Resumen
Steering large-scale particle or robot systems is challenging because of their high dimensionality. We use a centralized stochastic approach that allows for optimal control at the cost of a central element instead of a decentralized approach. Previous works are often restricted to the assumption of fully actuated robots. Here we propose an approach for underactuated robots that allows for energy-efficient control of the robot system. We consider a simple task of gathering the robots (minimizing positional variance) and steering them towards a goal point within a bounded area without obstacles. We make two main contributions. First, we present a generalized coordinate transformation for underactuated robots, whose physical properties should be considered. We choose Euler-Lagrange systems that describe a large class of robot systems. Second, we propose an optimal control mechanism with the prime objective of energy efficiency. We show the feasibility of our approach in robot simulations.