Affine Multirobot Formation Control Based on a Modular Team Structure

We present a leaderless distributed controller for driving a multirobot team in a planar workspace toward an affine formation, i.e., an affine transformation of a nominal configuration. Our central idea is to organize the team in interlaced modules. Specifically, we define a module as a group of four robots, and we consider two given modules interlaced if they have three robots in common. For each module we define a cost, based on least-squares affine alignment between the positions of the four robots in the current and nominal configurations. Our strategy for formation achievement is to make the robots descend along the gradient of the sum of module costs. Based on this strategy, we propose a distributed control law considering the single-integrator dynamic model. Our main contribution is that the proposed modular approach allows design and reconfiguration to be done locally, i.e., involving only the robots that belong to the modules being designed or reconfigured. We present a formal stability study and an implementation algorithm. To motivate the practical interest of the proposed approach, we illustrate its usage in a multitarget enclosing and tracking scenario. The approach is experimentally validated using simulations and tests with physical unicycle robots.