发表机构
School of Automation Science and Electrical Engineering, Beihang University; Tianmushan Laboratory, Beihang University（北京航空航天大学自动化科学与电气工程学院; 北京航空航天大学天目山实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对机器人导航规划的计算成本问题，提出VIP框架，通过变分迭代学习优化规划命令，在单/多机器人场景中高效生成并改进运动规划，兼具有效性与可扩展性。
AI 中文摘要
过去十年，自主机器人系统越来越多地部署在勘测、搜救和最后一公里配送等应用场景中。这些应用要求机器人在大型、复杂且障碍物密集的环境中生成安全、高效的运动规划，且通常受限于有限的机载计算资源。然而，传统规划方法通常依赖有限维轨迹参数化或日益增长的预测时域，导致计算成本快速上升，尤其是在多机器人场景中。本文提出了一种新颖的基于变分的迭代学习规划（VIP）框架，用于单机器人和机器人群的高效运动规划。VIP 不优化大量离散轨迹变量，而是直接将规划命令更新为无限维函数空间中的连续函数。这种基于变分的更新可在模型在环（用于离线规划）或机器人在环（用于在线物理执行之间）的方式中实现。通过避免与时域扩展和高维轨迹离散化相关的计算负担，VIP 保持了每次迭代的计算复杂度为$\boldsymbol{\textit{O}}(n)$，其中$n$表示空间离散点的数量。大量仿真和真实世界实验表明，该框架可针对不同规划目标、机器人平台和集群配置高效生成并迭代改进运动规划，凸显其作为通用规划方法的有效性、计算效率和可扩展性。
英文摘要
Over the past decade, autonomous robotic systems have been increasingly deployed in applications such as surveying, search and rescue, and last-mile delivery. These applications require robots to generate safe and efficient motion plans in large, complex, and obstacle-dense environments, often under limited onboard computing resources. However, conventional planning methods commonly rely on finite-dimensional trajectory parameterization or increasingly long prediction horizons, leading to rapidly growing computational costs, particularly in multi-robot scenarios. This paper presents a novel variation-based iterative-learning planning (VIP) framework for efficient motion planning of both single robots and robotic swarms. Instead of optimizing a large number of discrete trajectory variables, VIP directly updates the planning command as a continuous function in an infinite-dimensional function space. The same variation-based update can be implemented in a model-in-the-loop manner for offline planning or in a robot-in-the-loop manner between online physical executions. By avoiding the computational burden associated with horizon expansion and high-dimensional trajectory discretization, VIP maintains a per-iteration computational complexity of $\mathcal{O}(n)$, where $n$ denotes the number of spatial discretization points. Extensive simulations and real-world experiments demonstrate that the proposed framework can efficiently generate and iteratively improve motion plans for different planning objectives, robotic platforms, and swarm configurations, highlighting its effectiveness, computational efficiency, and scalability as a general planning methodology.
