Learning Trajectories for Robot Programing by Demonstration Using a Coordinated Mixture of Factor Analyzers

This paper presents an approach for learning robust models of humanoid robot trajectories from demonstration. In this formulation, a model of the joint space trajectory is represented as a sequence of motion primitives where a nonlinear dynamical system is learned by constructing a hidden Markov model (HMM) predicting the probability of residing in each motion primitive. With a coordinated mixture of factor analyzers as the emission probability density of the HMM, we are able to synthesize motion from a dynamic system acting along a manifold shared by both demonstrator and robot. This provides significant advantages in model complexity for kinematically redundant robots and can reduce the number of corresponding observations required for further learning. A stability analysis shows that the system is robust to deviations from the expected trajectory as well as transitional motion between manifolds. This approach is demonstrated experimentally by recording human motion with inertial sensors, learning a motion primitive model and correspondence map between the human and robot, and synthesizing motion from the manifold to control a 19 degree-of-freedom humanoid robot.