An Algorithm to Determine the Self-Motion Manifold of a Robotic System Consisting of a DLR Lightweight Robot and Linear Axis

In order to achieve dexterous manipulation and interaction in dynamic environments, robots that were desired for human-robot interaction commonly have more degrees of freedom (DOFs) than typical industrial robots. In addition to fulfilling a primary task, the redundant DOFs can be exploited to achieve various secondary goals, e.g. the avoidance of obstacles or the minimization of certain cost functions. In general, it is beneficial to analyze (if possible) possible self-motions of the robot to develop suitable null space control strategies. In this bachelor thesis, an algorithm is developed to determine the self-motion manifold of a robotic system, which consists of a 7-DOF revolute-jointed lightweight robot that is augmented by a linear axis. In the algorithm two independent self-motions, obtained by orthogonal null space velocities, are numerically integrated over time which results in trajectories along the self-motion manifold surface. The end-effector position error of the generated grid is analyzed in detail and a correction term to decrease this error and remove the integration drift is proposed. Furthermore, a controller for the self-motion manifold coordinates is embedded into Cartesian impedance control framework. To ensure the best possible decoupling, null space projections are constructed such that the images are orthogonal sets. Finally, two applications for the null space controller and the self-motion manifold grid are implemented and experimentally verified.