Abstract-This paper presents a method to learn discrete robot motions from a set of demonstrations. We model a motion as a nonlinear autonomous (i.e., time-invariant) dynamical system (DS) and define sufficient conditions to ensure global asymptotic stability at the target. We propose a learning method, which is called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions closely follow the demonstrations while ultimately reaching and stopping at the target. Timeinvariance and global asymptotic stability at the target ensures that the system can respond immediately and appropriately to perturbations that are encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions.Index Terms-Dynamical systems (DS), Gaussian mixture model, imitation learning, point-to-point motions, stability analysis.

This paper presents a novel approach to real-time obstacle avoidance based on dynamical systems (DS) that ensures impenetrability of multiple convex shaped objects. The proposed method can be applied to perform obstacle avoidance in Cartesian and Joint spaces and using both autonomous and non-autonomous DS-based controllers. Obstacle avoidance proceeds by modulating the original dynamics of the controller. The modulation is parameterizable and allows to determine a safety margin and to increase the robot's reactiveness in the face of uncertainty in the localization of the obstacle. The method is validated in simulation on different types of DS including locally and globally asymptotically stable DS, autonomous and non-autonomous DS, limit cycles, and unstable DS. Further, we verify it in several robot experiments on the 7 degrees of freedom Barrett WAM arm.

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Abstract-Motion imitation requires reproduction of a dynamical signature of a movement, i.e. a robot should be able to encode and reproduce a particular path together with a specific velocity and/or an acceleration profile. Furthermore, a human provides only few demonstrations, that cannot cover all possible contexts in which the robot will need to reproduce the motion autonomously. Therefore, the encoding should be able to efficiently generalize knowledge by generating similar motions in unseen context. This work follows a recent trend in Programming by Demonstration in which the dynamics of the motion is learned. We present an algorithm to estimate multivariate robot motions through a Mixture of Gaussians.The strengths of the proposed encoding are three-fold: i) it allows to generalize a motion to unseen context; ii) it provides fast on-line replanning of the motion in the face of spatio-temporal perturbations; iii) it may embed different types of dynamics, governed by different attractors.The generality of the method to estimate arbitrary nonlinear motion dynamics is demonstrated by accurately estimating a set of known non-linear dynamical systems. The platformindependency and real-time performance of the method are further validated to learn the non-linear motion dynamics of manipulation tasks with different robotic platforms. We provide an experimental comparison of our approach with an related state-of-the-art method.

Abstract-This paper presents a methodology for learning arbitrary discrete motions from a set of demonstrations. We model a motion as a nonlinear autonomous (i.e. time-invariant) dynamical system, and define the sufficient conditions to make such a system globally asymptotically stable at the target. The convergence of all trajectories is ensured starting from any point in the operational space. We propose a learning method, called Stable Estimator of Dynamical Systems (SEDS), that estimates parameters of a Gaussian Mixture Model via an optimization problem under non-linear constraints. Being time-invariant and globally stable, the system is able to handle both temporal and spatial perturbations, while performing the motion as close to the demonstrations as possible. The method is evaluated through a set of robotic experiments.