Impedance Control of a Delta Robot

A delta robot is an attractive platform for robotic applications involving contacts and collisions, such as object assembly, because of its low mass and inertia (for low impedance and high speed), low link and joint compliance (for precision), and mechanical simplicity (for low cost). For these types of applications, impedance control is desirable, enabling a task-level controller to modulate the manipulator impedance to minimize the transfer of energy, momentum and force between the manipulator and the environment or task. In this paper, a feedback linearizing control law in task space is derived and used to construct an impedance controller for a three degree of freedom delta robot. Because the robot is a complex closed chain, neither the forward kinematics nor the feedback linearizing control law can be expressed analytically, in closed form. However we show that both can be computed algorithmically. We also show how tactile sensors, integrated into the gripper, may be used in an outer loop feedback to modify, and specifically reduce, the robot impedance. This is useful for manipulating objects of relatively low mass, or where transfer of energy, momentum or force from the robot to an object to be grasped must be minimized. We demonstrate the controller in simulation for a soft grasping primitive, and also in a laboratory experiment, where it plays speed chess.