Controlling Shapes of Ensembles of Robots of Finite Size with Nonholonomic Constraints

In this paper we focus on the construction of distributed formation control laws that permit the control of individual mobile ground robots in a formation to a desired distribution with minimal knowledge of the global state. As in previous work, we consider an abstraction of the team that is derived from a shape descriptor of the ensemble and the position and orientation of the ensemble. We consider the control of the abstract state with decentralized control laws which are independent of the number of agents. However, we incorporate an important departure from previous work by explicitly modeling the shape of the robot, the geometric, non-interpenetration constraints and nonholonomic, kinematic constraints. Further, we propose a motion planning technique to plan motions for ensembles of robots and a technique for the splitting and merging of groups and subgroups. We demonstrate the effectiveness of the algorithms on a team of differential drive robots in simulation and on real hardware.