cs.ROMar 20, 2026

High-Speed, All-Terrain Autonomy: Ensuring Safety at the Limits of Mobility

Authors: James R. Baxter, Bogdan I. Epureanu, Paramsothy Jayakumar, Tulga Ersal

Organizations: Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI · U.S. Army Ground Vehicle Systems Center, Warren, MI

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Abstract

A novel local trajectory planner, capable of controlling an autonomous off-road vehicle on rugged terrain at high-speed is presented. Autonomous vehicles are currently unable to safely operate off-road at high-speed, as current approaches either fail to predict and mitigate rollovers induced by rough terrain or are not real-time feasible. To address this challenge, a novel model predictive control (MPC) formulation is developed for local trajectory planning. A new dynamics model for off-road vehicles on rough, non-planar terrain is derived and used for prediction. Extreme mobility, including tire liftoff without rollover, is safely enabled through a new energy-based constraint. The formulation is analytically shown to mitigate rollover types ignored by many state-of-the-art methods, and real-time feasibility is achieved through parallelized GPGPU computation. The planner's ability to provide safe, extreme trajectories is studied through both simulated trials and full-scale physical experiments. The results demonstrate fewer rollovers and more successes compared to a state-of-the-art baseline across several challenging scenarios that push the vehicle to its mobility limits.

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Fig. 1: Off-road vehicles experience significant vertical dynamics (evidenced by the extreme bend of the fiberglass flagpole) and even tire liftoff (shown in close-up view) when traveling over the rugged terrain considered in this work, even at moderate speed ( 5 m/s5\text{\,}\mathrm{m}\text{/}\mathrm{s} ). Since these dynamics contribute to rollover, navigation, especially at high speeds, is dangerous. This work demonstrates a method to mitigate the risk of rollover through advanced control design.
Fig. 2: The extended single-track vehicle dynamics model, a state-of-the-art baseline
Fig. 3: The single rigid body vehicle dynamics model, a higher-fidelity alternative to the extended single-track model
Fig. 4: Relative height used to compute the Energy Stability Margin (ESM)
Fig. 5: Normalized soft constraint formulation: The additional cost rate added by incremental violation of a soft constraint is shown and compared to the equivalent additional cost of violating a hard constraint.
Fig. 6: Safety constraint implementations: The rollover prevention constraints are normalized equivalently to minimize bias. Each constraint begins contributing cost at 10% safety factor and has an identical value at full violation. The ESM constraint is shown with the top axis, and the lateral-acceleration constraint is shown on the bottom one.
Fig. 7: The physical location and vehicle used for navigation trials
Fig. 8: Route geometry for scenarios 1 and 3, visualized over reconstructed terrain imagery. The vehicle must navigate from the starting point (white circle) to the goal (green circle), while staying inside the path boundary (black polygon) and outside all obstacles (red polygons).
Fig. 9: Snapshots of terrain encountered while autonomously driving scenario 1 (viewed left-to-right, top-to-bottom). The images span approximately 25 seconds of footage from a physical trial of the proposed formulation carried out at a speed of 5 m/s\mathrm{m}\text{/}\mathrm{s} .
Fig. 10: 3D rendering of terrain at three levels-of-detail (LODs). Left: plant LOD, Center: single rigid body LOD, Right: extended single-track LOD.
SetupPlant Co-SimulatorSingle Rigid Body FormulationExtended Single-Track Formulation
1plant LODsingle rigid body LODextended single-track LOD
2single rigid body LODsingle rigid body LODextended single-track LOD
3extended single-track LODextended single-track LODextended single-track LOD
TABLE I: Terrain levels of detail (LODs) used in each setup of the simulated study
Fig. 11: Results of simulated trials evaluating local trajectory planner performance. Rollover proportion is plotted as a function of speed, and each row provides results of a single setup, ranging from most realistic (top) to most equivalent (bottom). The single rigid body formulation consistently outperforms the extended single-track formulation in regions where a visible difference beyond the bounds of uncertainty exists, indicating that it has superior ability to ensure safety against rollover.
Fig. 12: Results of simulated trials evaluating local trajectory planner performance, Success proportion is plotted as a function of speed, and each row provides results of a single setup, ranging from most realistic (top) to most equivalent (bottom). Superior performance is more often achieved by the single rigid body formulation than the extended single-track formulation, indicating that its superior ability to ensure safety against rollover does not come at the expense of success.
Target SpeedTrials per Formulation
4.0 m/s4.0\text{\,}\mathrm{m}\text{/}\mathrm{s}5
4.5 m/s4.5\text{\,}\mathrm{m}\text{/}\mathrm{s}9
5.0 m/s5.0\text{\,}\mathrm{m}\text{/}\mathrm{s}5
5.5 m/s5.5\text{\,}\mathrm{m}\text{/}\mathrm{s}5
TABLE II: Distribution of trials during physical experiments
Target SpeedExtended Single-TrackSingle Rigid Body
4.0 m/s4.0\text{\,}\mathrm{m}\text{/}\mathrm{s}5 successes, 0 failures5 successes, 0 failures
4.5 m/s4.5\text{\,}\mathrm{m}\text{/}\mathrm{s}9 successes, 0 failures9 successes, 0 failures
5.0 m/s5.0\text{\,}\mathrm{m}\text{/}\mathrm{s}4 successes, 1 failure5 successes, 0 failures
5.5 m/s5.5\text{\,}\mathrm{m}\text{/}\mathrm{s}5 successes, 0 failures5 successes, 0 failures
TABLE III: Outcomes of trials during physical experiments
Fig. 13: Composite time-lapse image of the failure experienced by the extended single-track formulation during a scenario 1 trial at 5 m/s5\text{\,}\mathrm{m}\text{/}\mathrm{s}
Fig. 14: Measured vehicle trajectories during physical trials. The extended single-track formulation experienced one failure, where the vehicle exited the path boundary and collided with an obstacle. The single rigid body formulation’s route is also more consistent, indicating greater authority over the vehicle’s trajectory.
Fig. 15: Total accrued costs during physical trials (note: the x-axis is categorical; deviation from the axis ticks is for visual clarity only). The single rigid body formulation has a statistically significant reduction in cost in the 4.5 m/s4.5\text{\,}\mathrm{m}\text{/}\mathrm{s} trials.
Figure 24
Figure 25
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Figure 27
Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

ParameterMeaning
MMvehicle mass
JxxJ_{xx}vehicle moment of inertia about bx\mathbf{b}_{x}
JyyJ_{yy}vehicle moment of inertia about by\mathbf{b}_{y}
JzzJ_{zz}vehicle moment of inertia about bz\mathbf{b}_{z}
LfL_{f}long. distance from CoM to front axle
LrL_{r}long. distance from CoM to rear axle
Appendix
TABLE IV: Notation for common inertial and geometric parameters
ParameterValue
MM969 kg969\text{\,}\mathrm{kg}
JxxJ_{xx}280.9\text{\,}\mathrm{kg}\text{{}\cdot{}}{\mathrm{m}}^{2}
JyyJ_{yy}692.1\text{\,}\mathrm{kg}\text{{}\cdot{}}{\mathrm{m}}^{2}
JzzJ_{zz}810.7\text{\,}\mathrm{kg}\text{{}\cdot{}}{\mathrm{m}}^{2}
LfL_{f}1.565 m1.565\text{\,}\mathrm{m}
LrL_{r}1.148 m1.148\text{\,}\mathrm{m}
Appendix
TABLE V: Model parameters
ParameterValue
CC6.1 rad−16.1\text{\,}{\mathrm{rad}}^{-1}
μ\mu0.6
Appendix
TABLE VI: Tire parameters for simulated trials
ParameterValue
CC1.7 rad−11.7\text{\,}{\mathrm{rad}}^{-1}
μ\mu0.4
Appendix
TABLE VII: Tire parameters for physical trials
Fig. 16: Subset of simulated trajectories used for open-loop analysis, focusing on the ridge and turn included in scenario 1 where the extended single-track formulation experienced a failure during physical testing. The plant trajectory is shown as a black line, open-loop model predictions are shown as colored lines, and black points mark the locations where the former originate. The trajectories display decreased overshoot error by the single rigid body model.
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