挑战传统约束定义，拓展飞行器运动规划的可行轨迹范围。
Virtual Holonomic Constraints in Motion Planning: Revisiting Feasibility and Limitations
- 重新审视虚拟完整约束的定义，指出其过度限制
- 证明多数周期性轨迹无法满足现有约束条件
- 适合机器人运动规划与控制领域的研究者参考
本文针对单自由度欠驱动机械系统在运动规划中虚拟完整约束（VHC）的可行性问题展开研究。尽管现有文献已建立广泛接受的VHC定义，但本文认为该定义过于严格，排除了大量可接受的轨迹。通过分析平面垂直起降（PVTOL）飞行器的周期运动，发现其满足所有标准运动规划要求，包括轨道稳定性，却无法对应任何符合传统VHC定义的约束。进一步的严格证明表明，该定义对一大类机械系统轨迹必然失效。这些结果呼吁重新审视现行的VHC定义，有望显著拓展其在运动规划中的应用范围。
原文摘要 · Abstract (English)
This paper addresses the feasibility of virtual holonomic constraints (VHCs) in the context of motion planning for underactuated mechanical systems with a single degree of underactuation. While existing literature has established a widely accepted definition of VHC, we argue that this definition is overly restrictive and excludes a broad class of admissible trajectories from consideration. To illustrate this point, we analyze a periodic motion of the Planar Vertical Take-Off and Landing (PVTOL) aircraft that satisfies all standard motion planning requirements, including orbital stabilizability. However, for this solution -- as well as for a broad class of similar ones -- there exists no VHC that satisfies the conventional definition. We further provide a formal proof demonstrating that the conditions imposed by this definition necessarily fail for a broad class of trajectories of mechanical systems. These findings call for a reconsideration of the current definition of VHCs, with the potential to significantly broaden their applicability in motion planning.
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