用泊松方程从感知数据生成机器人安全区域，实现实时避障。
Dynamic Safety in Complex Environments: Synthesizing Safety Filters with Poisson's Equation
- 基于泊松方程与边界条件，从局部占据图生成安全函数。
- 通过梯度引导场设计，使安全函数能刻画动态环境中的安全集。
- 已在四足与人形机器人上验证实时避障能力，适用于复杂动态场景。
在复杂动态环境中为机器人系统合成安全集是一个挑战性问题。解决该问题可构建保障安全控制动作的安全滤波器，尤其依赖于控制屏障函数（Control Barrier Functions, CBF）。本文提出一种算法，通过椭圆型偏微分方程——泊松方程——从感知数据中生成安全集。给定局部占据图，我们在狄利克雷边界条件下求解泊松方程，引入一种新颖的强迫项：设计一个平滑的引导向量场，编码安全所需的梯度信息。由此构成一个变分问题，其唯一极小值即为安全函数，用于刻画安全集。理论建立后，展示了安全函数在基于CBF的安全滤波中的应用。通过四足与人形机器人在动态障碍物环境中的硬件演示，验证了该方法的实时可用性。
原文摘要 · Abstract (English)
Synthesizing safe sets for robotic systems operating in complex and dynamically changing environments is a challenging problem. Solving this problem can enable the construction of safety filters that guarantee safe control actions -- most notably by employing Control Barrier Functions (CBFs). This paper presents an algorithm for generating safe sets from perception data by leveraging elliptic partial differential equations, specifically Poisson's equation. Given a local occupancy map, we solve Poisson's equation subject to Dirichlet boundary conditions, with a novel forcing function. Specifically, we design a smooth guidance vector field, which encodes gradient information required for safety. The result is a variational problem for which the unique minimizer -- a safety function -- characterizes the safe set. After establishing our theoretical result, we illustrate how safety functions can be used in CBF-based safety filtering. The real-time utility of our synthesis method is highlighted through hardware demonstrations on quadruped and humanoid robots navigating dynamically changing obstacle-filled environments.
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