Second-Order Cone Programming (SOCP) Techniques for Coordinating Large-Scale Robot Teams in Polygonal Environments

In this paper, we present an online optimization approach for coordinating large-scale robot teams in both convex and non-convex polygonal environments. In the former, we investigate the problem of moving a team of m robots from an initial shape to an objective shape while minimizing the total distance the team must travel within the specified workspace. Employing SOCP techniques, we establish a theoretical complexity of O(k 1.5 m 1.5) for this problem with O(km) performance in practice – where k denotes the number of linear inequalities used to model the workspace. Regarding the latter, we present a multi-phase hybrid optimization approach. In Phase I, an optimal path is generated over an appropriate tessellation of the workspace. In Phase II, model predictive control techniques are used to identify optimal formation trajectories over said path while guaranteeing against collisions with obstacles and workspace boundaries. Once again employing SOCP, we establish complementary complexity measures of O(l 3.5 m 1.5) and O(l 1.5 m 3.5) for this problem with O(l 3 m) and O(lm 3) performance in practice – where l denotes the length of the optimization horizon.

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