Investigation of Cyclicity of Kinematic Resolution Methods for Serial and Parallel Planar Manipulators

Kinematic redundancy of manipulators is a well-understood topic, and various methods were developed for the resolution in order to solve inverse kinematics problem, at least serial manipulators. An important question, with high practical relevance, whether solution cyclic, i.e., leads closed path joint space as task space. This paper investigates cyclicity property two widely used methods, namely projected gradient method (PGM) augmented Jacobian (AJM), by means examples. Both determine solutions that minimize an objective function, from application point view, sensitivity on initial configuration crucial. Numerical results are reported redundant robotic arms parallel kinematic While AJM known be it turns out also PGM exhibits cyclicity. However, only converges local optimum function when starting cyclic trajectory.