State-Constrained Adaptive Guidance for Three-Body Pursuit-Evasion Using Super Twisting Algorithm

In this paper, we address the problem of robust guidance for a three-body pursuit-evasion problem involving a target, a defender, and an attacker, where the goal is to safeguard the target (an aircraft) from the attacker, using the defender. Thus, the target and the defender may act as a team of vehicles whose common goal is to safeguard the target from the attacker. Additionally, it is desired to maintain necessary constraints on certain states. An adaptive guidance law is proposed for the target-defender team to ensure optimal performance within this set-up. The target-defender dynamics are considered for designing the guidance law with only approximate knowledge of the unknown parameters of the attacker. A robust guidance command is designed using a super-twisting algorithm with adaptive gains. The unknown disturbance bounds required for control implementation are obtained using a novel norm observer. We consider the complete nonlinear model of the system for control design, thereby enabling a wider domain of applicability of the proposed approach. The convergence is established using Lyapunov analysis, which also ensures satisfaction of the required state constraints. Relevant simulation results are presented to study the efficacy of the proposed approach.