Pursuer-Evader Study Steve Rogers Pursuer-Evader Study..................................................................................................................................1 Introduction.............................................................................................................................................1 Linearization Process...............................................................................................................................2 Pursuer Control Law Development..........................................................................................................3 Evader Control Law Development...........................................................................................................4 Conclusion...............................................................................................................................................6 Appendix – Results with Random Target Motions...................................................................................6 Appendix – Results with Intelligently Controlled Target Motions..........................................................12
Introduction In this study a solution to the game of pursuer evader is presented based on the LQR state space method. In a pursuer evader game the pursuer attempts to capture (intercept or minimize the miss distance) the evader while the evader tries to avoid the pursuer. The 1 st phase of the study will deal with a ‘dumb’ evader which only has random or fixed acceleration inputs for its control logic. Ultimately, the pursuer guidance must be able to deal with an ‘intelligent’ evader that is attempting to maximize the miss distance. A straightforward approach is to utilize the regulator concept. The intention with a regulator is to force all states to zero with a feedback controller. Therefore, the pursuer’s objective is to drive the miss distance relevant states to zero. The evader’s objective is to drive the miss distance relevant states to infinity. A simple point mass model is given.
This equation may be used for each dimension
of a 2D model study. A guidance algorithm can be easily derived from these equations which can then be fed as a desired force input to an autopilot for more detailed control. A clearer equation statement
follows:
. A state space formulation of each dimension is:
. For a 2D representation they are placed in parallel so that