In this paper, a centralized method for collision avoidance among multiple agents is presented. It builds on the velocity obstacle (VO) concept and its extensions to arbitrary kino-dynamics and is applicable to heterogeneous groups of agents (with respect to size, kino-dynamics, and aggressiveness) moving in 2D and 3D spaces. In addition, both static and dynamic obstacles can be considered in the framework. The method maximizes a joint utility function and is formulated as a mixed-integer quadratic program, where online computation can be achieved as a trade-off with solution optimality. In experiments with groups of two to 50 agents, the benefits of the joint utility optimization are shown. By construction, it’s suboptimal variant is at least as good as comparable decentralized methods, while retaining online capability for small groups of agents. In its optimal variant, the proposed algorithm can provide a benchmark for distributed collision avoidance methods, in particular for those based on the VO concept that takes interaction into account.
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