Variational path optimization of linear pentapods with a simple singularity variety. (November 2020) - Rasoulzadeh, Arvin; Nawratil, Georg
Highlights: Thorough analysis of the geometry of the simple pentapod's singularity variety. Present a novel algorithm optimizing the platform motion w.r.t. its singularity distance. It is based on a motion discretization into poses considering the chosen resolution. The guaranteed singularity-free result also takes some joint limits into account. Abstract: The class of linear pentapods with a simple singularity variety is obtained by imposing architectural restrictions on the design of a linear pentapod in a way that the manipulator's singularity variety is linear in orientation/position variables. It turns out that such a simplification leads to crucial computational advantages while maintaining the machine's applications in some fundamental industrial tasks such as 5-axis milling and laser cutting. Assuming that a singularity-free path between a given start- and end-pose of the end-effector within the manipulator's workspace is known, an optimization process of this path is proposed in such a way that the robot increases its distance to the singularity loci while the motion is being smoothed. In this case the computation time of the optimization is improved as these pentapods have a simple singularity variety allowing the symbolic solutions for the local extrema of the singularity-distance function. The whole process is called variational path optimization and takes place through defining a novel cost function. Finally, the optimization takes the physical limits of prismatic joints and base spherical joints into account.