Spacecraft orbital pursuit–evasion games with [formula omitted] perturbations and direction-constrained thrust

Abstract

In this paper, we study spacecraft orbital pursuit–evasion games under J2 perturbations. We consider that situation where the thrust of each player is constrained and the control direction cannot deviate from the velocity more than a given angle. After characterizing the optimal control of players under direction constraints, we transfer the pursuit–evasion game into a two point boundary value problem, which is solved by the shooting method. Different with the classical research, the initial guess for the unknown initial adjoint variables and the game ending time are not generated by heuristic approaches, but from the solution of the orbital one-side interception problem with a non-maneuverable evader. We solve the one-side interception problem also by shooting, starting iteratively from multiple initial guesses. In each initial guess, the initial adjoint vector is chosen randomly small while the interception termination time is selected from contiguous feasible time subintervals. The simulations show that the shooting method for the one-side interception problem can converge even if the feasible interval of the termination time is partitioned into a small number of subintervals, and the whole method for solving the pursuit–evasion game can quickly find the saddle-point solution. The effect of the control direction constraint on the game ending time is also discussed.