 pixel stereo correlation accuracy, against a pose error of 1 to 2 percent of distance traveled [5].

The journal version of the learned predictor reports 21.8 percent slip prediction error on about 2000 held-out frames of soil, sand, gravel and woodchips, and 11.2 percent when the terrain class is correct [8]. Its framing contribution is the nongeometric obstacle: terrain that is geometrically traversable but mechanically not, which a geometry-only hazard detector cannot see. It was analyzed offline on terrestrial field data, never run onboard and never shown on Mars terrain, and its ground truth is the rover’s own visual odometry.

Model-based families

Three families of approach sit beside the learned one. None has flown as a slip estimator.

Analytic wheel-soil models. Bekker-type pressure-sinkage models with Mohr-Coulomb shear were the basis of the Apollo Lunar Roving Vehicle performance prediction. Wheel-soil tests on five lunar simulants at the Army Waterways Experiment Station and 1/6 g wheel tests on an aircraft fed a computer model that predicted slip, speed and energy use [9]. Against post-mission data it overpredicted energy consumption with a median deviation of about 30 percent, and the report states that the LRV carried no instrumentation for slip, drawbar pull or sinkage, so no lunar slip was measured. The agreement is attributed to compensating errors, not to the model being correct.

Terramechanics in control. Ishigami and colleagues derived a counter-steer angle for a four-wheel-steer rover crossing a sandy side slope from a three-axis wheel model, and compared it with feedback control that measures vehicle sideslip and wheel longitudinal and lateral slip with a telecentric visual odometry sensor. On a 2.0 by 1.0 m tilted sandbox of Toyoura sand at 5 and 10 degrees, feed-forward gave 0.051 m rms lateral error and feedback 0.011 m. The feed-forward angles were wrong because the real soil differed from the assumed parameters, and there was no in-situ soil estimation [12]. Gradient-based predictive control needs a smooth wheel-soil model; a three-layer neural surrogate of the Soil Contact Model inside an unscented Kalman filter estimated the sinkage exponent to within 1.9 percent against 3.8 percent for a Bekker-based surrogate, at 5.2 ms against 10.5 ms per iteration [11]. That result is simulation only, scored against the model it imitates [11].

Particle simulation and gravity. Discrete element models resolve the soil directly. A parallel-particles formulation was tested against parabolic flight single-wheel data in Martian simulant, where drawbar pull coefficient fell about 20 percent and sinkage rose about 38 percent in lunar gravity relative to Earth [13]. With sinkage matched, simulated drawbar pull came out about 45 percent low, and the author attributes this to omitted particle rotation [13].

Reduced-gravity testing

Slip models are calibrated in 1 g, so the credibility of any model-based estimator depends on how well 1 g tests predict lunar or Martian behavior [9][10]. In two parabolic flight campaigns on a single-wheel testbed, reduced-weight testing overstated mobility: drawbar pull to weight fell 20 percent or more and sinkage rose up to 40 percent at equal load [10]. Matching the cone index gradient of the simulant overstated drawbar pull to weight by 44 percent mean squared percentage error, while granular scaling laws came within 8.5 percent on drawbar pull and 2.7 percent on sinkage. The cone index gradient of the same soil at unchanged density was about 4 times lower in lunar gravity than in 1 g [10]. All of this is wheel-level ground testing, not flight.

Terramechanics as a wheel life problem

On Curiosity the terramechanics question became a hardware survival question. Driving across well-indurated sandstone outcrops that wind erosion had shaped into sharp, immobile surfaces produced an unacceptable rate of punctures and cracks in the 0.75 mm aluminum wheel skins [4]. Experiments and modeling showed that static wheel loads would not cause those initial punctures and cracks. The damage comes from the driving mode: with all six drive actuators holding commanded angular velocities, a wheel on a leading suspension arm is forced onto a rock by the wheels behind it, and the resulting loads are much higher than the static normal load [4]. Obstacle runs with the Scarecrow test rover reproduced the effect and showed the load transfer around the bogie pivot that drives it [4].

The mechanism in drive terms is a wheel-speed mismatch. Under double Ackermann control every wheel turns at a speed derived from a flat-terrain assumption, so a front wheel climbing a rock must cover more distance than the other five in the same time; commanding all six at the planar speed makes the five push the climbing wheel forward, and a sharp embedded rock tip that fits between the treads punctures the skin [3]. Those punctures initiate the damage for a skin section and grow to merge with stress concentration cracking at the grouser chevron tips.

TRCTL

The Traction Control algorithm estimates wheel-terrain contact angles in real time from the measured attitude rates and rocker-bogie suspension angles through a rigid-body kinematic model, and commands the idealized no-slip angular rate for each wheel. It uses no prior or visual knowledge of the terrain, because generating a height map is resource-intensive enough to reduce traverse speed materially and its noise plus accumulated pose uncertainty would make wheel-speed optimization from a mesh impractical [3]. Free-floating wheelies are detected and damped autonomously.

TRCTL property	Value
Command rate	8 Hz
Implementation	flight software hot patch on top of R12, loaded at each boot
Added CPU usage while driving	under 3 percent
Added high-rate data volume	roughly doubled, from 8 Hz per-wheel speed records
Predicted slowdown from ground testing	up to 25 percent
Measured Speed Ratio, sols 1646 to 1822	0.899 over 351,992 samples, about 10 percent slower
Slowdown on visual odometry drives	under 4 percent
First nominal use	sol 1678

Source: [3]. The Speed Ratio is the median, over the five fastest wheels, of commanded speed divided by the speed the planar Ackermann algorithm would have commanded, evaluated at each 8 Hz sample. Nominal use from sol 1678 is also the point after which Curiosity’s mission statistics separate into pre-TRCTL and post-TRCTL populations [2].

The reason the 10 percent wheel-speed penalty costs under 4 percent of drive time is the visual odometry duty cycle: Curiosity drives long distances in 1 m steps and the stop-and- process time is nearly double the time spent driving the step, so under 40 percent of a drive activity is physical motion [3].

Measured flight effect

Over a matched 3.6 km of driving before and after nominal use began [3]:

Metric	Traction control disabled	Traction control enabled	Change
Mean of average wheel current, all wheels	0.353 A	0.287 A	18.7 percent reduction
Max of average wheel current, all wheels	0.375 A	0.312 A	16.8 percent reduction
Mean of mean current, left front wheel			9.7 percent reduction
Mean of mean current, right front wheel			12.4 percent reduction
Mean absolute heading error on straight arcs			44 percent reduction
Average wheel slip			0.8 percent lower
Forward driving share	88.3 percent	79.1 percent	backward driving rose from 3.8 to 14.5 percent

The per-wheel current reduction meets statistical significance at alpha 0.05 for every wheel except the left middle one [3]. Ground testing on relatively benign terrain had measured load reductions of 19 percent for front leading wheels and 11 percent for middle leading wheels. Wheel slip binned by 1 degree of average rover tilt was lower with traction control enabled in every bin up to 20 degrees, despite more time being spent at higher tilts in the enabled period [3]. A separate 1 km comparison, in which the enabled period ran at 3.6 degrees higher average pitch and 26.88 m more elevation gain, still showed 8.3 and 6.6 percent current reductions and a 30 percent heading error reduction, with average wheel slip 0.7 percent higher.

Curiosity drove 3.587 km in 149 drives with traction control through 3 September 2018, 99.38 percent of it with the algorithm enabled [3]. Independently, the mean and standard deviation of heading error on straight arcs fell 41 percent after nominal TRCTL use began on sol 1678, across 9990 pre-TRCTL and 4840 post-TRCTL straight arcs [2].

Failure modes

Traction control introduces exactly one new fault: a per-drive-step timeout. One of the first 146 nominal-use drives ended on it, the sol 1786 drive faulting after 15.86 m of a planned 27.9 m when a 32.77 s timeout expired while the right rear wheel climbed a large rock; the right bogie angle was at that moment 0.3 degrees from its 18 degree limit, so the drive was seconds from a suspension fault instead [3].

Slip estimation inherits every visual odometry failure mode. Sandy terrain is simultaneously the terrain where slip matters most and the terrain where the feature detector is most likely to fail to converge [1][2]. The MER workaround was that pliable sand records the vehicle’s own tracks, which supply the features [1].

Slip prediction inherits terrain classification error, which is where roughly half its total error comes from [5]. It also depends on the vision system having range data at all: on the LAGR vehicle, tilt-based estimates were of the robot rather than the ground plane and could be wrong or missing when too few cells lay under the robot [6].

Mitigation for the wheel damage was operational rather than algorithmic in the first instance: track the damage with the rover’s own imaging instruments, and map the terrain units from orbital and surface imagery so that traverses can be planned around the sharp outcrop units where possible [4]. Crack propagation still increased between landing in August 2012 and June 2016, because some drives across irregular sharp sandstone could not be avoided; wheel life testing on a kinematically correct half-suspension in the Mars Yard supported an estimate of at least ten more kilometers of driving with careful path planning [4]. Backward driving reduces forces on the middle and front wheels but has not been shown to change the outcome by itself, which is why forward driving remains the default [2].

Estimation methods that have not flown

Surveys group slip estimation into proprioceptive, exteroceptive and model-based methods, with torque-based and velocity-based compensation, and illustrate them with slip incidents from the Lunar Roving Vehicle, Lunokhod, Spirit, Opportunity and Curiosity [14]. Flown rovers use only the exteroceptive one, visual odometry. The others are laboratory or field results.

Slip-compensating path following. A Kalman filter fused visual odometry, inertial data and full six-wheel kinematics on a Rocky 8 research rover, differenced the filtered pose against the no-slip kinematic pose to form a slip vector, and drove that vector to zero through inverse kinematics [17]. The field test ran a simplified system, with the Mahalanobis comparator not yet implemented and rocker and bogie angles assumed zero, and no onboard processor cost is reported [16].

Slip in path planning. A computational slip model for MER planning adds a sliding vector to the no-slip kinematic simulation, weighted from empirically measured slip tables and local wheel-ground geometry. Agreement with measured behavior on a 14 degree slope is shown qualitatively, not scored by an error metric [15]. Thermal inertia from orbit has also been tried as a predictor: across 135 Curiosity visual odometry slip measurements at nine sandy sites to sol 986, root mean squared error fell from 22.0 percent for a slope-only model to 16.8 percent with thermal inertia added, though the two thermal inertia data sets disagree strongly in absolute scale [19].

Proprioceptive and track-based sensing. A proposal to estimate slip and sinkage separately on a rocker-bogie rover from suspension articulation, attitude and the hazard-detection ranger was demonstrated only in simulation on smooth synthetic terrain [20]. A rear-facing camera that images the wheel’s own track and extracts the lateral slip angle by edge detection, a Hough transform and fuzzy inference was tested on beach sand at 1 g, with its single accuracy figure drawn from one 7 m run on a 5 degree slope [18].

Slip as a controlled variable. Controlling slip ratio to minimize drive power used wheel-soil terramechanics and was checked on a single-wheel testbed and a rover; the reported minimum effective work differs by a factor of 2.6 between experiment and simulation [21]. Coupling a Bekker-Wong wheel model to a rocker-bogie multibody model reproduced the behavior of a small six-wheeled testbed on dry terrestrial sand [22]. A terramechanics model with an explicit side-force term supports steering simulation on FJS-1 simulant at 1 g, with every soil parameter fitted to that test bed [24]. Propagating uncertainty in cohesion and friction angle through such a model by a stochastic response surface gives confidence ellipses on predicted rover paths, checked on a 13.4 kg four-wheeled testbed in a 2.0 by 1.0 m sandbox [25].

Recent learned slip prediction and lugged-wheel models

Terrain classification feeding slip curves. SPOC is a fully convolutional network that labels terrain per pixel, with a six-class variant trained on Curiosity Navcam images whose labels were paired with visual odometry slip to compare Earth-calibrated Mars Yard slip curves against Gaussian process regression fit to Mars data [39]. It has not flown as a slip predictor. Sand, the class that matters most for slip, was the weakest, with 50.5 percent recall and 44.4 percent of sand labeled Small Rocks, and neither slip model predicted sand slip adequately [39]. The Gaussian process was scored on the data it was fit to [39].

Segmentation-to-slip-cost networks. SlipNet takes a terrain segmentation map plus in-situ wheel slip and speed and outputs a per-segment slip cost map without pre-classified terrain types [41]. All results come from a simulated 10 kg rover in a physics simulator, with no hardware and no characterized simulant, and the improvement over the baseline holds in 4 of 5 test samples [41]. Deep probabilistic traversability uses an ensemble of 10 networks to predict slip mean and variance from color and elevation maps, with a risk-aware cost and few-shot test-time adaptation from in-situ slip [42]. It was evaluated on 400 synthetic path planning problems only, and the preprint’s own uncertainty calibration on real terrain is untested [42].

Lugged-wheel terramechanics. A semiempirical model for rigid lugged wheels extends the Bekker and Janosi stress models with lug, slip-sinkage, wheel-dimension and load effects, and was fit to single-wheel data on HIT-LSS1 lunar simulant [40]. Its residual under 10 percent is a fit residual, since fit and validation use the same test bed, the tests were at 1 g, and slip above 0.6 is not modeled. Parameters must be refitted for each wheel and soil.

Terramechanics theory and its limits

The wheel-soil models above descend from Bekker’s load-sinkage law p = kz^n and Coulomb shear treatment of thrust and motion resistance [30]. Wong and Reece’s stress-distribution approach to rigid wheels established the transition point on the wheel-soil interface where tangential stress reverses, though its authors state the theory needed more experimental support [29]. A 1968 critique of the pressure-sinkage and shear stress-displacement equations, which space terramechanics still uses, questioned their foundations [31]. The competing dimensional-analysis school collected the wheel-on-soft-soil data published to 1962, all from terrestrial pneumatic tires at low speed [32]. Slip sinkage, the extra sinkage that slip adds to static load-sinkage, has an analytical formula validated against decades-old terrestrial shear-plate and tire data [23].

Current NASA review classes tire-ground models as semi-empirical, numerical (finite element, SPH continuum, discrete element) and empirical lookup, and states that its model comparison is preliminary and not an accuracy ranking, since soil parameters differ between the models compared [35]. The classical models are quasistatic; four dynamic pressure-sinkage extensions address wheel velocity and strain rate for rovers approaching or exceeding 1 m/s, and are surveyed without new measurement [36].

Flight and test-yard slip measurements

Mars-weight slip-versus-slope tests of the Curiosity rover on bedrock, cohesive soil and cohesionless sand, with GPS and motion-capture ground truth, were compared with the first 250 sols of flight data [34]. The Curiosity megaripple crossings to sol 710 recorded sinkage up to 30 percent of wheel diameter and slip up to 77 percent, with single-wheel rig tests described by the authors as only hinting at causes [33].

Gravity scaling of wheel tests

Parabolic flights give the direct data. A rigid wheel on FJS-1 simulant and Toyoura sand was tested at 1/6 g to 2 g against equivalent load variation at 1 g, with one wheel geometry and no grousers [38]. An ExoMars flexible wheel prototype driven at controlled slip through ES-2 Martian simulant on a Falcon 20 aircraft is the primary reduced-gravity wheel-soil dataset, on Martian simulant and not lunar regolith [26]. Granular scaling laws for grouser and helical wheels were checked at Earth gravity in sandboxes of silica sand and BP-1, with lunar gravity only simulated [27], and an enhanced law for slopes of minus 10 to plus 10 degrees was validated against discrete element simulation alone, with no physical wheel test [28]. Discrete element simulation of a MER spare wheel in Mojave Martian Simulant matched single-wheel drawbar pull and sinkage only up to slip 0.7; the 0.9 and 0.99 predictions have no test data [37].

What is not established

No slip model has flown as an estimator. Flown slip is measured after the fact by visual odometry, and the only learned predictor in the record was run offline on terrestrial data with visual odometry as its own ground truth, so its error is bounded below by the noise of that reference [8][6]. The Apollo LRV carried no slip instrumentation, so lunar wheel-soil models were never checked against measured lunar slip [9]. Terramechanics control results rest on tabletop sandbox runs with two runs per condition and unmeasured field soil [12], and neural surrogates are validated against the models they replace [11]. Particle simulation did not reproduce flight-gravity drawbar pull [13], and the reduced-gravity test data are 20 to 30 second parabolas in simulant weaker than Apollo in-situ soil [10]. Whether traction control’s slip reduction on Curiosity holds on terrain other than the matched 3.6 km comparison is not shown [3].