Distributed Optimal Control Framework based on Coordinate Descent Optimization for Multi-Agent Robots

In this paper, we present a distributed optimal control framework for a multi-agent robotics system based on coordinate descent optimization. Our framework exploits the underlying graph topology to compute the optimal control trajectory in a distributed manner. It only requires a modest amount of information exchange among the neighboring robot, and the computation depends on the underlying graph structure connecting the agents. Hence, if the underlying graph topology is sparse, e.g. a line graph, then it scales well with the problem's dimension, and any fast convergent algorithm can be used to ensure real-time computation. To show the efficacy of the framework, we apply it to a problem where a team of robots is tasked with establishing a communication link between source and destination while minimizing the overall system's mobility and communication energy. We analyzed its performance in simulation and on actual robots using an experimental robotic testbed, robotarium [1], and compare it to the centralized solution of the same problem. The results show that the distributed framework converges and outperforms its centralized version as the problem's dimension increases. While the aforementioned energy-balancing problem serves to motivate the paper, the algorithm is defined and presented in a more general setting, and its potential extensions to other types of systems are pointed out.