arXiv:2604.00320cs.ROcs.SY2026-04

在未知非线性系统中实现安全高效运动规划,兼顾实时性和可靠性。

Hierarchical Motion Planning and Control under Unknown Nonlinear Dynamics via Predicted Reachability

论文配图:Hierarchical Motion Planning and Control under Unknown Nonlinear Dynamics via Predicted Reachability
图 1 · 摘自论文原文
  • 分区域构建分段仿射模型,动态识别局部系统特性。
  • 通过可证明的到达时间与信息熵权重,实现在线路径优化与探索平衡。
  • 适用于欠驱动系统,支持真实场景下的安全导航与实时控制。

在未知非线性动力学下实现自主运动规划,需在导航过程中同时学习系统特性。本文提出一种分层规划-控制框架,可在先验知识有限的情况下实现在线运动合成。状态空间被划分为多面体区域,利用分段仿射(PWA)模型近似未知非线性系统,当智能体进入某区域后即识别其局部仿射模型。为降低计算复杂度,引入非均匀自适应状态空间划分策略,仅在任务相关区域进行细化。生成的PWA系统被抽象为有向加权图,边的存在性通过可达控制理论和预测可达性条件逐步验证。已验证边赋予可证明的到达时间边界作为权重,不确定边则采用信息论权重以引导探索。图结构随新数据在线更新,高层规划采用图搜索,低层则合成仿射反馈控制器执行动作。针对欠驱动系统中经典可达控制条件难以满足的问题,引入松弛化可达性条件以扩展适用范围。仿真结果表明该方法能有效实现探索与利用的平衡,并提供形式化的可达性保证。

原文摘要 · Abstract (English)

Autonomous motion planning under unknown nonlinear dynamics requires learning system properties while navigating toward a target. In this work, we develop a hierarchical planning-control framework that enables online motion synthesis with limited prior system knowledge. The state space is partitioned into polytopes and approximates the unknown nonlinear system using a piecewise-affine (PWA) model. The local affine models are identified once the agent enters the corresponding polytopes. To reduce computational complexity, we introduce a non-uniform adaptive state space partition strategy that refines the partition only in task-relevant regions. The resulting PWA system is abstracted into a directed weighted graph, whose edge existence is incrementally verified using reach control theory and predictive reachability conditions. Certified edges are weighted using provable time-to-reach bounds, while uncertain edges are assigned information-theoretic weights to guide exploration. The graph is updated online as new data becomes available, and high-level planning is performed by graph search, while low-level affine feedback controllers are synthesized to execute the plan. Furthermore, the conditions of classical reach control theory are often difficult to satisfy in underactuated settings. We therefore introduce relaxed reachability conditions to extend the framework to such systems. Simulations demonstrate effective exploration-exploitation trade-offs with formal reachability guarantees.

运动规划非线性系统在线控制可达性

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