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

2026-03-25

AI Summary

This work addresses the challenge of generating time-optimal, continuously safe, collision-free trajectories for non-differentially flat systems, where high computational complexity and safety guarantees are difficult to reconcile. The authors propose a decoupled approach that, for the first time, separates the computation of separating hyperplanes from trajectory optimization, reformulating it as an independent linear system or quadratic programming classification problem. This transformation converts non-convex obstacle avoidance constraints into linear ones. By integrating spline-based trajectory representation with an optimal control framework, the method achieves significant computational speedups while ensuring strict continuous-time safety. Experimental results in dense obstacle environments demonstrate up to a 60% reduction in trajectory computation time compared to fully coupled approaches.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• time-optimal motion planning
• continuous safety guarantees
• non-differentially flat systems
• collision avoidance
• computational complexity

Innovation

• decoupled optimization
• spline-based motion planning
• continuous collision avoidance
• separating hyperplanes
• time-optimal trajectory