From nonholonomy to holonomy: Time-optimal velocity control of differential drive robots

There is a large body of literature studying problems such as consensus, flocking, or formation control of multi-agent systems using simple dynamic models, such as first-order integrators. This raises the question of how to implement such results on nonholonomic mobile robot platforms, for example, differential-drive or unicycle-type robots. Since the nonholonomic constraints must be taken into account when commanding a desired velocity change for such robots, we investigate the problem of reaching a desired velocity in minimum time. Using the Pontryagin Maximum Principle, we investigate the time-optimal control for systems with bounded wheel torques as the control input.