Trajectory learning and reproduction for differential drive mobile robots based on GMM/HMM and dynamic time warping using learning from demonstration framework

In this paper, we present new Learning from Demonstration-based algorithm that generalizes and extracts relevant features of desired motion trajectories for differential drive mobile robots. The algorithm is tested through series of simulations and real world experiments in which desired task is demonstrated by the human teacher while teleoperating the mobile robot in the working environment. In the first step of the developed method, Gaussian Mixture Model (GMM) is built for incremental motions of the mobile robot between two consecutive poses. After this, the hidden Markov model is used to capture transitions between states (temporal variations of the data between clusters) which are missing from static GMM representation. Generalization of the motion is achieved by using the concept of keyframes, defined as points in which significant changes between GMM/HMM states occur. In the second step, the resulting GMM/HMM representation is used to generate optimal state sequences for each demonstration and to temporally align them, using 1D dynamic time warping, with respect to the one most consistent with the GMM/HMM model. This phase implies extraction of keyframes along all state sequences and projecting them into control space, in which controls are aligned in time as well. Finally, the generalized controls are obtained by averaging over all controls at the keyframes; simple piecewise cubic spline method is used for interpolation between generated control values. The main advantage of the developed algorithm is its ability to learn and generalize from all demonstrated examples which results in high quality reproductions of the motion. The proposed approach is verified both in simulated environment and using real mobile robot.