Range-only based circumnavigation of a group of moving targets by a non-holonomic mobile robot

We consider a single planar non-holonomic Dubins-car like robot traveling with a constant and given longitudinal speed and controlled by the angular velocity, which is upper limited in absolute value. There also is a group of moving targets in the plane. The robot measures only the relative distances to the targets and cannot distinguish among them. A sliding mode control law is proposed that drives the root mean square distance to the targets to a pre-specified value. This law is justified by a non-local convergence result, along with description of the domain of convergence. Specifically, we first disclose requirements to the averaged characteristics of the group’s motion, which should be necessarily met in order for the constant-speed robot with a limited turning capacity be able to maintain the desired root mean square distance to the group. Then we show that under slight and partly unavoidable enhancements of these necessary conditions, the proposed controller does drive this distance to the desired value and ensures its stable maintenance afterwards provided that the controller is properly tuned. Recommendations on its tuning are also provided. The convergence and performance of the control law are confirmed by computer simulations.