Robust Time-Optimal Guidance in a Partially Uncertain Time-Varying Flow-Field
- 125 Downloads
In this paper, we address the problem of guiding an aerial or aquatic vehicle to a fixed target point in a partially uncertain flow-field. We assume that the motion of the vehicle is described by a point-mass linear kinematic model. In addition, the velocity of the flow-field, which is taken to be time varying, can be decomposed into two components: one which is known a priori and another one which is uncertain and only a bound on its magnitude is known. We show that the guidance problem can be reformulated as an equivalent pursuit evasion game with time-varying affine dynamics. To solve the latter game, we propose an extension of a specialized solution approach, which transforms the pursuit–evasion game (whose terminal time is free) via a special state transformation into a family of games with fixed terminal time. In addition, we provide a simple method to visualize the level sets of the value function of the game, along with the corresponding reachable sets. Furthermore, we compare our conservative game-theoretic solution with a pure optimal control solution, for the special case in which the flow-field is perfectly known a priori.
KeywordsPursuit–evasion game Time-varying winds Minimum-time guidance Input constraints
Mathematics Subject Classification91A23 49N90 49N75
This work was supported in part by the NSF under Grant 1562339. The first author also acknowledges support from the Zonta International Foundation.
- 4.Pontryagin, L.S.: Mathematical Theory of Optimal Processes. CRC Press, Boca Raton (1987)Google Scholar
- 9.Bernhard, P.: Linear pursuit–evasion games and the isotropic rocket. Tech. rep, DTIC Document (1970)Google Scholar
- 12.Breitner, M.H., Pesch, H.J.: Reentry trajectory optimization under atmospheric uncertainty as a differential game. In: T. Basar et al. (eds.) Advances in Dynamic Games and Applications, pp. 70–86. Springer, Berlin (1994)Google Scholar
- 14.Trottemant, E., Scherer, C., Weiss, M., Vermeulen, A.: Robust minimax strategies for missile guidance design. In: AIAA Guidance, Navigation and Control Conference and Exhibit. AIAA, Honolulu, HI (2008)Google Scholar
- 26.Selvakumar, J., Bakolas, E.: Optimal guidance of the isotropic rocket in a partially uncertain flow field. In: Control Conference (ECC), 2015 European, pp. 3328–3333 (2015)Google Scholar