Solving Reach-Avoid-Stay Problems Using Deep Deterministic Policy Gradients

TL;DR

This paper introduces a deep reinforcement learning approach using DDPG to solve reach-avoid-stay problems, enabling systems to reach targets, avoid obstacles, and stay safe in complex, high-dimensional environments.

Contribution

It extends RL-based reachability analysis to RAS problems by proposing a two-step DDPG method that finds the maximal robust RAS set, handling complex environments and high-dimensional systems.

Findings

Achieves higher success rates than previous methods.

Enables RAS in complex, high-dimensional environments.

Validated through simulation and high-dimensional experiments.

Abstract

Reach-Avoid-Stay (RAS) optimal control enables systems such as robots and air taxis to reach their targets, avoid obstacles, and stay near the target. However, current methods for RAS often struggle with handling complex, dynamic environments and scaling to high-dimensional systems. While reinforcement learning (RL)-based reachability analysis addresses these challenges, it has yet to tackle the RAS problem. In this paper, we propose a two-step deep deterministic policy gradient (DDPG) method to extend RL-based reachability method to solve RAS problems. First, we train a function that characterizes the maximal robust control invariant set within the target set, where the system can safely stay, along with its corresponding policy. Second, we train a function that defines the set of states capable of safely reaching the robust control invariant set, along with its corresponding policy. We prove that this method results in the maximal robust RAS set in the absence of training errors and demonstrate that it enables RAS in complex environments, scales to high-dimensional systems, and achieves higher success rates for the RAS task compared to previous methods, validated through one simulation and two high-dimensional experiments.