Inconsistency Between Actuation and Task Spaces under Active Stiffness Control for Robotic Drilling

Authors: Gürsel ALICI

Abstract: From the robot users point of view, it is essential to specify the desired manipulator trajectory in task space, i.e. in Cartesian space, and therefore, to design any putative control strategy in the same space. However, a manipulator inherently works in the coordinate space of its joint angles, and it is straightforward to design a control strategy in joint space. If the task to be executed by the manipulator is a hard-on-hard task, e.g., robotic drilling, and the task requirement is such that there should not be any coupling between rotational and translational Cartesian movements of the end point, it will be problematic to design the control strategy in joint space due to the interaction between the joint-based servo gains and the centre of stiffness (compliance) seen at the end of the manipulator. As a result of the inconsistency between the desired trajectory space and the control (actuation) space, there exists coupling among the possible degrees of freedom of the end point when an end point force is applied along one of the degrees of freedom. In this paper, we, therefore, address the problem of how the joint servo gains should be selected so that there cannot be any coupling among degrees of freedom of the end point while the manipulator is conducting a contact-force control task under active stiffness control. A two link revolute manipulator is considered as a case study. We conclude that under certain conditions it is possible to avoid the inconsistency between the control and task spaces for the two link manipulator as long as the resulting manipulator joint position-dependent servo gains do not cause instability.

Keywords: Robot Manipulator, Active Stiffness Control, Robot Force Control, Robotic Drilling.