arXiv subjects

Joscha F. Bongard

Publications and source records attributed to Joscha F. Bongard.

3 recordsLinked to original sources

arXiv2026

Robust Nonlinear Trajectory Tracking Control for Autonomous Racing on Three-Dimensional Tracks

We propose a robust nonlinear model predictive control (MPC) scheme for trajectory-tracking control of autonomous vehicles at the limits of handling on non-planar road surfaces. We derive the dynamics from first principles and selectively omit terms with negligible dynamic influence to maintain real-time capability. The resulting MPC with a three-dimensional (3D) dynamic single-track model integrates relevant dynamic effects directly into the prediction model and leverages them to improve prediction accuracy and therefore control performance. Even if the influence of terrain-induced vertical loads on the total acceleration potential is modeled, tire-road interactions are subject to uncertainty and disturbance. The uncertainty-aware constraint tightening scheme introduces a margin to constraint bounds to keep the vehicle controllable and stable in this environment. To validate our proposed approach, we perform high-fidelity dynamic double-track vehicle dynamics simulations on a model of a real circuit. We find that our algorithm can improve trajectory-tracking accuracy while maintaining low computation times.

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arXiv2026

Dynamic Constraint Tightening for Nonlinear MPC for Autonomous Racing via Contraction Analysis

This work develops a robust nonlinear Model Predictive Control (MPC) framework for path tracking in autonomous vehicles operating at the limits of handling utilizing a Control Contraction Metric (CCM) derived from a perturbed dynamic single track model. We first present a nonlinear MPC scheme for autonomous vehicles. Building on this nominal scheme, we assume limited uncertainty in tire parameters as well as bounded force disturbances in both lateral and longitudinal directions. By simplifying the perturbed model, we optimize a CCM for the uncertain model, which is validated through simulations at the dynamic limits of vehicle performance. This CCM is subsequently employed to parameterize a homothetic tube used for constraint tightening within the MPC formulation. The resulting robust nonlinear MPC is computationally more efficient than competing methods, as it introduces only a single additional state variable into the prediction model compared to the nominal scheme. Simulation results demonstrate that the homothetic tube expands most significantly in regions where the nominal scheme would otherwise violate constraints, illustrating its ability to capture all uncertain trajectories while avoiding unnecessary conservatism.

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arXiv2026

Control Lyapunov Functions for Optimality in Sontag-Type Control

Given a Control Lyapunov Function (CLF), Sontag's famous Formula provides a nonlinear state-feedback guaranteeing asymptotic stability of the setpoint. At the same time, a cost function that depends on the CLF is minimized. While there exist methods to construct CLFs for certain classes of systems, the impact on the resulting performance is unclear. This article aims to make two contributions to this problem: (1) We show that using the value function of an LQR design as CLF, the resulting Sontag-type controller minimizes a classical quadratic cost around the setpoint and a CLF-dependent cost within the domain where the CLF condition holds. We also show that the closed-loop system is stable within a local region at least as large as that generated by the LQR. (2) We show a related CLF design for feedback-linearizable systems resulting in a global CLF in a straight-forward manner; The Sontag design then guarantees global asymptotic stability while minimizing a quadratic cost at the setpoint and a CLF-dependent cost in the whole state-space. Both designs are constructive and easily applicable to nonlinear multi-input systems under mild assumptions.

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