Learning Augmented Joint-Space Task-Oriented Dynamical Systems: A Linear Parameter Varying and Synergetic Control Approach

In this paper, we propose an asymptotically stable joint-space dynamical system (DS) that captures desired behaviors in joint-space while converging towards a task-space attractor in both position and orientation. To encode joint-space behaviors while meeting the stability criteria, we propose a DS constructed as a Linear Parameter Varying (LPV) system combining different behavior synergies and provide a method for learning these synergy matrices from demonstrations. Specifically, we use dimensionality reduction to find a low-dimensional embedding space for modulating joint synergies, and then estimate the parameters of the corresponding synergies by solving a convex semi-definite optimization problem that minimizes the joint velocity prediction error from the demonstrations. Our proposed approach is empirically validated on a variety of motions that reach a target in position and orientation, while following a desired joint-space behavior.