提出安全轨迹生成新方法，确保多目标到达与避障后稳定至目标点。
Reach-Avoid-Stabilize Using Admissible Control Sets
- 基于可接受控制集思想设计递进式控制策略
- 保证在指定时序下完成多目标到达与避障，最终稳定于目标点
- 提供安全集合的保守估计，适合高安全性要求的机器人控制
哈密顿-雅可比可达性分析在机器人与控制任务中已取得成功，尤其适用于计算可达-避障集及满足状态约束的控制律。然而，原始的HJR公式无法保证在规定时间窗之后或目标达成后的安全性。因此，可达-避障-稳定（RAS）问题受到广泛关注：寻找初始状态集（即RAS集），使得轨迹能到达目标并稳定于某兴趣点（POI），同时避开障碍物。使用HJR求解RAS问题通常需定义新的值函数，其零下水平集即为RAS集。现有方法未考虑一系列目标需依次到达或多个障碍需规避的情况。本文提出一种基于可接受控制集的方法，确保系统按给定时序序列依次到达各目标、避开障碍，并最终稳定于POI。该方法给出RAS集的下近似，保证安全性。数值实验验证了理论的有效性。
原文摘要 · Abstract (English)
Hamilton-Jacobi Reachability (HJR) analysis has been successfully used in many robotics and control tasks, and is especially effective in computing reach-avoid sets and control laws that enable an agent to reach a goal while satisfying state constraints. However, the original HJR formulation provides no guarantees of safety after a) the prescribed time horizon, or b) goal satisfaction. The reach-avoid-stabilize (RAS) problem has therefore gained a lot of focus: find the set of initial states (the RAS set), such that the trajectory can reach the target, and stabilize to some point of interest (POI) while avoiding obstacles. Solving RAS problems using HJR usually requires defining a new value function, whose zero sub-level set is the RAS set. The existing methods do not consider the problem when there are a series of targets to reach and/or obstacles to avoid. We propose a method that uses the idea of admissible control sets; we guarantee that the system will reach each target while avoiding obstacles as prescribed by the given time series. Moreover, we guarantee that the trajectory ultimately stabilizes to the POI. The proposed method provides an under-approximation of the RAS set, guaranteeing safety. Numerical examples are provided to validate the theory.
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