Robot Learning by Visual Observation

5Task Planning

Task planning in the context of trajectory learning is related to generation of a plan for reproduction of a demonstrated task. The task planning approaches presented in this chapter employ the task modeling methodology reviewed in Chapter 4. Gaussian mixture regression (GMR) is used for tasks modeled with a Gaussian mixture model (GMM) (Section 4.1). Spline regression is employed with tasks represented with a set of salient trajectory key points. Hidden Markov models (HMMs) (Section 4.2) and conditional random fields (CRFs) (Section 4.3) are commonly used for extracting trajectory key points where the task planning step is performed with spline regression. Locally weighted regression is applied for generation of a reproduction strategy with tasks modeled with the dynamic motion primitives (DMPs) approach (Section 4.4).

5.1 Gaussian Mixture Regression

GMR is used for generating a generalized trajectory for reproduction of tasks represented mathematically with a GMM. As explained in Section 4.1, GMM encodes parametrically a set of observed trajectories with multiple Gaussian probability density functions. For n number of Gaussian components, the model parameters are π_n, μ_n and Σ_n. GMR in this case is employed to find the conditional expectation of the temporal components of observed trajectories given the spatial component of observed trajectories. Or, for a temporal vector indexing the observation times in the recorded sequences denoted by t_k for , and corresponding ...