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

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.

Kinodynamic planning for car-like vehicles on uneven terrain requires simultaneously optimizing competing objectives such as path efficiency and pose stability. This work presents an adaptive epsilon-constraint method integrated into a Model Predictive Control (MPC) framework, where the epsilon bounds are dynamically adjusted based on terrain descriptors to explore the Pareto front in real time. To capture vehicle-terrain dynamics, we develop a semi-parametric model combining analytical vehicle dynamics with a Sparse Gaussian Process (SGP) trained on the same terrain descriptors. The proposed epsilon-MPC is evaluated against MPPI and GAKD baselines, achieving a 94% navigation success rate while reducing maximum orientation deviation by 24% and improving multi-objective trade-off quality by 23%.

Autonomous racing requires accurate trajectory tracking near the handling limits of a vehicle while maintaining low computational latency. Geometric controllers are computationally efficient, but the Ackermann steering geometry becomes invalid under limit-handling conditions. Model- and Acceleration-based Pursuit (MAP) preserves the simplicity of geometric approaches while leveraging tire dynamics. Yet MAP remains fundamentally a geometric controller that relies on Ackermann steering geometry, and its tire model may not fully capture the vehicle's actual dynamic response. This paper presents MAP2, a model-based pursuit controller that combines a curvature-based kinematic MPC and a Sparse Gaussian Process (SGP) residual correction. The proposed algorithm uses MPC to optimize kinematic control inputs over a prediction horizon and maps them to steering commands through a tire dynamics model augmented with SGP residual correction. Real-world vehicle experiments demonstrate substantial reductions in lateral tracking error and lap time. Compared with MAP and Pure Pursuit (PP), MAP2 reduces the average lateral tracking error by 37.99% and 44.65%, respectively, while reducing average lap time by at least 1.5%.