Visualization of Stable Heteroclinic Channel-Based Movement Primitives

Abstract

Movement primitives are a well-established approach to robot motion planning, as they offer a modular basis for robot motion planning. Dynamic movement primitives (DMPs) are a popular control framework based on nonlinear differential equations which, when scaled in time, produce a smooth kinematic movement plan. In this letter, we introduce an adjusted movement primitive framework which replaces the stable equilibria of DMPs with saddle points. These saddle points are linked together in stable heteroclinic channels (SHCs) which are in turn part of dynamical systems called stable heteroclinic networks. SHC-based movement primitives (SMPs) form a framework where the weights of the kernel functions have spatial significance in the task space. In this letter, we show that SMPs and DMPs perform comparably according to a kinematic-based cost function. We also show that SMP kernel weights follow a given trajectory when plotted in the task space. The plotted kernel weights provide an intuitive tool for managing the controller.