Configuration-based compliance control of kinematically redundant robot arm Part I: Theoretical framework

Abstract

When the robot endpoint compliance is dominantly influenced by the flexibility of its joints, the robot taskspace generalized stiffness matrix can be mapped onto jointspace using appropriate congruence transformation. Thus produced, the jointspace stiffness matrix is generally nondiagonal. Off-diagonal elements can be generated by redundant actuation only (polyarticular actuators). Although this kind of actuation is widely present in biological systems, its practical implementation in engineering systems is very difficult. To overcome this problem, use of kinematic redundancy is proposed. This two-part paper presents an approach to the control of robot endpoint compliance, i.e., elasto-mechanical interaction between a robot and its environment using kinematic redundancy instead of actuation redundancy. In Part I this approach is developed by proposing the Configuration-based Stiffness Control (CSC) method for kinetostatically consistent control of robot compliant behaviour, based on the gradient projection of the cost function which minimizes the norm of off-diagonal elements of the jointspace matrix.

Keywords

• kinematic redundancy
• compliance control
• nullspace stiffness