Control of Robot Manipulators in Terms of Quasi-Velocities

Abstract

In this paper we present new control algorithms for robots with dynamics described in terms of quasi-velocities (Kozlowski, Identification of articulated body inertias and decoupled control of robots in terms of quasi-coordinates. In: Proc. of the 1996 IEEE International Conference on Robotics and Automation, pp. 317---322. IEEE, Piscataway, 1996a; Zeitschrift fur Angewandte Mathematik und Mechanik 76(S3):479---480, 1996c; Robot control algorithms in terms of quasi-coordinates. In: Proc. of the 34 Conference on Decision and Control, pp. 3020---3025, Kobe, 11---13 December 1996, 1996d). The equations of motion are written using spatial quantities such as spatial velocities, accelerations, forces, and articulated body inertia matrices (Kozlowski, Standard and diagonalized Lagrangian dynamics: a comparison. In: Proc. of the 1995 IEEE Int. Conf. on Robotics and Automation, pp. 2823---2828. IEEE, Piscataway, 1995b; Rodriguez and Kreutz, Recursive Mass Matrix Factorization and Inversion, An Operator Approach to Open- and Closed-Chain Multibody Dynamics, pp. 88---11. JPL, Dartmouth, 1998). The forward dynamics algorithms incorporate new control laws in terms of normalized quasi-velocities. Two cases are considered: end point trajectory tracking and trajectory tracking algorithm, in general. It is shown that by properly choosing the Lyapunov function candidate a dynamic system with appropriate feedback can be made asymptotically stable and follows the desired trajectory in the task space. All of the control laws have a new architecture in the sense that they are derived, in the so-called quasi-velocity and quasi-force space, and at any instant of time generalized positions and forces can be recovered from order $O({\cal N})$ recursions, where ${\cal N}$ denotes the number of degrees of freedom of the manipulator. This paper also contains the proposition of a sliding mode control, originally introduced by Slotine and Li (Int J Rob Res 6(3):49---59, 1987), which has been extended to the sliding mode control in the quasi-velocity and quasi-force space. Experimental results illustrate behavior of the new control schemes and show the potential of the approach in the quasi-velocity and quasi-force space.