Learning Dynamical System Modulation for Constrained Reaching Tasks

In this paper we combine kinesthetic demonstrations and dynamical systems to enable a humanoid robot to imitate constrained reaching gestures directed toward a target. Using a learning algorithm based on Gaussian mixture regression, the task constraints are extracted from several demonstrations. Those constraints take the form of desired velocity profiles for the end-effector and joint angle variables, with associated covariance matrices describing the variations allowed around the desired profiles. Those constraints are then used to modulate a dynamical system which has the reaching target as attractor. This way, the reaching trajectory can be reshaped in order to satisfy the constraints of the task, while preserving the adaptability and robustness provided by the dynamical system. In particular, the system can adapt to changes in the initial conditions and to target displacements occurring during the movement execution. We first evaluate the potential of this method on experiments involving the Hoap3 humanoid robot putting an object into a box. We then show how a manipulation tasks can be executed as sequences of such constrained reaching movement. This is illustrated on a packaging task performed by the robot