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Model Predictive Control for Aggressive Driving Over Uneven Terrain

Tyler Han, Alex Liu, Anqi Li, Alex Spitzer, Guanya Shi, Byron Boots

TL;DR

This work tackles safe, aggressive autonomous driving over uneven off-road terrain by deriving physics-based traversability constraints from a torque-balance model and integrating them into a parallelizable MPPI planner. The approach yields two key constraints—rollover and ditch handling—that are independent of time and can be evaluated across samples and horizons in real time. The system couples perception-driven elevation maps with a GPU-accelerated MPPI implementation and a low-level PI controller, achieving up to 22% faster completion than a geometry-based baseline while maintaining safety on hills, ditches, and complex courses on a full-scale vehicle. The results demonstrate the practical viability of physics-informed planning for high-speed, unstructured-terrain autonomy and highlight avenues for future improvements in sampling density and dynamic modeling.

Abstract

Terrain traversability in unstructured off-road autonomy has traditionally relied on semantic classification, resource-intensive dynamics models, or purely geometry-based methods to predict vehicle-terrain interactions. While inconsequential at low speeds, uneven terrain subjects our full-scale system to safety-critical challenges at operating speeds of 7--10 m/s. This study focuses particularly on uneven terrain such as hills, banks, and ditches. These common high-risk geometries are capable of disabling the vehicle and causing severe passenger injuries if poorly traversed. We introduce a physics-based framework for identifying traversability constraints on terrain dynamics. Using this framework, we derive two fundamental constraints, each with a focus on mitigating rollover and ditch-crossing failures while being fully parallelizable in the sample-based Model Predictive Control (MPC) framework. In addition, we present the design of our planning and control system, which implements our parallelized constraints in MPC and utilizes a low-level controller to meet the demands of our aggressive driving without prior information about the environment and its dynamics. Through real-world experimentation and traversal of hills and ditches, we demonstrate that our approach captures fundamental elements of safe and aggressive autonomy over uneven terrain. Our approach improves upon geometry-based methods by completing comprehensive off-road courses up to 22% faster while maintaining safe operation.

Model Predictive Control for Aggressive Driving Over Uneven Terrain

TL;DR

This work tackles safe, aggressive autonomous driving over uneven off-road terrain by deriving physics-based traversability constraints from a torque-balance model and integrating them into a parallelizable MPPI planner. The approach yields two key constraints—rollover and ditch handling—that are independent of time and can be evaluated across samples and horizons in real time. The system couples perception-driven elevation maps with a GPU-accelerated MPPI implementation and a low-level PI controller, achieving up to 22% faster completion than a geometry-based baseline while maintaining safety on hills, ditches, and complex courses on a full-scale vehicle. The results demonstrate the practical viability of physics-informed planning for high-speed, unstructured-terrain autonomy and highlight avenues for future improvements in sampling density and dynamic modeling.

Abstract

Terrain traversability in unstructured off-road autonomy has traditionally relied on semantic classification, resource-intensive dynamics models, or purely geometry-based methods to predict vehicle-terrain interactions. While inconsequential at low speeds, uneven terrain subjects our full-scale system to safety-critical challenges at operating speeds of 7--10 m/s. This study focuses particularly on uneven terrain such as hills, banks, and ditches. These common high-risk geometries are capable of disabling the vehicle and causing severe passenger injuries if poorly traversed. We introduce a physics-based framework for identifying traversability constraints on terrain dynamics. Using this framework, we derive two fundamental constraints, each with a focus on mitigating rollover and ditch-crossing failures while being fully parallelizable in the sample-based Model Predictive Control (MPC) framework. In addition, we present the design of our planning and control system, which implements our parallelized constraints in MPC and utilizes a low-level controller to meet the demands of our aggressive driving without prior information about the environment and its dynamics. Through real-world experimentation and traversal of hills and ditches, we demonstrate that our approach captures fundamental elements of safe and aggressive autonomy over uneven terrain. Our approach improves upon geometry-based methods by completing comprehensive off-road courses up to 22% faster while maintaining safe operation.
Paper Structure (44 sections, 40 equations, 7 figures, 3 tables)

This paper contains 44 sections, 40 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Physics-Based Traversability Constraints
  4. Dynamics Model with Residual Torque
  5. Rollover
  6. Ditches
  7. System Overview
  8. Perception
  9. MPPI
  10. Preliminaries
  11. Fast and Parallel Model Rollouts
  12. Cost Function
  13. Tuning
  14. Handling Control Delays
  15. Sampling Control Sequences
  16. ...and 29 more sections

Figures (7)

  • Figure 1: (1) Robot in uneven terrain. (2) Poor ditch traversal. (3) Slalom on a steep hill. (4) Poor rollover handling. (5) Chasing robot through crater ditch. (6) Expert driver performing aggressive circles. Note that (2) and (4) are not outcomes of our approach.
  • Figure 2: Rollouts are sampled in the 2D kinematic plane then constrained by their implicit dynamics on the elevation map (left). Frames and forces for rollover analysis (rear-view, upper-right) and for ditch analysis (side-view, bottom-right).
  • Figure 4: Information flow across perception and control. The focus of this work are highlighted in purple.
  • Figure 5: Top row. Spatial plot over elevation contour map of 15-meter radius circles on a 10-degree incline hill. Results for each experiment are averaged over at least five loops. Speed and $RR$ are reflected by the line color and marker width, respectively. Autonomy results of decreasing ${RR}_{\text{max}}$ control parameter are shown in the right column. Bottom row. Plots of speed and rollover risk as a function of heading angle. Off-camber turning highlighted by grey box. Thicker and opaquer autonomy lines correspond with higher ${RR}_{\text{max}}$ settings (Autonomy ${RR}_{\text{max}}\in\{3.0, 3.2, \textbf{3.4}\}$; Autonomy (Sim) ${RR}_{\text{max}}\in\{4, 5, \textbf{6}\}$). Autonomy (Sim) simulates MPPI for higher than tolerable ${RR}_{\text{max}}$ values. Baseline results are simulated due to unsafe behavior.
  • Figure 6: Robotic platform crossing the V-Ditch (pictured above; driver is present only for safety purposes). Average velocity is plotted as a function of the position through the ditch over the elevation profile (brown). Individual ditch traversals are plotted transparently.
  • ...and 2 more figures