Formation Shape Control using the Gromov-Wasserstein Metric
This addresses formation control for multi-agent systems, but it is incremental as it adapts existing relaxation techniques to handle the computational challenges of the Gromov-Wasserstein metric.
The paper tackles the problem of steering a population of agents to a desired formation shape by introducing an optimal control algorithm that uses the Gromov-Wasserstein distance as a terminal cost, resulting in a numerical example to demonstrate the approach.
This article introduces a formation shape control algorithm, in the optimal control framework, for steering an initial population of agents to a desired configuration via employing the Gromov-Wasserstein distance. The underlying dynamical system is assumed to be a constrained linear system and the objective function is a sum of quadratic control-dependent stage cost and a Gromov-Wasserstein terminal cost. The inclusion of the Gromov-Wasserstein cost transforms the resulting optimal control problem into a well-known NP-hard problem, making it both numerically demanding and difficult to solve with high accuracy. Towards that end, we employ a recent semi-definite relaxation-driven technique to tackle the Gromov-Wasserstein distance. A numerical example is provided to illustrate our results.