A nonparametric Bayesian approach toward robot learning by demonstration

Abstract

In the last years, many authors have considered application of machine learning methodologies to effect robot learning by demonstration. Gaussian mixture regression (GMR) is one of the most successful methodologies used for this purpose. A major limitation of GMR models concerns automatic selection of the proper number of model states, i.e. the number of model component densities. Existing methods, including likelihood-or entropy-based criteria, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori. Under this motivation, to resolve the aforementioned issues of GMR-based methods for robot learning by demonstration, in this paper we introduce a nonparametric Bayesian formulation for the GMR model, the Dirichlet process GMR model. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally investigate its efficacy as a robot learning by demonstration methodology, considering a number of demanding robot learning by demonstration scenarios.

A tutorial on task-parameterized movement learning and retrieval

“…It is worth noting that the constraint (33) defines the same set of relations as (21) and (22) used in trajectory-GMM (GMM with dynamic features). The main difference between the two problems is that trajectory-GMM seeks for a reference trajectory, while the above problem seeks for a controller.…”

“…Model selection (i.e., determining the number of Gaussians in the GMM) is compatible with the techniques employed in standard GMM, such as the use of a Bayesian information criterion [82], Dirichlet process [22,50,65,74], iterative pairwise replacement [83], spectral clustering [53,69,84] or based on segmentation points [56]. Model selection in mixture modeling shares a similar core challenge as that of data-driven sparse kernel regression techniques, which requires to find the right bandwidth parameters to select a subset of existing/new datapoints that are the most representatives of the dataset.…”

Online quantum mixture regression for trajectory learning by demonstration

“…For robotic applications of conventional mixture regression and Dirichlet process mixture regression we refer to [8], [22], [11], where trajectory positions serve as predictor and velocities as response variables y t = [x t , υ t ].…”

“…Two well-established approaches towards trajectory level LbD are the Gaussian mixture regression (GMR) [10], [11] and the locally weighted projection regression (LWPR) [12]. Regarding the comparative merits of both methods, it has been shown that GMR performs better for low dimensional demonstrations [13], while LWPR should be preferred for inputs of high dimensionallity, which lie in lower dimensional manifolds, and/or inputs that may contain irrelevant dimensions.…”

Online Multimodal Ensemble Learning Using Self-Learned Sensorimotor Representations

“…One possibility to acquire a target trajectory and to learn inverse models from data is to collect multiple demonstrations of each task. This approach has been explored for example in [39][40][41][42][43], where statistical methods have been proposed to infer models from multiple demonstrated trajectory. However, this approach requires multiple demonstrations, which might be difficult to obtain.…”