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Nonplanar Model Predictive Control for Autonomous Vehicles with Recursive Sparse Gaussian Process Dynamics

Ahmad Amine, Kabir Puri, Viet-Anh Le, Rahul Mangharam

TL;DR

The paper addresses autonomous navigation on nonplanar terrain by introducing a geometry-aware residual dynamics model that couples a nominal single-track bicycle model with an online sparse Gaussian Process conditioned on terrain geometry. This learning-based residual is integrated into a nonplanar Model Predictive Control framework solved via Model Predictive Path Integral (MPPI) control, with horizon-based trajectory rollouts that account for elevation-derived angles. Key contributions include the terrain representation (height map, normals, slope, and orientation), online recursive sparse GP updates with inducing points, and GPU-accelerated MPPI rollouts for real-time control, validated in a custom Isaac Sim environment across multiple nonplanar tracks. The results demonstrate improved tracking accuracy and stability over a baseline planar model, with computation times suitable for real-time operation, highlighting the practical impact for off-road autonomous driving.

Abstract

This paper proposes a nonplanar model predictive control (MPC) framework for autonomous vehicles operating on nonplanar terrain. To approximate complex vehicle dynamics in such environments, we develop a geometry-aware modeling approach that learns a residual Gaussian Process (GP). By utilizing a recursive sparse GP, the framework enables real-time adaptation to varying terrain geometry. The effectiveness of the learned model is demonstrated in a reference-tracking task using a Model Predictive Path Integral (MPPI) controller. Validation within a custom Isaac Sim environment confirms the framework's capability to maintain high tracking accuracy on challenging 3D surfaces.

Nonplanar Model Predictive Control for Autonomous Vehicles with Recursive Sparse Gaussian Process Dynamics

TL;DR

The paper addresses autonomous navigation on nonplanar terrain by introducing a geometry-aware residual dynamics model that couples a nominal single-track bicycle model with an online sparse Gaussian Process conditioned on terrain geometry. This learning-based residual is integrated into a nonplanar Model Predictive Control framework solved via Model Predictive Path Integral (MPPI) control, with horizon-based trajectory rollouts that account for elevation-derived angles. Key contributions include the terrain representation (height map, normals, slope, and orientation), online recursive sparse GP updates with inducing points, and GPU-accelerated MPPI rollouts for real-time control, validated in a custom Isaac Sim environment across multiple nonplanar tracks. The results demonstrate improved tracking accuracy and stability over a baseline planar model, with computation times suitable for real-time operation, highlighting the practical impact for off-road autonomous driving.

Abstract

This paper proposes a nonplanar model predictive control (MPC) framework for autonomous vehicles operating on nonplanar terrain. To approximate complex vehicle dynamics in such environments, we develop a geometry-aware modeling approach that learns a residual Gaussian Process (GP). By utilizing a recursive sparse GP, the framework enables real-time adaptation to varying terrain geometry. The effectiveness of the learned model is demonstrated in a reference-tracking task using a Model Predictive Path Integral (MPPI) controller. Validation within a custom Isaac Sim environment confirms the framework's capability to maintain high tracking accuracy on challenging 3D surfaces.
Paper Structure (12 sections, 17 equations, 5 figures, 1 table)

This paper contains 12 sections, 17 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Learning-Based Nonplanar Vehicle Model
  3. Terrain Modeling
  4. Learning-Based Nonplanar Dynamics
  5. Sparse Gaussian Processes with Recursive Updates
  6. Nonplanar Model Predictive Control
  7. MPC Formulation
  8. Trajectory Rollouts and MPPI
  9. Results and Discussions
  10. Simulation Setup and Implementation Details
  11. Results
  12. Conclusions

Figures (5)

  • Figure 1: The elevation map of the terrain for a specific track.
  • Figure 2: The simulation environment for autonomous nonplanar vehicle navigation in Isaac Sim.
  • Figure 3: Top panels: Trajectories of the vehicle on different nonplanar tracks using a single-track model and the proposed Recursive GP. Bottom panels: Cross-track errors of the vehicle trajectories in simulation using the two different models.
  • Figure 4: Distributions of absolute cross-track errors using the recursive GP residual model and the single-track dynamic model.
  • Figure 5: Distributions of control frequencies using the recursive GP residual model and the single-track dynamic model. The minimum desired frequency of 50Hz is shown in red.