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.

翻译：自主移动机器人的时间最优无碰撞轨迹生成需要在保证安全性与控制计算复杂度之间进行基本权衡。现有最先进方法将基于样条的运动规划建模为单一最优控制问题（OCP），但由于需将分离超平面参数作为决策变量以确保持续无碰撞，此类方法常面临较高计算成本。本文提出一种新颖方法，通过将分离超平面确定过程与OCP解耦以缓解该瓶颈。通过将分离定理视为可通过线性系统或二次规划独立求解的分类问题，所提方法从优化变量中移除超平面参数，有效将非凸约束转化为线性约束。实验验证表明，在障碍密集环境中，与完全耦合方法相比，该解耦方法可将轨迹计算时间降低近60%，同时保持严格的持续安全保证。