Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems

• URL: http://arxiv.org/abs/2603.24133v1
• Date: Wed, 25 Mar 2026 09:53:04 GMT
• Title: Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems
• Abstract summary: State-of-the-art approaches formulate spline-based motion planning as a single Control Problem (OCP)<n>By treating separation as an independent classification problem solvable via a linear system or quadratic program, the proposed method eliminates hyperplane parameters from the OCP variables.<n> Experimental validation demonstrates that this decoupled approach reduces trajectory times up to almost 60% compared to fully-rich environments.
• Score: 6.862015448582809
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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