Learning Stable Task Sequences from Demonstration with Linear Parameter Varying Systems and Hidden Markov Models

The problem of acquiring multiple tasks from demonstration is typically divided in two sequential processes: (1) the segmentation or identification of different subgoals/subtasks and (2) a separate learning process that parameterizes a control policy for each subtask. As a result, segmentation criteria typically neglect the characteristics of control policies and rely instead on simplified models. This paper aims for a single model capable of learning sequences of complex time-independent control policies that provide robust and stable behavior. To this end, we first present a novel and efficient approach to learn goal-oriented timeindependent motion models by estimating both attractor and dynamic behavior from data guaranteeing stability using linear parameter varying (LPV) systems. This method enables learning complex task sequences with hidden Markov models (HMMs), where each state/subtask is given by a stable LPV system and where transitions are most likely around the corresponding attractor. We study the dynamics of the HMM-LPV model and propose a motion generation method that guarantees the stability of task sequences. We validate our approach in two sets of demonstrated human motions.