Learning Non-linear Multivariate Dynamics of Motion in Robotic Manipulators

Abstract

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.

Learning motion dynamics to catch a moving object

“…In previous work of ours, we addressed different aspects of encoding motions with dynamical systems, specifically: effective and smooth adaptation in the case of spatio-temporal perturbations [14], learning of asymptotically stable estimates [19], learning of position and orientation control for motion generation [1]. The present paper continues research in this direction and presents new results on learning motions of both the robot's end-effector and external objects.…”

“…Next, we briefly review these works according to (1) how they predict trajectories of moving objects and (2) how they generate the robot's motions [14]. To catch a moving object properly, prediction of the trajectory of moving objects is required.…”

“…This problem has been largely overlooked in the literature sofar. In [14], we proposed a means to learn timeindependent dynamical systems (autonomous dynamical systems) so as to become robust to temporal perturbations. Here, we extend this work and address the problem of controlling the duration of the motion when encoded in an autonomous DS.…”

Online Trajectory Planning in Dynamic Environments for Surgical Task Automation

“…However, this is not applicable to tasks where the topological features of the trajectory must be adapted according to the state of the environment. Another important previous work is presented by Billard et al [7,6,4]. They developed a scheme of learning tasks as a time-invariant dynamic system and adapting the motion trajectory in realtime for obstacle avoidance [6].…”

Learning motions from demonstrations and rewards with time-invariant dynamical systems based policies

“…It is then sufficient to spread the basis function regularly along this single dimension. The second approach, which is less common, is to use the state variables of the system as input to the basis function [12,7,13]. Those two approaches have different limitations.…”