Due to redundant degrees of freedom, the second-order kinematics mapping from the joint acceleration to the acceleration of the end-effector can provides the robot with the possibility of more safety and flexibility. However, joint self-motion instability occurs as the second-order kinematic control methods were adopted in the actual application. Based on the analysis of the instability in second-order kinematics, a null-space velocity clamping general form was proposed in this paper. It cannot only track the main task trajectory and adjust the self-motion manifold of the subtasks, but also suppress the homogeneous acceleration, A clamping term is introduced to track the desired self-motion, which provides the possibility to guarantee the main task and subtasks while ensuring the joint motion stability simultaneously. Furthermore, the prominent self-motion stable control methods can be obtained based on the null-space velocity clamping general form by properly choosing the null-space projection and clamping term. The null-space velocity clamping control methods are finally compared in several simulations on a redundant robot. A thorough discussion of the theoretical and simulation results completes this survey.
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