Consensus-based Distributed 3D Pose Estimation with Noisy Relative Measurements

In this paper we study consensus-based tributed estimation algorithms for estimating the global translation and rotation of each agent in a multi-agent system. We consider the case in which agents measure the noisy relative pose of their neighbors and communicate their estimates to agree upon the global poses in an arbitrary reference frame. The main contribution of this paper is a formal analysis that provides necessary and sufficient conditions to guarantee stability (in a Lyapunov sense) of the estimation system''s equilibria. We prove that consensus-based algorithms will diverge, even with arbitrarily small inconsistencies on the relative pose, unless the measurements satisfy minimum consistency conditions. We determine these consistency conditions for translation-only, rotation-only, and combined 3D pose estimation using the axis-angle rotation representation over undirected graphs. We then propose an initialization method based on these conditions that guarantees consistency and stability of the estimator''s equilibria. Additionally, we show that existing distributed estimation methods in literature exploit these conditions to guarantee convergence of their algorithms. Lastly, we perform simulations that show convergence when consistency conditions hold and divergence when they do not

Mathematical Philology: Entropy Information in Refining Classical Texts' Reconstruction, and Early Philologists' Anticipation of Information Theory

Philologists reconstructing ancient texts from variously miscopied manuscripts anticipated information theorists by centuries in conceptualizing information in terms of probability. An example is the editorial principle difficilior lectio potior (DLP): in choosing between otherwise acceptable alternative wordings in different manuscripts, “the more difficult reading [is] preferable.” As philologists at least as early as Erasmus observed (and as information theory's version of the second law of thermodynamics would predict), scribal errors tend to replace less frequent and hence entropically more information-rich wordings with more frequent ones. Without measurements, it has been unclear how effectively DLP has been used in the reconstruction of texts, and how effectively it could be used. We analyze a case history of acknowledged editorial excellence that mimics an experiment: the reconstruction of Lucretius's De Rerum Natura, beginning with Lachmann's landmark 1850 edition based on the two oldest manuscripts then known. Treating words as characters in a code, and taking the occurrence frequencies of words from a current, more broadly based edition, we calculate the difference in entropy information between Lachmann's 756 pairs of grammatically acceptable alternatives. His choices average 0.26±0.20 bits higher in entropy information (95% confidence interval, P = 0.005), as against the single bit that determines the outcome of a coin toss, and the average 2.16±0.10 bits (95%) of (predominantly meaningless) entropy information if the rarer word had always been chosen. As a channel width, 0.26±0.20 bits/word corresponds to a 0.790.79+0.09−0.15 likelihood of the rarer word being the one accepted in the reference edition, which is consistent with the observed 547/756 = 0.72±0.03 (95%). Statistically informed application of DLP can recover substantial amounts of semantically meaningful entropy information from noise; hence the extension copiosior informatione lectio potior, “the reading richer in information [is] preferable.” New applications of information theory promise continued refinement in the reconstruction of culturally fundamental texts

A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing

In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms amodel predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others'' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to 1.25m/s

Asymmetric optical nuclear spin pumping in a single uncharged quantum dot

A highly asymmetric dynamic nuclear spin pumping is observed in a single self assembled InGaAs quantum dot subject to resonant optical pumping of the neutral exciton transition leading to a large maximum polarization of 54%. This dynamic nuclear polarization is found to be much stronger following pumping of the higher energy Zeeman state. Time-resolved measurements allow us to directly monitor the buildup of the nuclear spin polarization in real time and to quantitatively study the dynamics of the process. A strong dependence of the observed dynamic nuclear polarization on the applied magnetic field is found, with resonances in the pumping efficiency being observed for particular magnetic fields. We develop a model that fully accounts for the observed behaviour, where the pumping of the nuclear spin system is due to hyperfine-mediated spin flip transitions between the states of the neutral exciton manifold.Comment: published version; 4+ pages, 3 figures (eps

Carbon and nitrogen partitioning in Vitis vinifera L.: Responses to nitrogen supply and limiting irradiance

Potted Vitis vinifera L. plants were grown under controlled environmental conditions at five different levels of nitrogen (0, 1, 5, 10, 100 mM NH4NO3) in combination with two different levels of irradiance (photon flux densities: 30 and 140 µ mol · m-2 s-1 PAR) during bloom. Elevated N supply increased available N (particularly NO3-), K, Ca and Mg, and reduced P in the soil. Soil-NO3- and K were higher in the lower light regime, but NH4+ and other nutrients were not influenced by irradiance. The concentration of total N in the xylem sap increased as N supply was increased, although there was no further rise above intermediate soil-N levels. NO3- was the principal xylem solute, in particular under severe light restriction and high N availability. In the lower light regime, only traces of organic N could be detected in the xylem sap, whereas in the higher light treatment, glutamine and glutamate increased with increasing N application level. Light limitation reduced the concentrations of P, K and Mg in the xylem sap by about 50 %, but no response to N supply could be observed. There was a strong positive relationship between N availability and N concentration in all plant parts, while the effect on C content was minor and depended on the type and physiological age of the tissue. The amounts of total N per vine were not affected by the light treatments, although low-light stress increased N concentrations in the dry matter of the annual organs by 34-86 %. By contrast, low light led to a slight decrease of the C concentration in the annual plant parts. In the higher light regime, non-structural carbohydrates in the permanent parts of the vine declined as N availability increased. Under severe light restriction, however, the C reserve fraction was depleted and was not altered by N supply, indicating that reserves had been remobilized to support maintenance and growth processes, in order to guarantee survival of the vine

Scaling properties of granular materials

Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab-size.Comment: 4 pages, 2 figure

Collision of One-Dimensional Nonlinear Chains

We investigate one-dimensional collisions of unharmonic chains and a rigid wall. We find that the coefficient of restitution (COR) is strongly dependent on the velocity of colliding chains and has a minimum value at a certain velocity. The relationship between COR and collision velocity is derived for low-velocity collisions using perturbation methods. We found that the velocity dependence is characterized by the exponent of the lowest unharmonic term of interparticle potential energy