Learning Partially Contracting Dynamical Systems from Demonstrations

An algorithm for learning the dynamics of point-to-point motions from demonstrations using an autonomous nonlinear dynamical system, named contracting dynamical system primitives (CDSP), is presented. The motion dynamics are approximated using a Gaussian mixture model (GMM) and its parameters are learned subject to constraints derived from partial contraction analysis. Systems learned using the proposed method generate trajectories that accurately reproduce the demonstrations and are guaranteed to converge to a desired goal location. Additionally, the learned models are capable of quickly and appropriately adapting to unexpected spatial perturbations and changes in goal location during reproductions. The CDSP algorithm is evaluated on shapes from a publicly available human handwriting dataset and also compared with two state-of-the-art motion generation algorithms. Furthermore, the CDSP algorithm is also shown to be capable of learning and reproducing point-to-point motions directly from real-world demonstrations using a Baxter robot.