Level Sets and Stable Manifold Approximations for Perceptually Driven Nonholonomically Constrained Navigation

This paper addresses problems of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We focus on a unicycle motion model and a variety of artificial beacon constellations motivated by relevance to the autonomous hexapod, RHex. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case by switching back and forth between moving down and across the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide some reasonably general sufficient conditions under which the new procedure guarantees convergence to the goal. Simulations are provided for perceptual models previously introduced by other authors

Visual Registration and Navigation using Planar Features

This paper addresses the problem of registering the hexapedal robot RHex, relative to a known set of beacons, by real-time visual servoing. A suitably constructed navigation function represents the task, in the sense that for a completely actuated machine in the horizontal plane, the gradient dynamics guarantee convergence to the visually cued goal without ever losing sight of the beacons that define it. Since the horizontal plane behavior of RHex can be represented as a unicycle, feeding back the navigation function gradient avoids loss of beacons, but does not yield an asymptotically stable goal. We address new problems arising from the configuration of the beacons and present preliminary experimental results that illustrate the discrepancies between the idealized and physical robot actuation capabilities

Perception Based Navigation for Underactuated Robots.

Robot autonomous navigation is a very active field of robotics. In this thesis we propose a hierarchical approach to a class of underactuated robots by composing a collection of local controllers with well understood domains of attraction. We start by addressing the problem of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal. We summarize with simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons. Next we explore the possibility of adapting the resulting first order hybrid feedback controller to its dynamical counterpart by introducing tunable damping terms in the control law. Just as gradient controllers for standard quasi-static mechanical systems give rise to generalized "PD-style" controllers for dynamical versions of those standard systems, we show that it is possible to construct similar "lifts" in the presence of non-holonomic constraints notwithstanding the necessary absence of point attractors. Simulation results corroborate the proposed lift. Finally we present an implementation of a fully autonomous navigation application for a legged robot. The robot adapts its leg trajectory parameters by recourse to a discrete gradient descent algorithm, while managing its experiments and outcome measurements autonomously via the navigation visual servoing algorithms proposed in this thesis.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58412/1/glopes_1.pd

Rigid body visual servoing using navigation functions

Visual servo controllers in the literature rarely achieve provably large domains of attraction, and seldom address two important sensor limitations: (i) susceptibility to self-occlusions and (ii) finite field of view (FOV). We tackle the problem of global, occlusion-free visual servoing of a fully actuated rigid body by recourse to navigation functions on a compact manifold which encode these restrictions as control obstacles. For occlusion free rigid body servoing, the manifold of interest is the visible set of rigid body configurations, that is, those for which the feature points are within the field of view and unoccluded by the body. For a set of coplanar feature points on one face of a convex polyhedron, we show that a slightly conservative subset of the visible set has a simple topology amenable to analytical construction of a navigation function. We construct the controller via a closed form coordinate transformation from our problem domain into the topological model space and conclude with simulation results

Entropy Maximization in the Presence of Higher-Curvature Interactions

Within the context of the entropic principle, we consider the entropy of supersymmetric black holes in N=2 supergravity theories in four dimensions with higher-curvature interactions, and we discuss its maximization at points in moduli space at which an excess of hypermultiplets becomes massless. We find that the gravitational coupling function F^(1) enhances the maximization at these points in moduli space. In principle, this enhancement may be modified by the contribution from higher F^(g)-couplings. We show that this is indeed the case for the resolved conifold by resorting to the non-perturbative expression for the topological free energy.Comment: 22 pages, 8 figures, AMS-LaTe

Automated Gait Adaptation for Legged Robots

Gait parameter adaptation on a physical robot is an error-prone, tedious and time-consuming process. In this paper we present a system for gait adaptation in our RHex series of hexapedal robots that renders this arduous process nearly autonomous. The robot adapts its gait parameters by recourse to a modified version of Nelder-Mead descent while managing its self-experiments and measuring the outcome by visual servoing within a partially engineered environment. The resulting performance gains extend considerably beyond what we have managed with hand tuning. For example, the hest hand tuned alternating tripod gaits never exceeded 0.8 m/s nor achieved specific resistance helow 2.0. In contrast, Nelder-Mead based tuning has yielded alternating tripod gaits at 2.7 m/s (well over 5 body lengths per second) and reduced specific resistance to 0.6 while requiring little human intervention at low and moderate speeds. Comparable gains have been achieved on the much larger ruggedized version of this machine

Black hole entropy functions and attractor equations

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N=2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.Comment: 21 pages,LaTeX,minor change

Black hole partition functions and duality

The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N=2 supergravity theories follow from a variational principle for a certain `entropy function'. We present this function in the presence of R^2-interactions and non-holomorphic corrections. The variational principle identifies the entropy as a Legendre transform and this motivates the definition of various partition functions corresponding to different ensembles and a hierarchy of corresponding duality invariant inverse Laplace integral representations for the microscopic degeneracies. Whenever the microscopic degeneracies are known the partition functions can be evaluated directly. This is the case for N=4 heterotic CHL black holes, where we demonstrate that the partition functions are consistent with the results obtained on the macroscopic side for black holes that have a non-vanishing classical area. In this way we confirm the presence of a measure in the duality invariant inverse Laplace integrals. Most, but not all, of these results are obtained in the context of semiclassical approximations. For black holes whose area vanishes classically, there remain discrepancies at the semiclassical level and beyond, the nature of which is not fully understood at present.Comment: 36 pages, Late

Alkaline electrochemical reduction of a magnesium ferrospinel into metallic iron for the valorisation of magnetite-based metallurgical waste

The electrochemical reduction of iron oxides in alkaline media arises as a novel approach for ironmaking and iron-rich waste valorisation. Strong advantages and attractive aspects of alkaline electroreduction include lower electric energy consumption, absence of CO2 emissions, and non-polluting valuable by-products such as H2 and O2. Another potential advantage originates from the compatibility of this concept with intermittent renewable energies. However, to bring this technology to a competitive level, especially compared to the traditional steelmaking, innovative approaches and developments in materials processing and their appropriate integration into the electrolysis process are required. This research work explores the prospects for electrochemical reduction of a magnesium-containing ferrospinel, as a potential component in iron-containing wastes. The experimental approach considers bulk cathode- and suspension-based electrolysis concepts, which allow reaching 55% and 20% Faradaic efficiencies of the reduction to metallic iron, respectively. The effects imposed by the magnesium presence on the electroreduction kinetics, phase composition and morphology of the electroreduction products are evaluated and discussed. The obtained results open new perspectives for the recovery of metallurgical residues with low magnesium impurities content.publishe

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential