Abstract
This paper addresses a multi-agent Homicidal Chauffeur reach-avoid game, where M simple-motion evaders aim to reach the goal region, while N Dubins-car pursuers aim to prevent that by capturing evaders, and it is assumed that \(N \ge M\) and only incomplete information can be obtained by pursuers. We begin with one-pursuer-one-evader situation, and the optimal path types of the agents are inferred by the Hamiltonian of the differential game based on Homicidal Chauffeur dynamical model. Further, the optimal strategies of the agents are deduced from the engagement line we construct. Afterwards, the situation is expanded to two-pursuer-one-evader, where the intersection of engagement lines is introduced to describe the cooperation of two pursuers. Then, we analyze the N-pursuer-M-evader game by the combination of one-pursuer-one-evader and two-pursuer-one-evader games, and a potential game-based matching approach is proposed to achieve the combination with incomplete information. Simulation and reality experiments are provided to illustrate the theoretical results, where Joint Strategy Fictitious Play (JSFP) with inertia algorithm is executed to obtain the pure strategy Nash equilibrium. It is verified that the optimal pursuer-evader assignment is switchable and our scheme is feasible.
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References
Arslan, G., Marden, J., Shamma, J.: Autonomous vehicle-target assignment: a game-theoretical formulation. J. Dyn. Syst. Measur. Control-Trans. ASME 129 (2007). https://doi.org/10.1115/1.2766722
Boissonnat, J.D., Robotique, P., Prisme, P.: Accessibility region for a car that only moves forwards along optimal paths (1994)
Chen, M., Zhou, Z., Tomlin, C.J.: Multiplayer reach-avoid games via low dimensional solutions and maximum matching. In: 2014 American Control Conference, pp. 1444–1449 (2014). https://doi.org/10.1109/ACC.2014.6859219
Chen, M., Zhou, Z., Tomlin, C.J.: Multiplayer reach-avoid games via pairwise outcomes. IEEE Trans. Autom. Control 62(3), 1451–1457 (2017). https://doi.org/10.1109/TAC.2016.2577619
Chun, W.H., Papanikolopoulos, N.: Robot surveillance and security. In: Siciliano, B., Khatib, O. (eds.) Springer Handbook of Robotics, pp. 1605–1626. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32552-1_61
Cockayne, E.J., Hall, G.W.C.: Plane motion of a particle subject to curvature constraints. SIAM J. Control 13(1), 197–220 (1975). https://doi.org/10.1137/0313012
D’Alfonso, L., Fedele, G., Bono, A.: Distributed region following and perimeter surveillance tasks in star-shaped sets. Syst. Control Lett. 172, 105437 (2023). https://doi.org/10.1016/j.sysconle.2022.105437
Garcia, E., Casbeer, D.W., Von Moll, A., Pachter, M.: Cooperative two-pursuer one-evader blocking differential game. In: 2019 American Control Conference (ACC), pp. 2702–2709 (2019). https://doi.org/10.23919/ACC.2019.8814294
Garcia, E., Casbeer, D.W., Von Moll, A., Pachter, M.: Multiple pursuer multiple evader differential games. IEEE Trans. Autom. Control 66(5), 2345–2350 (2021). https://doi.org/10.1109/TAC.2020.3003840
Huang, H.: Reachability-based control for human and autonomous agents in adversarial games. Ph.D. thesis, Stanford University (2012)
Huang, H., Ding, J., Zhang, W., Tomlin, C.J.: A differential game approach to planning in adversarial scenarios: a case study on capture-the-flag. In: 2011 IEEE International Conference on Robotics and Automation, pp. 1451–1456 (2011). https://doi.org/10.1109/ICRA.2011.5980264
Huang, H., Ding, J., Zhang, W., Tomlin, C.J.: Automation-assisted capture-the-flag: a differential game approach. IEEE Trans. Control Syst. Technol. 23(3), 1014–1028 (2015). https://doi.org/10.1109/TCST.2014.2360502
Isaacs, R.: Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. Wiley, New York (1965)
Karpinski, M., Rytter, W.: Fast Parallel Algorithms for Graph Matching Problems. A Clarendon Press Publication (1998)
Marden, J.R., Arslan, G., Shamma, J.S.: Joint strategy fictitious play with inertia for potential games. IEEE Trans. Autom. Control 54(2), 208–220 (2009). https://doi.org/10.1109/TAC.2008.2010885
Oyler, D.W., Girard, A.R.: Dominance regions in the homicidal chauffeur problem. In: 2016 American Control Conference (ACC), pp. 2494–2499 (2016). https://doi.org/10.1109/ACC.2016.7525291
Pu, H., He, L., Cheng, P., Sun, M., Chen, J.: Security of industrial robots: vulnerabilities, attacks, and mitigations. IEEE Network 37(1), 111–117 (2023). https://doi.org/10.1109/MNET.116.2200034
Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency, vol. B (2003)
Yan, R., Shi, Z., Zhong, Y.: Reach-avoid games with two defenders and one attacker: an analytical approach. IEEE Trans. Cybern. 49(3), 1035–1046 (2019). https://doi.org/10.1109/TCYB.2018.2794769
Zhou, Z., Takei, R., Huang, H., Tomlin, C.J.: A general, open-loop formulation for reach-avoid games. In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 6501–6506 (2012). https://doi.org/10.1109/CDC.2012.6426643
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This work was supported by National Science and Technology Major Project (2022ZD0116401).
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Ren, L., Qian, L., Niu, Z., Zhang, X., Yao, W., Zhang, X. (2025). Optimal Strategies for Multiple Agents in Homicidal Chauffeur Reach-Avoid Games via Potential Game-Based Matching. In: Lan, X., Mei, X., Jiang, C., Zhao, F., Tian, Z. (eds) Intelligent Robotics and Applications. ICIRA 2024. Lecture Notes in Computer Science(), vol 15209. Springer, Singapore. https://doi.org/10.1007/978-981-96-0789-1_2
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