Generalizing manipulation skills to new situations requires extracting invariant patterns from demonstrations. For example, the robot needs to understand the demonstrations at a higher level while being invariant to the appearance of the objects, geometric aspects of objects such as its position, size, orientation and viewpoint of the observer in the demonstrations. In this paper, we propose an algorithm that learns a joint probability density function of the demonstrations with invariant formulations of hidden semi-Markov models to extract invariant segments (also termed as sub-goals or options), and smoothly follow the generated sequence of states with a linear quadratic tracking controller. The algorithm takes as input the demonstrations with respect to different coordinate systems describing virtual landmarks or objects of interest with a task-parameterized formulation, and adapt the segments according to the environmental changes in a systematic manner. We present variants of this algorithm in latent space with low-rank covariance decompositions, semi-tied covariances, and non-parametric online estimation of model parameters under small variance asymptotics; yielding considerably low sample and model complexity for acquiring new manipulation skills. The algorithm allows a Baxter robot to learn a pick-and-place task while avoiding a movable obstacle based on only 4 kinesthetic demonstrations.
A number of variants of HMMs have been proposed to address some of its shortcomings, including: 1) how to bias learning towards models with longer self-dwelling states, 2) how to robustly estimate the parameters with high-dimensional noisy data, 3) how to adapt the model with newly observed data, and 4) how to estimate the number of states that the model should possess. For example, @cite_31 used HMMs to incrementally group whole-body motions based on their relative distance in HMM space. @cite_8 presented an iterative motion primitive refinement approach with HMMs. @cite_24 used the Beta Process Autoregressive HMM for learning from unstructured demonstrations. used the transformation invariant covariance matrix for encoding tasks with a Bayesian non-parametric HMM @cite_12 .
@cite_24 @cite_31 @cite_12 @cite_8
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We present a novel method for segmenting demonstrations, recognizing repeated skills, and generalizing complex tasks from unstructured demonstrations. This method combines many of the advantages of recent automatic segmentation methods for learning from demonstration into a single principled, integrated framework. Specifically, we use the Beta Process Autoregressive Hidden Markov Model and Dynamic Movement Primitives to learn and generalize a multi-step task on the PR2 mobile manipulator and to demonstrate the potential of our framework to learn a large library of skills over time. This paper describes a novel approach for autonomous and incremental learning of motion pattern primitives by observation of human motion. Human motion patterns are abstracted into a dynamic stochastic model, which can be used for both subsequent motion recognition and generation, analogous to the mirror neuron hypothesis in primates. The model size is adaptable based on the discrimination requirements in the associated region of the current knowledge base. A new algorithm for sequentially training the Markov chains is developed, to reduce the computation cost during model adaptation. As new motion patterns are observed, they are incrementally grouped together using hierarchical agglomerative clustering based on their relative distance in the model space. The clustering algorithm forms a tree structure, with specialized motions at the tree leaves, and generalized motions closer to the root. The generated tree structure will depend on the type of training data provided, so that the most specialized motions will be those for which the most training has been received. Tests with motion capture data for a variety of motion primitives demonstrate the efficacy of the algorithm. In this work, we tackle the problem of transform-invariant unsupervised learning in the space of Covariance matrices and applications thereof. We begin by introducing the Spectral Polytope Covariance Matrix (SPCM) Similarity function; a similarity function for Covariance matrices, invariant to any type of transformation. We then derive the SPCM-CRP mixture model, a transform-invariant non-parametric clustering approach for Covariance matrices that leverages the proposed similarity function, spectral embedding and the distance-dependent Chinese Restaurant Process (dd-CRP) (Blei and Frazier, 2011). The scalability and applicability of these two contributions is extensively validated on real-world Covariance matrix datasets from diverse research fields. Finally, we couple the SPCM-CRP mixture model with the Bayesian non-parametric Indian Buffet Process (IBP) - Hidden Markov Model (HMM) (, 2009), to jointly segment and discover transform-invariant action primitives from complex sequential data. Resulting in a topic-modeling inspired hierarchical model for unsupervised time-series data analysis which we call ICSC-HMM (IBP Coupled SPCM-CRP Hidden Markov Model). The ICSC-HMM is validated on kinesthetic demonstrations of uni-manual and bi-manual cooking tasks; achieving unsupervised human-level decomposition of complex sequential tasks. We present an approach for kinesthetic teaching of motion primitives for a humanoid robot. The proposed teaching method allows for iterative execution and motion refinement using a forgetting factor. During the iterative motion refinement, a confidence value specifies an area of allowed refinement around the nominal trajectory. A novel method for continuous generation of motions from a hidden Markov model (HMM) representation of motion primitives is proposed, which incorporates relative time information for each state. On the real-time control level, the kinesthetic teaching is handled by a customized impedance controller, which combines tracking performance with soft physical interaction and allows to implement soft boundaries for the motion refinement. The proposed methods were implemented and tested using DLR's humanoid upper-body robot Justin.