Digital Control of Free Floating Space Robot Manipulators Using Transpose of Generalized Jacobian Matrix

Space robots having manipulators are expected to work in future space missions (Xu & Kanade, 1993). Since it is difficult to supply fuel to the robots equipped with rocket motors during manipulation, control methods for free-floating space robots consisting of a base and a manipulator have been proposed (Dubowsky & Papadopulos, 1993; Masutani et al., 1989a;b; Sagara et al., 1998a;b; Shin et al., 1995; Umetani & Yoshida, 1989; Yamamoto et al., 1995). Most of them use the inverse of the Generalized Jacobian Matrix (GJM) which is a coefficient matrix between the velocity of the end-effector of the manipulator and the manipulator’s joint velocity (Umetani & Yoshida, 1989). Therefore, in a case that the robot manipulator gets into a singular configuration, the inverse of the GJM does not exist and the manipulator is out of control. For this problem, a continuous-time control method using the transpose of the GJM has been proposed for manipulators equipped with joint torque controllers (Masutani et al., 1989a;b). In practical systems digital computers are utilized for controllers. So, we have proposed a discrete-time control method using the transpose of the GJM (Taira et al, 2001). The control method using the transpose of the GJM uses position and orientation errors between the desired and actual values of the end-effector. Namely, the control method belongs to a class of constant value control such as PID control. Therefore, the value of the errors depends on the desired linear and angular velocities of the end-effector based on the desired trajectory. To obtain higher control performance we have proposed a digital trajectory tracking control method that has variable feedback gains depending on the desired linear and angular velocities of the end-effector (Sagara & Taira, 2007). Moreover, we have also proposed the control method for manipulators with velocity type joint controllers (Sagara & Taira, 2008b). In addition, it is considered that many tasks will be achieved by cooperative motions of several space robots in future space missions. We have studied control problems for realizing cooperative manipulations, and reported that a system consisting of space robots with manipulators and a floating object can be treated as a kind of distributed system (Katoh et al., 1997; Sagara et al., 1998b). Using the distributed system representation, each robot consisting of the distributed system can be designed by the control system individually, and we have reported a cooperative manipulation of a floating object by some space robots with the control methods using the transpose of the GJM (Sagara & Taira, 2008a; 2009). 2