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

2025-05-08

AI Summary

This paper addresses real-time motion planning for vehicles in confined spaces, focusing on collision avoidance with polygonal obstacles. To overcome the computational bottleneck of traditional mixed-integer programming (MIP), it proposes a convex, integer-free modeling framework for polygonal collision constraints. The method integrates two key innovations into a model predictive control (MPC) architecture: (1) SVM-based reconstruction of polygonal boundaries to enhance collision detection accuracy; and (2) a minimum signed directed edge (MSDE) distance function—convex, differentiable, and computationally lightweight—to formulate obstacle-avoidance constraints. Experimental results demonstrate that the SVM-enhanced boundary representation significantly improves parking maneuver accuracy in narrow environments, while the MSDE formulation enables millisecond-scale online optimization on an RC car platform, with only marginal degradation in obstacle avoidance performance. The approach thus achieves an effective trade-off between geometric fidelity and real-time computational efficiency.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Vehicle motion planning with polygonal obstacle avoidance in tight spaces
• Reducing computational cost of disjunctive OR constraints in MPC
• Real-time collision avoidance using SVM and MSDE formulations

Innovation

• Uses convex-polygon approximations for collision avoidance
• Reformulates OR constraints as AND constraints via SVM
• Implements real-time MSDE for efficient distance metrics