Lukas Messner, Hubert Gattringer, and Hartmut Bremer
Motion Planning, Automation and Manufacturing, Realtime
This paper presents a discrete time-optimal online algorithm for the determination of smooth robot state trajectories along specified geometric paths. A complete dynamic model including Coulomb and viscous friction limits the actuator torque values. Additionally, the presented method constrains the joint velocities and joint jerks in order to avoid vibrations due to (not-modeled) gear or structure flexibilities. The underlying optimal control problem uses the path jerk as an input. The corresponding state vector contains path position, speed and acceleration. From optimal control theory it follows that the path jerk has to be chosen at it's boundaries, which can be computed for each state in each step. Continuous state progress is assured via so called test trajectories which are additionally computed in each step. As an example the algorithm is applied to a six-axis industrial robot moving along a straight line in Cartesian space.
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