Mismatch-Aware Adaptive Constraint Tightening for Bicycle-Model Trajectory Optimization

TL;DR

This paper introduces a theoretically grounded, adaptive constraint tightening method for bicycle-model trajectory optimization that improves safety and reduces margin waste by accounting for vehicle dynamics mismatch.

Contribution

It derives a characteristic speed, proves mismatch scaling laws, and proposes MACT, a state-dependent margin adjustment method for safer, more efficient trajectory planning.

Findings

MACT achieves 100% safety with 84% less margin waste.

It extends to nonlinear leaning bicycles.

In MPC, MACT reduces applied margin by 34% while maintaining safety.

Abstract

Trajectory optimization for autonomous vehicles usually relies on the kinematic bicycle model because of its computational simplicity. However, when the planned trajectory is executed under the true vehicle dynamics, which include lateral slip, tire stiffness and yaw-lateral coupling, safety constraints can be violated owing to the model mismatch. In this paper, we make three theoretical contributions. First, we derive a characteristic speed $v_c=\sqrt{C_\alpha L/M}$ which separates two different mismatch regimes: below $v_c$ the dynamic bicycle initially oversteers inward (safe); above $v_c$ it understeers outward (safety-critical). Second, we prove that the peak outward deviation $\varepsilon^*$ follows a $T^2$ horizon scaling whose coefficient transitions between a transient bound $\frac{1}{2}(v^2-v_c^2)\kappa$ and a steady-state bound. Third, we obtain a simulation-free analytical coefficient $a_2^{\mathrm{anal}}=\frac{1}{2}(1-v_c^2/v_{\max}^2)T^2$ that is computable from vehicle parameters and the planning horizon alone. Putting these together, we propose Mismatch-Aware Adaptive Constraint Tightening (MACT), $\epsilon(v,\kappa)=a_2 v^2|\kappa|$, which replaces a fixed worst-case margin by a state-dependent one that is large at high speed/curvature but nearly zero on gentle paths. Eight numerical experiments confirm the scaling laws. MACT reaches 100% safety with 84% less wasted margin than a fixed-margin baseline on the 2-DOF vehicle, extends to a nonlinear leaning bicycle, and in a closed-loop direct-shooting MPC comparison it cuts the applied margin by 34% compared with tube MPC while keeping the same safety.