Dynamic movement primitives based on positive and negative demonstrations

Dynamic motion primitive has been the most prevalent model-based imitation learning method in the last few decades. Gaussian mixed regression dynamic motion primitive, which draws upon the strengths of both the motion model and the probability model to cope with multiple demonstrations, is a very practical and conspicuous branch in the dynamic motion primitive family. As Gaussian mixed regression dynamic motion primitive only learns from expert demonstrations and requires full environmental information, it is incapable of handling tasks with unmodeled obstacles. Aiming at this problem, we proposed the positive and negative demonstrations-based dynamic motion primitive, for which the introduction of negative demonstrations can bring additional flexibility. Positive and negative demonstrations-based dynamic motion primitive extends Gaussian mixed regression dynamic motion primitive in three aspects. The first aspect is a new maximum log-likelihood function that balances the probabilities on positive and negative demonstrations. The second one is the positive and negative demonstrations-based expectation-maximum, which involves iteratively calculating the lower bound of a new Q-function. And the last is the application framework of data set aggregation for positive and negative demonstrations-based dynamic motion primitive to handle unmodeled obstacles. Experiments on several typical robot manipulating tasks, which include letter writing, obstacle avoidance, and grasping in a grid box, are conducted to validate the performance of positive and negative demonstrations-based dynamic motion primitive.