Hyperplane Collision Avoidance Formulations for Safe Path Following Model Predictive Control of Autonomous Vehicles
Year: 2026
Type: article
Abstract: Collision avoidance is critical for safe autonomous vehicles, particularly in optimization-based motion planning and control methods like model predictive control (MPC). Diverse exact formulations exist to avoid collisions between convex polygons, explicitly and accurately accounting for the shapes of both the ego vehicle and the obstacles. A subset of these methods can be classified as reformulations of the non-differentiable signed distance condition into separating hyperplane conditions that result in differentiable nonlinear optimization problems (NLPs) and can be solved using standard NLP solvers. Furthermore, they allow for the specification of a Euclidean safety distance and enable controlled relaxations in cases where the safety distance cannot be enforced. However, existing formulations differ in the number of collision avoidance optimization variables and constraints they introduce into the NLP, and a general overview, analysis, and comparison of the formulations is lacking. Therefore, this work provides an overview and comparison of hyperplane-based collision avoidance formulations in an MPC setting. We discuss three established formulation classes from the literature and introduce two novel formulations that offer intuitive geometric interpretability while reducing the number of optimization variables. All formulations are compared analytically and benchmarked in MPC-based path-following simulations for an autonomous vehicle navigating around obstacles. The results show that the proposed Hesse Normal Formulation achieves favorable computational performance in the investigated benchmark scenarios. Furthermore, we present an initial experimental validation of the proposed Hesse Normal Formulation on a full-scale autonomous ferry.
Institution: RWTH Aachen University
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,075
OpenAlex ID: W7223901835