Design of a Cartesian Impedance Controller for a Humanoid Robot with Significant Passive Compliance

Abstract

In this master thesis the development of a Cartesian impedance controller for the humanoid robot Justin is treated, where the hitherto neglected compliances of a tendon system in its torso are considered. First the robot Justin is described and second the exact tasks of this work are listed. Then the existing kinematics and dynamical model of the robot is extended by the passive flexibility. Therefore, the known equations of motion of the rigid body model of the robot are reviewed. Subsequently, it is shown how these equations have to be modified to account for the effects of the elasticities in the dynamic behavior of the robot. The next part of this work presents two methods (static, dynamic), which allow the identification of the necessary parameters of the compliances for the dynamical equations. Here, the approach, the implementation and the evaluation of the identification for both methods are presented. Then, based on the new dynamical model a Cartesian impedance controller is designed, which achieves a desired stiffness and damping in the Cartesian coordinates of both end effectors of Justin’s arms. The controller requests the measurement of the tendon deflections, however since these values are not directly measured they are determined using an inertial measurement unit (IMU), which is located in Justin’s head. It is shown that the Cartesian coordinates of both arm TCPs are local asymptotic stable for the desired equilibrium points in the case of a constant external interaction. Furthermore, the experimental verification and evaluation of the close-loop system demonstrates the improvement in accuracy. Thereby, it is shown that the position error in z-direction is reduced by up to 4 cm. This improvement is especially needed for positioning tasks, where a high accuracy is required, e. g. by interactions in the near of obstacles. An example of such a task is a horizontal motion above a table, where an increasing position error in z-direction would leads to a collision between manipulator and table.