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

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

cs.ROFeb 18, 2026

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

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

Organizations: Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA

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.

Figures & tables

Panel of Figure 1 — Fig. 1 : The elevation map of the terrain for a specific track.

Fig. 2 : The simulation environment for autonomous nonplanar vehicle navigation in Isaac Sim .

Panel of Figure 3 — Fig. 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.

Panel of Figure 4 — Fig. 4 : Distributions of absolute cross-track errors using the recursive GP residual model and the single-track dynamic model.

Panel of Figure 5 — Fig. 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.

Metric	Kidney	L-Track	Oval
Min elevation (m)	-5.389	-0.183	-5.523
Max elevation (m)	5.696	6.234	5.538
Elevation range (m)	11.085	6.416	11.061
Max slope (degrees °)	27.811	75.760	23.177
Median slope (degrees °)	10.051	14.698	11.819

TABLE I : Map Statistics

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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Institute for Dynamic Systems and Control, ETH Zürich, CH-8092 Zürich, Switzerland.

Model Predictive Control Gaussian Processes Gaussian Process Regression Residual Dynamics Learning Robot Dynamics Learning

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Learning-based model predictive control (MPC) can enhance control performance by correcting for model inaccuracies, enabling more precise state trajectory predictions than traditional MPC. A common approach is to model unknown residual dynamics as a Gaussian process (GP), which leverages data and also provides an estimate of the associated uncertainty. However, the high computational cost of online learning poses a major challenge for real-time GP-MPC applications. This work presents an efficient implementation of an approximate spatio-temporal GP model, offering online learning at constant computational complexity. It is optimized for GP-MPC, where it enables improved control performance by learning more accurate system dynamics online in real-time, even for time-varying systems. The performance of the proposed method is demonstrated by simulations and hardware experiments in the exemplary application of autonomous miniature racing.

Abstract

Model Predictive Control

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