A geometric approach to single and multiple robot control

Abstract

This paper describes the control of single and multiple robot teams in the framework of Hilbert spaces. For single robots the control problem is defined in terms of the convergence between the set of feasible velocities, defined by the robot kinematics, and the set of goal velocities, defined by the mission specifications and environment data acquired along the mission. The convergence between these velocity sets is obtained by chosing a set of controls leading to a decrease in the distance between them. This distance is measured through the use of a monotonic and non-expansive projection map.Team control is approached through the definition of neighboring relationships among the teammates, to be preserved along the mission. Each robot monitors these relationships for relevant changes and adapts its motion to the rest of the team according to a negotiation procedure supervised by a finite state automaton. Simulation results on single and multiple cart robot systems are presented.