Distributed Linear Control of Multirobot Formations Organized in Triads

This letter addresses the problem of controlling multiple robots to form a prescribed team shape in two-dimensional space. We consider a team organization in interlaced triads (i.e., groups of three robots). For each triad we define a measure of geometric deformation relative to its prescribed shape. Our main contribution is a novel distributed control law, defined as the gradient descent on the sum of these triangular deformation measures. We show that this geometrically motivated control law is linear, and bears analogies with existing formulations. Moreover, in comparison with these formulations our controller is simpler and more flexible to design, converges to the globally optimal shape by construction, and allows analysis of the team size dynamics. We illustrate the proposed approach in simulation.