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

TL;DR

This paper introduces a faster spline-based motion planning method that guarantees continuous safety for non-differentially flat systems by decoupling collision avoidance constraints, significantly reducing computation time.

Contribution

It proposes a novel decoupling approach that transforms non-convex collision constraints into linear ones, improving computational efficiency in time-optimal motion planning.

Findings

Reduces trajectory computation time by up to 60%.

Maintains rigorous continuous safety guarantees.

Effective in obstacle-rich environments.

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.