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.

Nonlinear Multi-Object Differential Game Simulation Model in LabVIEW

“…Guo et al in [4] developed pursuit and evasion rules for multi-player model games in the 3D space, taking into account obstacle avoidance and speed limits.…”

“…where L is the length of ship 0; P s is the propeller thrust force; H 0 is the pitch of the propeller adjuster; n 0 is the rotational speed of the propeller; and q, h, r, s, and z are the coefficients of the dynamic equations of ship 0. The non-linear dynamics of the ship as a controlled object results from the non-linear equations of the ship's motion (4), which means that the state variables do not change in time proportionally to the control quantities. This is particularly visible when performing the anti-collision maneuver required by the COLREGs regulations, a larger change of own ship's course noticeable by another vessel.…”