In this paper, adaptive control of kinematically redundant robot manipulators is considered. An end-effector tracking controller is designed and the manipulator's kinematic redundancy is utilized to integrate a general sub-task controller for self-motion control. The control objectives are achieved by designing a feedback linearizing controller that includes a least-squares estimation algorithm to compensate for the parametric uncertainties.
I. INTRODUCTIONWhen the number of joints of a robot manipulator is greater than the dimension of its task-space position vector then it is called a kinematically redundant robot manipulator. In many applications, robot manipulators with such additional degrees of freedom are preferred to execute complicated tasks. This kinematic redundancy can result in joint motion in the null space of the Jacobian matrix that does not affect the end-effector position, this phenomenon is commonly referred to as self-motion. There are generally an infinite number of solutions for the inverse kinematics of redundant robot manipulators [1], [2], [3], this complicates the control of kinematically redundant robot manipulators since it is difficult to select a reasonable desired joint trajectory for a given desired task-space trajectory.In our previous work [4], an adaptive full-state feedback quaternion based controller developed in [5] was utilized and a general sub-task controller was designed. In [4], the sub-task controller was systematically integrated into the stability analysis and specific sub-task objectives (such as singularity avoidance, joint limit avoidance, bounding the impact forces and bounding the potential energy) were introduced to make use of the kinematic redundancy. In [6], configuration control of redundant robot manipulators was investigated. The proposed controller achieved taskspace tracking and the redundancy was utilized to impose kinematic and dynamic constraints or posture control. In [7], Hsu et al. proposed a dynamic feedback linearizing control law that guarantees asymptotic tracking of a desired task-space trajectory. However, the controller in [7] required