Automatic aircraft conflict resolution using genetic algorithms
SAC '96 Proceedings of the 1996 ACM symposium on Applied Computing
Optimal control of a ship for collision avoidance maneuvers
Journal of Optimization Theory and Applications
Robot Motion Planning
Motion Planning in Dynamic Environments
Motion Planning in Dynamic Environments
Towards a Geometric Theory of Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Symmetry Reduction of a Class of Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Approximating geodesics on point set surfaces
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
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In this paper we address the problem of designing energy minimizing collision-free maneuvers for multiple agents moving on a plane. We show that the problem is equivalent to that of finding the shortest geodesic in a certain manifold with nonsmooth boundary. This allows us to prove that the optimal maneuvers are C1 by introducing the concept of u-convex manifolds. Moreover, due to the nature of the optimal maneuvers, the problem can be formulated as an optimal control problem for a certain hybrid system whose discrete states consist of different "contact graphs". We determine the analytic expression for the optimal maneuvers in the two agents case. For the three agents case, we derive the dynamics of the optimal maneuvers within each discrete state. This together with the fact that an optimal maneuver is a C1 concatenation of segments associated with different discrete states gives a characterization of the optimal solutions in the three agents case.