Learning Fine Motion by Markov Mixtures of Experts

Compliant control is a standard method for performing fine manipulation tasks, like grasping and assembly, but it requires estimation of the state of contact (s.o.c.) between the robot arm and the objects involved. Here we present a method to learn a model of the movement from measured data. The method requires little or no prior knowledge and the resulting model explicitly estimates the s.o.c. The current s.o.c. is viewed as the hidden state variable of a discrete HMM. The control dependent transition probabilities between states are modeled as parametrized functions of the measurement. We show that their parameters can be estimated from measurements at the same time as the parameters of the movement in each s.o.c. The learning algorithm is a variant of the EM procedure. The E step is computed exactly ; solving the M step exactly is not possible in general. Here, gradient ascent is used to produce an increase in likelihood .