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Register a new userLearning Null Space Projections in Operational Space Formulation
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Added by
Matthew Howard
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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In recent years, a number of tools have become available that recover the underlying control policy from constrained movements. However, few have explicitly considered learning the constraints of the motion and ways to cope with unknown environment. In this paper, we consider learning the null space projection matrix of a kinematically constrained system in the absence of any prior knowledge either on the underlying policy, the geometry, or dimensionality of the constraints. Our evaluations have demonstrated the effectiveness of the proposed approach on problems of differing dimensionality, and with different degrees of non-linearity.
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In this paper, we carry out null space analysis for Class-Specific Discriminant Analysis (CSDA) and formulate a number of solutions based on the analysis. We analyze both theoretically and experimentally the significance of each algorithmic step. The innate subspace dimensionality resulting from the proposed solutions is typically quite high and we discuss how the need for further dimensionality reduction changes the situation. Experimental evaluation of the proposed solutions shows that the straightforward extension of null space analysis approaches to the class-specific setting can outperform the standard CSDA method. Furthermore, by exploiting a recently proposed out-of-class scatter definition encoding the multi-modality of the negative class naturally appearing in class-specific problems, null space projections can lead to a performance comparable to or outperforming the most recent CSDA methods.
For a robot to perform complex manipulation tasks, it is necessary for it to have a good grasping ability. However, vision based robotic grasp detection is hindered by the unavailability of sufficient labelled data. Furthermore, the application of semi-supervised learning techniques to grasp detection is under-explored. In this paper, a semi-supervised learning based grasp detection approach has been presented, which models a discrete latent space using a Vector Quantized Variational AutoEncoder (VQ-VAE). To the best of our knowledge, this is the first time a Variational AutoEncoder (VAE) has been applied in the domain of robotic grasp detection. The VAE helps the model in generalizing beyond the Cornell Grasping Dataset (CGD) despite having a limited amount of labelled data by also utilizing the unlabelled data. This claim has been validated by testing the model on images, which are not available in the CGD. Along with this, we augment the Generative Grasping Convolutional Neural Network (GGCNN) architecture with the decoder structure used in the VQ-VAE model with the intuition that it should help to regress in the vector-quantized latent space. Subsequently, the model performs significantly better than the existing approaches which do not make use of unlabelled images to improve the grasp.
Overparametrization has been remarkably successful for deep learning studies. This study investigates an overlooked but important aspect of overparametrized neural networks, that is, the null components in the parameters of neural networks, or the ghosts. Since deep learning is not explicitly regularized, typical deep learning solutions contain null components. In this paper, we present a structure theorem of the null space for a general class of neural networks. Specifically, we show that any null element can be uniquely written by the linear combination of ridgelet transforms. In general, it is quite difficult to fully characterize the null space of an arbitrarily given operator. Therefore, the structure theorem is a great advantage for understanding a complicated landscape of neural network parameters. As applications, we discuss the roles of ghosts on the generalization performance of deep learning.
By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one, we find that the key requirement in Harlow-Wus algorithm fails to be met in the whole covariant phase space. Instead, it can be satisfied in its submanifold with the null boundaries given by the expansion free and shear free hypersurfaces in Einsteins gravity, which can be regarded as the origin of the non-triviality of null boundaries in terms of Wald-Zoupass prescription. But nevertheless, by sticking to the variational principle as our guiding principle and adapting Harlow-Wus algorithm to the aforementioned submanifold, we successfully reproduce the Hamiltonians obtained previously by Wald-Zoupas prescription, where not only are we endowed with the expansion free and shear free null boundary as the natural stand point for the definition of the Hamiltonian in the whole covariant phase space, but also led naturally to the correct boundary term for such a definition.
In this paper we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson-Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen hypersurfaces in Lorentzian space forms and provide a local characterization of such hypersurfaces.
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