用时变密度函数实现动态环境下的安全导航，提供理论保证。
Safe Navigation in Dynamic Environments using Density Functions
- 构建时变密度场，通过梯度生成反馈控制律。
- 证明系统几乎处处安全收敛，适用于单积分器模型。
- 可扩展至多智能体和机械臂等复杂系统，适合机器人导航研究者。
本文提出一种基于密度函数的框架，用于在障碍物集合与目标区域随时间变化的动态环境中实现安全导航。我们提出了时变密度函数的解析构造方法，进而合成以该密度场正梯度定义的反馈控制器。主要贡献是首次为使用密度函数进行动态环境导航提供了严格的收敛性证明，适用于单积分器动力学系统。据我们所知，这是此类导航方法中首个分析性安全保障。通过反步法与逆动力学等标准控制设计技术，我们将该框架推广至具有更复杂动力学的系统，包括多智能体系统与机器人机械臂。这些结果为将基于密度的导航方法拓展至各类时变环境中的机器人系统奠定了基础。
原文摘要 · Abstract (English)
This work presents a density-based framework for safe navigation in dynamic environments characterized by time-varying obstacle sets and time-varying target regions. We propose an analytical construction of time-varying density functions that enables the synthesis of a feedback controller defined as the positive gradient of the resulting density field. The primary contribution of this paper is a rigorous convergence proof demonstrating almost-everywhere safe navigation under the proposed framework, specifically for systems governed by single-integrator dynamics. To the best of our knowledge, these are the first analytical guarantees of their kind for navigation in dynamic environments using density functions. We illustrate the applicability of the framework to systems with more complex dynamics, including multi-agent systems and robotic manipulators, using standard control design techniques such as backstepping and inverse dynamics. These results provide a foundation for extending density-based navigation methods to a broad class of robotic systems operating in time-varying environments.
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