Real-Time Model Predictive Control of Vehicles with Convex-Polygon-Aware Collision Avoidance in Tight Spaces

TL;DR

This paper introduces two novel convex-polygon-aware collision avoidance methods for vehicle MPC in tight spaces, reformulating complex disjunctive constraints into tractable forms, validated through simulations and hardware tests.

Contribution

It proposes two innovative convex-polygon-aware collision avoidance constraints that transform disjunctive OR constraints into tractable conjunctive constraints within MPC.

Findings

SVM-based method achieves higher navigation accuracy.

MSDE method operates in real time with slight performance loss.

Both methods effectively handle tight-space vehicle navigation.

Abstract

This paper proposes vehicle motion planning methods with obstacle avoidance in tight spaces by incorporating polygonal approximations of both the vehicle and obstacles into a model predictive control (MPC) framework. Representing these shapes is crucial for navigation in tight spaces to ensure accurate collision detection. However, incorporating polygonal approximations leads to disjunctive OR constraints in the MPC formulation, which require a mixed integer programming and cause significant computational cost. To overcome this, we propose two different collision-avoidance constraints that reformulate the disjunctive OR constraints as tractable conjunctive AND constraints: (1) a Support Vector Machine (SVM)-based formulation that recasts collision avoidance as a SVM optimization problem, and (2) a Minimum Signed Distance to Edges (MSDE) formulation that leverages minimum signed-distance metrics. We validate both methods through extensive simulations, including tight-space parking scenarios and varied-shape obstacle courses, as well as hardware experiments on an RC-car platform. Our results demonstrate that the SVM-based approach achieves superior navigation accuracy in constrained environments; the MSDE approach, by contrast, runs in real time with only a modest reduction in collision-avoidance performance.