用凸多边形建模车辆与障碍物，实现窄空间实时避障。
Real-Time Model Predictive Control of Vehicles with Convex-Polygon-Aware Collision Avoidance in Tight Spaces
- 将车辆和障碍物用凸多边形表示，提升狭窄空间碰撞检测精度。
- 提出两种新约束方法，使原本复杂的混合整数规划变为可实时求解的连贯约束。
- 硬件实测验证：一种方法精度高，另一种实现实时运行且性能损失小。
本文提出一种在狭窄空间中结合车辆与障碍物凸多边形近似的模型预测控制（MPC）运动规划方法，以实现精准避障。由于多边形建模带来离散的或约束（OR constraints），传统方法需依赖混合整数规划，计算成本高昂。为此，本文提出两种重构方法：(1) 基于支持向量机（SVM）的避障形式，将碰撞规避转化为SVM优化问题；(2) 最小有符号距离到边（MSDE）形式，利用最小有符号距离度量。通过大量仿真（包括窄空间泊车与异形障碍物路径）及遥控汽车平台的硬件实验验证，结果表明：基于SVM的方法在受限环境中导航精度更优；而MSDE方法可在保持适度避障性能的前提下实现真正实时运行。
原文摘要 · Abstract (English)
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.
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