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

TL;DR

This work advances real-time vehicle motion planning in tight spaces by reformulating convex-polygon collision constraints for MPC into conjunctions of inequalities. It introduces two methods: an SVM-based separating-hyperplane formulation with margin regularization and an MSDE approach using a minimum signed-distance operator, both converting disjunctions into conjunctive constraints. Through simulations and hardware experiments, the SVM method achieves higher navigation accuracy at the cost of computation time, suitable for offline planning, while MSDE delivers real-time performance with modest reductions in collision-avoidance quality. The results demonstrate practical viability for tight-space parking and obstacle courses, with MSDE enabling real-time control on an RC-car platform and SVM offering offline planning advantages. Future work targets dynamic obstacles and multi-vehicle coordination.

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.

Figures (10)

• Figure 1: A real-world experiment result using MSDE.
• Figure 2: Kinematic Bicycle Model
• Figure 3: Support Vector Machine
• Figure 4: Collision avoidance based on minimum signed distance. The collision between the ego vehicle and the obstacle can be detected by checking whether the ego vehicle's vertex $\mathrm{P}_2$, which has the minimum signed distance $d_2$, is inside (top) or outside (bottom) the obstacle.
• Figure 5: The application of the circular obstacle avoidance. We transform the polygon-to-circle avoidance problem (top) into the polygon-to-polygon avoidance problem (bottom).