A Path-Following Controller for Guiding a Single Robot or a Multi-robot System

A solution to the problem of path-following by a team of terrestrial mobile robots is proposed in this paper. The proposal, in this case, is a formation controller dealing with three robots navigating in a coordinate way (as a formation). Based on the controller proposed to guide the formation to follow a prescribed path, an extension to the case of path-following with a single terrestrial mobile robot is also proposed. When regarding a formation of mobile robots, the proposed solution consists in applying a path-following controller to the center of mass of the formation, dealt with as a single virtual robot, and trajectory-tracking controllers to the individual robots in the formation. The advantage of such approach is that it allows planning the motion of the desired formation without specifying how each robot should move. The movement is specified for the formation as a whole, using a representation called cluster-space, and the movement of the individual robots is derived from the specification of the formation movement directly, using transformations from the cluster-space to the space of the robots and vice versa. In the sequel, the path-following controller designed for the virtual robot is analyzed in detail, now dealing with the possibility of being also used as a path-following controller applied to a single real robot. Theoretical stability analysis is presented, as well as some experimental results, whose analysis allows claiming that the proposed controller is suitable to guide either a single robot or a multi-robot formation when following a path.