Solving the Singularity Problem of Non-Redundant Manipulators by Constaint Optimization

A solution to the singularity problem of a non-redundant robot is proposed by reformulating the inverse kinematic problem as a constraint optimization problem. The main idea is to allow a cartesian error in a certain subspace in the vicinity of a singularity and to minimize this error subject to operational constraints such as maximum motor speeds. As a result, in every sampling instant a series of linear least squares problems with linear equality and inequality constraints have to be solved. This task can be carried out on a Pentium processor within a few milliseconds. The new method is demonstrated at hand to some experiments with an industrial robot

The DLR Robot Motion Simulator Part II : Optimization based path-planning

In Part I of the paper, a noval motion simulator platform is presented, the DLR Robot Motion Simulator with 7 degrees of freedom (DOF). In this Part II, a path-planning algorithm for mentioned platform will be discussed. By replacing the widely used hexapod kinematics by an antropomorhic, industial robot arm mounted on a standard linerar axis, a comparably larger workspace at lower hardware costs can be achieved. But the serial, redundant kinematics of the industrial robot system also introduces challenges for the path-planning as singularities in the workspace, varying movability of the system and the handling of robot system´s kinematical redundancy. By solving an optimization problem with constraints in every sampling step, a feasible trajectory can be generated, fulfilling the task of motion cueing, while respecthing the robot´s dynamic constraints