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].

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].