Enhanced Adaptive QPSO-Enabled Game-Theoretic Model Predictive Control for AUV Pursuit–Evasion Under Velocity Constraints

Pursuit–evasion involves coupled, antagonistic decision-making and is prone to local-optimal behaviors when solved online under nonlinear dynamics and constraints. This study investigates a dual-AUV pursuit–evasion problem in ocean-current environments by integrating game theory with model predictive control (MPC). We formulated a game-theoretic MPC scheme that optimizes pursuit and evasion actions over a finite receding horizon, producing Nash-like responses. To solve the resulting nonconvex and multi-modal optimization problems reliably, we developed an Enhanced Adaptive Quantum Particle Swarm Optimization (EA-QPSO) method that incorporates chaos-based initialization and adaptive diversity-aware exploration with stagnation-escape perturbations. EA-QPSO is benchmarked against representative solvers, including fmincon, Differential Evolution (DE), and the Marine Predator Algorithm (MPA). Extensive 2D and 3D simulations demonstrate that EA-QPSO mitigates local-optimum trapping and yields more effective closed-loop behaviors, achieving longer escaping trajectories and more persistent pursuit until capture under the game formulation. In 3D scenarios, EA-QPSO better preserves high-speed motion while coordinating agile angular-rate adjustments, outperforming competing methods that exhibit premature deceleration or degraded maneuvering. These results validate the proposed framework for computing reliable competitive strategies in constrained underwater pursuit–evasion games.