Title :
BM: An iterative algorithm to learn stable non-linear dynamical systems with Gaussian mixture models
Author :
Khansari-Zadeh, S. Mohammad ; Billard, Aude
Author_Institution :
LASA Lab., Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland
Abstract :
We model the dynamics of non-linear point-to-point robot motions as a time-independent system described by an autonomous dynamical system (DS). We propose an iterative algorithm to estimate the form of the DS through a mixture of Gaussian distributions. We prove that the resulting model is asymptotically stable at the target. We validate the accuracy of the model on a library of 2D human motions and to learn a control policy through human demonstrations for two multi-degrees of freedom robots. We show the real-time adaptation to perturbations of the learned model when controlling the two kinematically-driven robots.
Keywords :
Gaussian distribution; iterative methods; learning systems; motion control; nonlinear dynamical systems; perturbation techniques; robot dynamics; robot kinematics; stability; Gaussian distribution; Gaussian mixture models; autonomous dynamical system; binary merging; iterative algorithm; kinematically-driven robot; learned model perturbation; multidegrees of freedom robots; nonlinear point-to-point robot motion dynamics; stable nonlinear dynamical system learning; time-independent system; Differential equations; Humans; Iterative algorithms; Nonlinear dynamical systems; Orbital robotics; Power system modeling; Robot motion; Robustness; Stability; Stochastic systems;
Conference_Titel :
Robotics and Automation (ICRA), 2010 IEEE International Conference on
Conference_Location :
Anchorage, AK
Print_ISBN :
978-1-4244-5038-1
Electronic_ISBN :
1050-4729
DOI :
10.1109/ROBOT.2010.5510001