Chapter 29: Cooperative Manipulators

This chapter is devoted to cooperative manipulation of a common object by means of two or more robotic arms. The chapter opens with a historical overview of the research on cooperative manipulation, ranging from early 1970s to very recent years. Kinematics and dynamics of robotic arms cooperatively manipulating a tightly grasped rigid object are presented in depth. As for the kinematics and statics, the chosen approach is based on the so-called symmetric formulation; fundamentals of dynamics and reduced-order models for closed kinematic chains are discussed as well. A few special topics, such as the definition of geometrically meaningful cooperative task space variables, the problem of load distribution, and the definition of manipulability ellipsoids, are included to give the reader a complete picture of modeling and evaluation methodologies for cooperative manipulators. Then, the chapter presents the main strategies for controlling both the motion of the cooperative system and the interaction forces between the manipulators and the grasped object; in detail, fundamentals of hybrid force/position control, proportional–derivative (PD)-type force/position schemes, feedback linearization techniques, and impedance control approaches are given. In the last section further reading on advanced topics related to control of cooperative robots is suggested; in detail, advanced nonlinear control strategies are briefly discussed (i. e., intelligent control approaches, synchronization control, decentralized control); also, fundamental results on modeling and control of cooperative systems possessing some degree of flexibility are briefly outlined.