Passing Through Jacobian Singularities in Motion Path Control of Redundant Robot Arms

Abstract

This paper presents a new approach for resolving Jacobian singularities borrowing ideas from Software engineering and the Continuity principle of Leibniz. It considers kinematic motion control of redundant robot arms in case the work operation is assigned in terms of a geometrical path and the motion along it in task space. The proposed visualization of motion allows to better understand the motion of a redundant robot in terms of vector space methods. The Null space of the Jacobian is geometrically visualized in relation to a corresponding Null space of configurations. This geometrical representation resolves the velocity of the robot arm into two components. One of them is responsible for reconfiguring the robot arm motion in the Null spaces of configurations, while the other component moves the end effector along the prescribed path in task space. The visualization shows also that Jacobian singularities serve as “gates” between Null spaces of non-singular configurations. It enables the formulation of a numerical procedure for identifying and resolving Jacobian singularities. Unlike existing approaches this procedure employs the Principle of continuity to “predict” the velocity in the joints in a singular configuration and pass through such a configuration instead of avoiding it.