Mathematical Model for Motion Control of Redundant Robot Arms

Motion planning is an essential activity in executing manipulation tasks with robot arms like welding, painting or simple “pick-and-place” operations. A typical requirement for such tasks is to achieve flexibility of the robot arm motion similar to that of a human hand. The objective of the here proposed mathematical model is to satisfy this requirement in path planning a robot arm motion with redundant degrees of freedom. This model provides an efficient procedure for the computation of the motion in the joints that makes the endeffector motion to trace a given geometrical curve with prescribed linear and angular velocity. The novelty of the mathematical model is the clear separation of concerns related to planning the geometrical path in task space on the one hand and on the other hand, the control of motion along this path. This guiding design principle is implemented through vector space methods. It enables a new insight about identifying and processing Jacobian singularities by means of the Continuity principle. The application of the model is enabled through a detailed algorithm for computing the Jacobian, equations for kinematic path control and a heuristic procedure for handling the singularities of the Jacobian. The obtained results can be extended to nonredundant robot