FP-411 2:40 Proceedings of the 29th Conference on Declaion and Control Honolulu, Hawaii December 1990 zyxw Kinematics and control of a space manipulator using the macro-micro manipulator concept zyxw Olav Egeland and Jan Richard Saglj Division of Engineering Cybernetics The Norwegian Institute of Technology 7034 Trondheim, Norway email: zyxwvut { oe,rich } Qitk.unit.no Abstract A control scheme for the coordination of motion in a spacecraft/- manipulator system is presented. The augmented task-space ap- proach is used for feedback linearization and decoupling of the sys- tem, and it is shown how end-effector motion can be decoupled from satellite motion, satellite rotation or total system momentum by se- lecting suitable coordinates to represent the motion of the satellite. The schemes are based on recursive calculation of kinematics and dynamics, and 12 degrees of freedom can be controlled without ex- cessive computational effort. Feedback linearization and decoupling of end-effector motion and total system momentum is discussed in detail. The satellite controller can then be developed independently from the manipulator controller, and reaction jets and momentum wheels are used only to reposition the satellite. The end-effector can be controlled accurately with a high bandwidth, while a slow, gross positioning can be used for the satellite. This results in a very fuel- efficient controller. The spacecraft-maiiipulator system is regarded zyxwvuts as a redundant manipulator of the macro-micro type with 12 degrees of freedom, and a redundancy resolution scheme is used to generate the position reference for the spacecraft. The proposed controller was simulated with a 12 degrees-of-freedom model which was generated with a recursive formulation of Jacobians and the dynamics, and the results are presented in the paper. 1 Introduction The coordination of motion between spacecraft and manipula- tor is important for repair and servicing satellites with one or more manipulators. The manipulator inertia may be signifi- cant compared to the satellite inertia, which gives kinematic and dynamic coupling. It is possible to decouple satellite and manipulator motion using momentum compensation wheels or reaction jets, but this may require excessive use of control en- ergy. Moreover, it may be necessary to use recursive formulations of satellite/manipulator kinematics and dynamics for real-time control of systems with 12 or more degrees of freedom. Several researchers have addressed this problem. One approach is to assume constant orientation of the space- craft, and eliminate three degrees of freedom using the holonomic conservation of linear momentum. This was done by Longman, Lindberg and Zedd [ll], who derived modified kinematics and dynamics in closed form for a spacecraft with a spherical-polar- coordinate manipulator. The model was derived under the as- sumption that the orientation of the spacecraft was kept constant with reaction wheels. Feedforward from the contact torques at the manipulator base could then be used in the satellite atti- tude control system. Vafa and Dubowsky [20, 211 introduced the concept of a virtual manipulator to simplify the kinemat- ics and dynamics of spacecraft/manipulator systems. The base of the virtual manipulator was termed virtual ground, and this point was found by eliminating the three degrees of freedom as- sociated with the holonomic conservation of linear momentum. The technique can be used for solving the inverse kinematics when the satellite attitude is constant. Vafa and Dubowsky (201 and Nakamura and Mukherjee [18] proposed to control both end-effector motion and satellite atti- tude using only manipulator torques. Alexander and Cannon [l] developed control scheme where end-effector motion was decoupled from spacecraft motion us- ing only joint torques in the manipulator, while feedforward compensation from satellite forces and torques was used. The method was implemented experimentally for a planar system with five degrees of freedom. The main drawback with the formulation was that the inverted inertia matrix of the space- craft/manipulator system was used explicitly in the algorithm. This matrix will be of dimension twelve hy twelve for a twelve- degrees-of-freedom system, and it requires much more computa- tion than the recursive formulations based on the Newton-Euler formalism. Also, satellite motion was not decoupled from the manipulator. In this paper we present a generalization of the metods pro- posed in [l] and [ll] using recursive formulations of the kinemat- ics and dynamics. Controllers for different spacecraft/manipulator systems are then easily derived without having to develop ana- lytic models for twelve-degrees-of-freedom systems. The recur- sive schemes are also computationally efficient, especially if they are custom-designed to take advantage of one’s and zeros in the matrices involved in the computations. In several applications it is interesting to control end-effector position accurately while using the satellite for slow gross po- sitioning. The satellite/manipulator system can be thought of as a macro-micro manipulator system zyxwv [5, S, 191 where the ma- nipulator gives a fast and accurate end-effector motion, and the spacecraft is a slower positioning part which provides a large workspace. We propose to do this by decoupling end-effector motion and total system momentum using the augmented task- space approach [5]. The energy consumption can then be consid- erably lower than if decoupling is used as in [ll], and the solution becomes more flexible than in [l, lS, 201 where only manipulator torques are used. For the nonlinear decoupling used in the feedback controller the satellite motion was described in terms of linear and angular momentum of the total system, while in the kinematic redun- CH2917-3/90/0000-3096$1 .OO @ 1990 IEEE 3096