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In recent years, a myriad of advanced results have been reported in thecommunity of imitation learning, ranging from parametric to non-parametric,probabilistic to non-probabilistic and Bayesian to frequentist approaches.Meanwhile, ample applications (e.g., grasping tasks and human-robotcollaborations) further show the applicability of imitation learning in a widerange of domains. While numerous literature is dedicated to the learning ofhuman skills in unconstrained environment, the problem of learning constrainedmotor skills, however, has not received equal attention yet. In fact,constrained skills exist widely in robotic systems. For instance, when a robotis demanded to write letters on a board, its end-effector trajectory mustcomply with the plane constraint from the board. In this paper, we aim totackle the problem of imitation learning with linear constraints. Specifically,we propose to exploit the probabilistic properties of multiple demonstrations,and subsequently incorporate them into a linearly constrained optimizationproblem, which finally leads to a non-parametric solution. In addition, aconnection between our framework and the classical model predictive control isprovided. Several examples including simulated writing and locomotion tasks arepresented to show the effectiveness of our framework.

A Linearly Constrained Nonparametric Framework for Imitation Learning