Collaborative Constrained Target-Reaching Control in a Multiplayer Reach-Avoid Game

For a high-value attacker, relocating it is more valuable than destroying it. This relocation issue involves luring an adversarial agent along a predefined path to reach a goal in a non-convex domain. Here, we define it as a collaborative constrained target-reaching (CTR) problem. We introduce a novel virtual defense channel to define a symmetric dynamic extend target set, enabling us to treat the CTR problem as an aggregation of individual two-player reach-Avoid (RA) games and obtain analytical strategies for defenders. First, we describe the partition of the game space and construct barriers using explicit policy methods and geometric analysis. This allows us to determine if a solution to the game exists based on players' initial conditions. Second, we develop nonlinear state feedback strategies using a suitable risk metric. These strategies are based on prescribed performance control, offering a viable framework for practical scenarios with control errors. Finally, simulations and experiments validate the effectiveness of our method.