Movement primitives with multiple phase parameters

Movement primitives are concise movement representations that can be learned from human demonstrations, support generalization to novel situations and modulate the speed of execution of movements. The speed modulation mechanisms proposed so far are limited though, allowing only for uniform speed modulation or coupling changes in speed to local measurements of forces, torques or other quantities. Those approaches are not enough when dealing with general velocity constraints. We present a movement primitive formulation that can be used to non-uniformly adapt the speed of execution of a movement in order to satisfy a given constraint, while maintaining similarity in shape to the original trajectory. We present results using a 4-DoF robot arm in a minigolf setup.