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In Programming by Demonstration, the robot learns novel skills from humandemonstrations. After learning, the robot should be able not only to reproducethe skill, but also to generalize it to shifted domains without collecting newtraining data. Adaptation to similar domains has been investigated in theliterature; however, an open problem is how to adapt learned skills todifferent conditions that are outside of the data distribution, and, moreimportant, how to preserve the precision of the desired adaptations. This paperpresents a novel supervised learning framework called Constrained EquationLearner Networks that addresses the trajectory adaptation problem inProgramming by Demonstrations from a constrained regression perspective. Whileconventional approaches for constrained regression use one kind of basisfunction, e.g., Gaussian, we exploit Equation Learner Networks to learn a setof analytical expressions and use them as basis functions. These basisfunctions are learned from demonstration with the objective to minimizedeviations from the training data while imposing constraints that represent thedesired adaptations, like new initial or final points or maintaining thetrajectory within given bounds. Our approach addresses three main difficultiesin adapting robotic trajectories: 1) minimizing the distortion of thetrajectory for new adaptations; 2) preserving the precision of the adaptations;and 3) dealing with the lack of intuition about the structure of basisfunctions. We validate our approach both in simulation and in real experimentsin a set of robotic tasks that require adaptation due to changes in theenvironment, and we compare obtained results with two existing approaches.Performed experiments show that Constrained Equation Learner Networksoutperform state of the art approaches by increasing generalization andadaptability of robotic skills.

Constrained Equation Learner Networks for Precision-Preserving Extrapolation of Robotic Skills