In this paper, we address the question of generative knowledge construction from sensorimotor experience, which is acquired by exploration. We show how actions and their effects on objects, together with perceptual representations of the objects, are used to build generative models which then can be used in internal simulation to predict the outcome of actions. Specifically, the paper presents an experiential cycle for learning association between object properties (softness and height) and action parameters for the wiping task and building generative models from sensorimotor experience resulting from wiping experiments. Object and action are linked to the observed effect to generate training data for learning a nonparametric continuous model using Support Vector Regression. In subsequent iterations, this model is grounded and used to make predictions on the expected effects for novel objects which can be used to constrain the parameter exploration. The cycle and skills have been implemented on the humanoid platform ARMAR-IIIb. Experiments with set of wiping objects differing in softness and height demonstrate efficient learning and adaptation behavior of action of wiping.
We establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space. The analysis combines the approaches for acoustic waves in Gopalakrishnan / Sepulveda (A spacetime DPG method for acoustic waves, arXiv 2017) and in Ernesti / Wieners (RICCAM proceedings, submitted 2017) and is based on the abstract definition of traces on the skeleton of the time-space substructuring. The method is evaluated by large-scale parallel computations motivated from applications in seismic imaging, where the computational domain can be restricted substantially to a subset of the full space-time cylinder.1991 Mathematics Subject Classification. 65N30.August 14, 2018.First results of space-time DPG methods are established in [8] for the Schrödinger equations and in [13,15] for acoustic waves. Here, we show that the analysis transfers to general wave equations in heterogeneous media and provides robust estimated in the energy norm. Therefore, we recall in Lem. 3 and Lem. 4 the abstract DPG analysis based on the technique introduced in [15] which avoids explicit traces. Then, following the arguments in [3] we show that a test space exists which guarantees discrete inf-sup stability for general wave equations, and we extend the analysis for the simplified DPG method with nonconforming traces as in [13] to this more general setting. Finally, we apply a Strang-type argument to estimate the consistency error of the DPG method due to inexact quadrature in heterogeneous media.
We apply the discontinuous Petrov-Galerkin (DPG) method to linear acoustic waves in space and time using the framework of first-order Friedrichs systems. Based on results for operators and semigroups of hyperbolic systems, we show that the ideal DPG method is wellposed. The main task is to avoid the explicit use of traces, which are difficult to define in Hilbert spaces with respect to the graph norm of the space-time differential operator. Then, the practical DPG method is analyzed by constructing a Fortin operator numerically. For our numerical experiments we introduce a simplified DPG method with discontinuous ansatz functions on the faces of the space-time skeleton, where the error is bounded by an equivalent conforming DPG method. Examples for a plane wave configuration confirms the numerical analysis, and the computation of a diffraction pattern illustrates a first step to applications.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.