An Analytical Approach to Operational Space Control of Robotic Manipulators with Kinematic Constraints

Abstract

This paper presents a novel control architecture for operational space control when the end effector or the robotic chain is kinematically constrained. Particularly, we address kinematic control of robots operating in the presence of obstacles such as point, plane, or barrier constraints imposed on a point on the manipulator. The main advantage of the proposed approach is that we are able to control the end-effector motion in the normal way using conventional operational space control schemes, and by re-writing the Jacobian matrix we also guarantee that the constraints are satisfied. The most challenging problem of obstacle avoidance of robotic manipulators is the extremely complex structure that arises when the obstacles are mapped from the operational space to joint space. We solve this by first finding a new set of velocity variables for a point on the robot in the vicinity of the obstacle, and on these new variables we impose a structure which guarantees that the robot does not hit the obstacle. We then find a mapping denoted the Constrained Jacobian Matrix from the joint variables to these new velocity variables and use this mapping to find a trajectory in joint space for which the constraints are not violated. We present for the first time the Constrained Jacobian Matrix which imposes a kinematic constraint on the manipulator chain and show the efficiency of the approach through experiments on a real robot.