Learning Stable Movement Primitives by Finding a Suitable Fuzzy Lyapunov Function from Kinesthetic Demonstrations

Transferring skills to roUots through human demonstrations is an interesting problem. Locally generated demonstrations of reaching motion, given by a human teacher are generally encoded in a dynamical model. Stability of this encoding system demands great attention while learning the model parameters. In that context, we present a new architecture of dynamical system to learn movement primitives from multiple demonstrations exploiting a fuzzy Lyapunov function (FLF). We assume that there exists a natural Lyapunov function (LF) that associates the demonstrations. The proposed FLF tries to approximate that LF. First, the dynamics of the demonstrations are encoded in a regressive model, learnt using Gaussian mixture regression with EM algorithm. Then the FLF is searched involving the learnt dynamics in an optimization process. The FLF in turn helps to learn a fuzzy controller. Our architecture is new in a sense that it combines the probabilistic model with a fuzzy controller to create a globally asymptotically stable motion model. The proposed algorithm can simultaneously learn position and orientation profiles in a single model. The algorithm is experimentally validated on a commercially available manipulator and also compared with a state-of-the-art technique.