Motion Behavior of Null Space in Redundant Robotic Manipulators

As well known, robot manipulator is utilized in many industrial fields. However manipulator motion has a single function at most and is so limited because of low degree-offreedom motion. To improve this issue, it is necessary for the robot manipulator to have redundant degree-of-freedom motion. The motion spaces of redundant manipulator are divided into work space motion and null space motion. A key technology of the redundant manipulator is dexterous use of null space motion. Then, the important issue is how to design null space controller for the dexterous motion control. However the control strategy of null space motion based on the stability analysis has not been established yet. Focusing on this issue, this chapter shows PID controller based on stability analysis considering passivity in null space motion of redundant manipulator. The PID controller which is passive controller plays a role to compensate disturbance of null space motion without deteriorating asymptotic stability. On the other hand, the work space control is stably achieved by a work space observer based PD control. In this chapter, work space controller and null space controller are considered separately. In the proposed controller design, the work space observer that compensates the work space disturbance affecting position response of end-effector is one of important key technologies [1]. Furthermore it brings null space motion without calculating kinematic transformation. Then the null space input can be determined arbitrary in joint space. In this chapter, PID control is utilized to synthesize the null space input. The null space motion is also affected by unknown disturbance even if the work space observer compensates the work space disturbance completely. In particular, null space disturbance denotes an interactive effect among null space responses. The large interaction affects the stability of not only the null space but also the work space motion. To increase both the stability margin and robustness of null space motion, this chapter introduces PID controller considering passivity [2]. The validity of the proposed approach is verified by simulations of 4-link redundant manipulator.