On the Virtual Joints for Kinematic Control of Redundant Manipulators With Multiple Constraints

The general weighted least-norm method introduces the concept of virtual joints to cope with the multiple constraints that are regarded as virtual joints with joint limits. With the perfect performance for joint-limit avoidances, the constraint could be handled well with kinematic control of redundant manipulators. However, the singularity of the map from joints to virtual joints has not been well addressed. Combining some constraints supposed not to be activated simultaneously into one constraint looks very special, but is required when the number of constraints is larger than the degree of freedom. In this paper, an improved formulation of virtual joints is presented to overcome the above-mentioned two drawbacks so as to complete the virtual joint concept. The proposed method is illustrated by simulation and experiment on a real manipulator for avoiding joint limits and obstacles while tracking a trajectory.