Representation and Reproduction of Skills to Adapt Affine Variations in Programming by Demonstration

Abstract

In this paper, we propose methods for representing and reproducing skills for a robot to adapt scale and position variations and external perturbations. The robot skill should be adaptable and reusable when there exist variation in scale and position (e.g. isotropic scaling, anisotropic scaling, rotation, deformation and so on) and under external perturbation. For example, consider a robot that learns the skill of drawing a square on a sketchpad placed on a table. The robot should be able to draw a square on a sketchpad moved in real-time and on a sketchpad placed at different angles and positions (e.g. a sketchpad hanging on the wall). The robot should also be able to draw a smaller or larger square using the same skill. It should also be able to draw deformed squares using the same skill, if the geometrical properties of the rectangle or the trapezoid are given. The most similar work for this was the method to use the product of the mixutre models based on both global coordinated trajectory and the local coordinated trajectory [1]. Unlike the previous work, our representation afford each mixture model to be controllable by separately modeling one transformation matrix at one mixture model, not the whole mixture models. In our approach, the skill is first modeled as a Gaussian Mixture Model (GMM) using training data. Based on geometric interpretation of the GMM, its mixture components are represented as the priors, the means, and the eigenvectors and eigenvalues of the covariances. This is because the means and the covariances need to be geometrically transformed according to variations and perturbations (see Fig. 1 (b)-(d». A skill is represented by combining the set of these mixture components with the transformation matrices. The skill is renewed by transforming mixture components based on the transformation matrices that are constructed to reflect the variations and the perturbations. We also propose a method for reproducing a skill that is based on a dynamical system using online Gaussian Mixture Regression (GMR). The online GMR provides mean and covariance trajectories in real-time to the dynamical system (see Fig. 2). The skill is reproduced based on the dynamical system subjected to external perturbations (see Fig. 4). To validate our proposed methods, three tasks, conducting beat patterns, drawing figures, and delivering a cup were tested using the KATANA robot arm shown in Fig. 1 (a).