Null-Space-Based Multi-Player Pursuit-Evasion Games Using Minimum and Maximum Approximation Functions

Abstract

In this article, pursuit and evasion policies are developed for multi-player pursuit–evasion games, while obstacle avoidance and velocity constraints are considered simultaneously. As minimum and maximum approximation functions are both differentiable, pursuit and evasion objectives can be transformed into solving the corresponding differential expressions. For obstacle avoidance, a modified null-space-based approach is designed, which can ensure that all pursuers and evaders of pursuit–evasions are safe to minimize pursuit objective and maximize evasion objective, respectively. Rigorous theoretical analyses are provided to design constrained pursuit and evasion policies with obstacle avoidance. Finally, the performance of proposed policies is demonstrated by simulation results in 3-dimensional space.