Bagging for Gaussian mixture regression in robot learning from demonstration
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Bagging for Gaussian mixture regression in robot learning from demonstration Congcong Ye1 · Jixiang Yang1
· Han Ding1
Received: 28 September 2019 / Accepted: 30 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Robot learning from demonstration (L f D) emerges as a promising solution to transfer human motion to the robot. However, because of the open-loop between the learner and task constraints, the precision of the reproduction at the desired task constraints cannot always be guaranteed and the model is not robust to changes of the training data. This paper proposes a closed-loop framework of L f D based on the bagging method of Gaussian Mixture Model and Gaussian Mixture Regression (GMM/GMR) to obtain a robust learner of L f D with high precision reproduction. The original demonstration data are divided into several sub-training data, from which multiple Gaussian mixture models are developed and combined through weighted average to provide predictions. A closed-loop is built between the reproduction of the combined learner and task constraints, and the weights that satisfy task constraints are estimated in the closed-loop. The prediction uncertainty of the models is automatically eliminated by the closed-loop, therefore, the low robustness of the L f D model to the training date is overcome. In experiments, tasks of the position and velocity are both constrained in dual closed-loop. It is shown that the proposed method can significantly meet the task constraints without increasing the complexity of the algorithm. Keywords Robot · Learning from demonstration · Bagging · GMM/GMR
List of symbols t ξ o, ξ ξs πk βk μk k K N (μk , k ) N (ξ i ; μk , k )
B 1
ξˆs Time step Training data before/after DTW Spatial component of the training data Parameters of GMM Prior probability of a Gaussian distribution in a GMM The probability of the component k to be responsible for t Mean of a Gaussian component Covariance matrix of a Gaussian distribution Number of Gaussian components Gaussian distribution described by mean μk and covariance matrix k Probability of ξ i where the density function is a Gaussian distribution
Jixiang Yang [email protected] School of Mechanical Science and Engineering, State Key Laboratory of Digital Manufacturing Equipments and Technology, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
ˆ ss Q D N M L G, G Gi , Gi yi , y ωi C Ad Bd Cq pi d i ,d i
Expected mean of the reproduction (spatial component) Expected covariance of the reproduction (spatial component) The number of the base learners Spatial dimensionality Number of datapoints Demonstration number Key-points number Combined learner The i-th base learner The output of G i /G The generalized weight of base learner Gi Task constraints The d-th dimension of C L × Q matrix consisted of the output of each base learners D × D diagonal matrix The i-th key-position point The distance between the reproduction of GMR/Bagging-GMR and the keypoints
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