Stochastic Models, Information Theory, and Lie Groups, Volume 1

Chirikjian, Gregory S.

doi:10.1007/978-0-8176-4803-9

Cited by 190 publications

(279 citation statements)

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“…Also, an analysis of the uncertainty would be necessary to achieve a successful execution of the grasp. Usually, the uncertainty analysis on manifolds is performed in the associated tangent bundle [45] and, thus, the atlas computed by the method could be of great help to this end. This point certainly deserves future attention.…”

Section: Discussionmentioning

confidence: 99%

Grasp Optimization Under Specific Contact Constraints

2013

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Abstract-This paper presents a procedure to synthesize highquality grasps for objects that need to be held and manipulated in a specific way, characterized by a pre-specified set of contact constraints to be satisfied. Due to the multi-modal nature of typical grasp quality measures, approaches that resort to local optimization methods are likely to get trapped into local extrema on such problem. An additional difficulty of the problem is that the set of feasible grasps is a highly-dimensional manifold, implicitly defined by a system of non-linear equations. The proposed procedure finds a way around these issues by focusing the exploration on a relevant subset of grasps of lower dimension, and tracing this subset exhaustively using a higher-dimensional continuation technique. A detailed atlas of the subset is obtained as a result, on which the highest-quality grasp according to any desired criterion, or a combination of criteria, can be readily identified. Examples are included that illustrate the application of the method to a three-fingered planar hand and to the Schunk anthropomorphic hand grasping several objects, using several quality indices.

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Section: Discussionmentioning

confidence: 99%

Grasp Optimization Under Specific Contact Constraints

2013

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“…Harremoës [9] presented a simplified proof of convergence. Chirikjian [10,11] has shown how classical inequalities used in information theory, such as those of de Bruijn, Fisher, Cramér, Rao, and Kullback, carry over in a natural way from Euclidean space to unimodular Lie groups. That connection is motivated by problems relating to information gathering in mobile robotics, satellite attitude control, tomographic image reconstruction, biomolecular structure determination, and quantum information theory.…”

Section: Shannon's Legacymentioning

confidence: 99%

On a Connection between Information and Group Lattices

Chong

2011

Entropy

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In this paper we review a particular connection between information theory and group theory. We formalize the notions of information elements and information lattices, first proposed by Shannon. Exploiting this formalization, we expose a comprehensive parallelism between information lattices and subgroup lattices. Qualitatively, isomorphisms between information lattices and subgroup lattices are demonstrated. Quantitatively, a decisive approximation relation between the entropy structures of information lattices and the log-index structures of the corresponding subgroup lattices, first discovered by Chan and Yeung, is highlighted. This approximation, addressing both joint and common entropies, extends the work of Chan and Yeung on joint entropy. A consequence of this approximation result is that any continuous law holds in general for the entropies of information elements if and only if the same law holds in general for the log-indices of subgroups. As an application, by constructing subgroup counterexamples, we find surprisingly that common information, unlike joint information, obeys neither the submodularity nor the supermodularity law. We emphasize that the notion of information elements is conceptually significant-formalizing it helps to reveal the deep connection between information theory and group theory. The parallelism established in this paper admits an appealing group-action explanation and provides useful insights into the intrinsic structure among information elements from a group-theoretic perspective.

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“…The simplest choice for the commands would be to sample a random command at each time step. The resulting trajectory would be a Brownian motion if the configuration space is Euclidean space, or an appropriate generalization if the configuration is a Lie group (Chirikjian, 2009). However, beside the fact that there is some some inertia in the platform so that it is impossible to realize in practice, Brownian motion is not an efficient way to explore environments because it tends to revisit the same places.…”

Section: B Experiments Setup 1) Hardwarementioning

confidence: 99%

Bootstrapping bilinear models of Simple Vehicles

Censi

Murray

2015

The International Journal of Robotics Research

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Abstract-Learning and adaptivity will play a large role in robotics in the future. Two questions that are open: 1) in principle, how much it is possible to learn; and, 2) in practice, how much should an agent be able to learn. The bootstrapping scenario describes the extreme case in which agents need to learn "everything" from scratch, including a torque-to-pixels model for its robotic body. This paper considers the bootstrapping problem for a subset of the set of all robots. The Simple Vehicles are idealization of mobile robots equipped with a set of "canonical" exteroceptive sensors: the camera, the rangefinder and the field sampler. The sensorimotor dynamics of these sensors are derived and shown to be surprising similar. These sensorimotor dynamics are well approximated by a class of nonlinear systems that assume an instantaneous bilinear relation among observations, commands, and changes in the observations. The bilinear approximation is sufficient to guarantee success in the task of generalized "servoing": driving the observations to a given goal snapshot. Simulations and experiments substantiate the theoretical results. This is the first instance of a bootstrapping agent that can learn the model of the dynamics of a relatively large universe of systems and use the models to solve well-defined tasks, with no parameter tuning or hand-designed features.

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Stochastic Models, Information Theory, and Lie Groups, Volume 1

Cited by 190 publications

References 0 publications

Grasp Optimization Under Specific Contact Constraints

Grasp Optimization Under Specific Contact Constraints

On a Connection between Information and Group Lattices

Bootstrapping bilinear models of Simple Vehicles

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