通过解耦分离超平面，60%提速安全轨迹规划。
Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems
- 将碰撞避免问题拆解为独立分类任务，避开复杂优化变量
- 在密集障碍物中计算速度提升近60%，保持连续安全约束
- 适合需要实时安全路径规划的移动机器人系统
为自主移动机器人生成时间最优、无碰撞轨迹时，需在安全性保证与计算复杂度之间权衡。现有基于样条的方法常将分离超平面参数作为优化变量，形成单个最优控制问题（OCP），但计算成本高。本文提出新方法，将分离超平面的确定从OCP中解耦。利用线性系统或二次规划求解分离定理，移除超平面参数作为优化变量，使非凸约束转化为线性约束。实验表明，在障碍物密集环境中，该解耦方法相较全耦合方法将轨迹计算时间减少近60%，同时维持严格的连续安全保证。
原文摘要 · Abstract (English)
Generating time-optimal, collision-free trajectories for autonomous mobile robots involves a fundamental trade-off between guaranteeing safety and managing computational complexity. State-of-the-art approaches formulate spline-based motion planning as a single Optimal Control Problem (OCP) but often suffer from high computational cost because they include separating hyperplane parameters as decision variables to enforce continuous collision avoidance. This paper presents a novel method that alleviates this bottleneck by decoupling the determination of separating hyperplanes from the OCP. By treating the separation theorem as an independent classification problem solvable via a linear system or quadratic program, the proposed method eliminates hyperplane parameters from the optimisation variables, effectively transforming non-convex constraints into linear ones. Experimental validation demonstrates that this decoupled approach reduces trajectory computation times up to almost 60% compared to fully coupled methods in obstacle-rich environments, while maintaining rigorous continuous safety guarantees.
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