Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910071031595008 |
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| author | Dirckx, Dries Swevers, Jan Decré, Wilm |
| author_facet | Dirckx, Dries Swevers, Jan Decré, Wilm |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24133 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems Dirckx, Dries Swevers, Jan Decré, Wilm Robotics 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. |
| title | Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems |
| topic | Robotics |
| url | https://arxiv.org/abs/2603.24133 |