Learning adaptive reaching skills with nonlinear dynamical systems directly from human demonstrations

In this work, we first discuss details about a novel motion planning approach for robot point to point reaching tasks called stable estimator of dynamical systems (SEDS). A human operator first demonstrates reaching movements several times, and Gaussian Mixture Model and Gaussian Mixture Regression are used to roughly encode human demonstrations through a first order ordinary differential equation. Then based on Lyapunov Stability Theorem, a constrained nonlinear optimization problem is formulated to iteratively refine the previously learned differential model and SEDS is derived. Since during human demonstrations, the velocity is usually quite low which heavily restricts the kinetic capability of the robot, and sometimes we expect the robot to move more fast, such as to catch flying objects and to avoid fast moving obstacles. Therefore, it is extremely significant to develop a method to control the velocity and duration of the robot movement. In this paper, we define a nonlinear function based on the distance between the robot and the target to adjust the velocity of the robot. Experiments have been conducted in simulation environments to verify three properties of the proposed method, namely global asymptotical stability, adaptation to spatial perturbations and velocity controllability.