Leader-follower and leaderless pose consensus of robot networks with variable time-delays and without velocity measurements

This paper proposes a novel distributed controller that solves the leader-follower and the leaderless consensus problems in the task space for networks composed of robots that can be kinematically and dynamically different (heterogeneous). In the leader-follower scenario, the controller ensures that all the robots in the network asymptotically reach a given leader pose (position and orientation), provided that at least one follower robot has access to the leader pose. In the leaderless problem, the robots asymptotically reach an agreement pose. The proposed controller is robust to variable time-delays in the communication channel and does not rely on velocity measurements. The controller is dynamic, it cancels-out the gravity effects and it incorporates a proportional to the error term between the robot and the controller virtual position. The controller dynamics consists of a simple proportional scheme plus damping injection through a second-order (virtual) system. The proposed approach employs the singularity free unit-quaternions to represent the orientation of the end-effectors, and the network is represented by an undirected and connected interconnection graph. The application to the control of bilateral teleoperators is described as a special case of the leaderless consensus solution. The paper presents numerical simulations with a network composed of four 6-Degrees-of-Freedom (DoF) and one 7-DoF robot manipulators. Moreover, we also report some experiments with a 6-DoF industrial robot and two 3-DoF haptic devices.