Mobile manipulation problems involving many objects are challenging to solve due to the high dimensionality and multi-modality of their hybrid configuration spaces. Planners that perform a purely geometric search are prohibitively slow for solving these problems because they are unable to factor the configuration space. Symbolic task planners can efficiently construct plans involving many varia...

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship between quantization and discretization of the configuration space is briefly discussed.

In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative control law. Simulations are provided to validate the controller performance.

With the sophisticated radiation transport codes available today, solving discrete inverse problems using transport is possible. We examine an inverse source problem where the unknowns are the • source spatial distribution and • source energy spectrum. For a tractable problem, we assume that the following are given: • the geometric configuration of the system and • the material properties (that...

Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results for the Markov bases, Graver bases and face posets of these configurations, and we discuss applications to the statistical theory of log-linear models.

We analyze the operation of a molecular machine driven by the nonadiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain a "no-pumping theorem" for cyclic processes with thermally activated transitions, and show that in the adiabatic limit the pumped current is given by a geometric expression.

For more than a century there have been examples of (n3) configurations without a Hamiltonian circuit. However, all these examples were only 2-connected. It has been believed that all geometric 3-connected configurations (n3) admit Hamiltonian circuits. We present a 3-connected configuration (253) of points and lines in the Euclidean plane which has no Hamiltonian circuit.

The topic of this review is geometric registration in robotics. Registration algorithms associate sets of data into a common coordinate system. They have been used extensively in object reconstruction, inspection, medical application, and localization of mobile robotics. We focus on mobile robotics applications in which point clouds are to be registered. While the underlying principle of those ...

Consideration of the geometric quantization of the phase space of a particle in an external Yang-Mills field allows the results of the Mackey-Isham quantization procedure for homogeneous configuration spaces to be reinterpreted. In particular, a clear physical interpretation of the ‘inequivalent’ quantizations occurring in that procedure is given.

The general theory in Pitteri (2003), to be recalled here for completeness, is used to study the full kinematics of β-quartz with special reference to its geometric and arithmetic symmetry. Describing the related decompositions of the β-quartz configuration space into irreducible invariant subspaces is the starting point for the analysis of the generic weak phase transitions of β-quartz under c...