Improving the Manipulability of a Redundant Arm Using Decoupled Hybrid Visual Servoing

This study proposes a hybrid visual servoing technique that is optimised to tackle the shortcomings of classical 2D, 3D and hybrid visual servoing approaches. These shortcomings are mostly the convergence issues, image and robot singularities, and unreachable trajectories for the robot. To address these deficiencies, 3D estimation of the visual features was used to control the translations in Z-axis as well as all rotations. To speed up the visual servoing (VS) operation, adaptive gains were used. Damped Least Square (DLS) approach was used to reduce the robot singularities and smooth out the discontinuities. Finally, manipulability was established as a secondary task, and the redundancy of the robot was resolved using the classical projection operator. The proposed approach is compared with the classical 2D, 3D and hybrid visual servoing methods in both simulation and real-world. The approach offers more efficient trajectories for the robot, with shorter camera paths than 2D image-based and classical hybrid VS methods. In comparison with the traditional position-based approach, the proposed method is less likely to lose the object from the camera scene, and it is more robust to the camera calibrations. Moreover, the proposed approach offers greater robot controllability (higher manipulability) than other approaches.

Projecting onto rectangular matrices with prescribed row and column sums

In 1990, Romero presented a beautiful formula for the projection onto the set of rectangular matrices with prescribed row and column sums. Variants of Romero’s formula were rediscovered by Khoury and by Glunt, Hayden, and Reams for bistochastic (square) matrices in 1998. These results have found various generalizations and applications.In this paper, we provide a formula for the more general problem of finding the projection onto the set of rectangular matrices with prescribed scaled row and column sums. Our approach is based on computing the Moore–Penrose inverse of a certain linear operator associated with the problem. In fact, our analysis holds even for Hilbert–Schmidt operators, and we do not have to assume consistency. We also perform numerical experiments featuring the new projection operator.

The generalized projection methods in countably normed spaces

Let E be a Banach space with dual space $E^{*}$ E ∗ , and let K be a nonempty, closed, and convex subset of E. We generalize the concept of generalized projection operator “$\Pi _{K}: E \rightarrow K$ Π K : E → K ” from uniformly convex uniformly smooth Banach spaces to uniformly convex uniformly smooth countably normed spaces and study its properties. We show the relation between J-orthogonality and generalized projection operator $\Pi _{K}$ Π K and give examples to clarify this relation. We introduce a comparison between the metric projection operator $P_{K}$ P K and the generalized projection operator $\Pi _{K}$ Π K in uniformly convex uniformly smooth complete countably normed spaces, and we give an example explaining how to evaluate the metric projection $P_{K}$ P K and the generalized projection $\Pi _{K}$ Π K in some cases of countably normed spaces, and this example illustrates that the generalized projection operator $\Pi _{K}$ Π K in general is a set-valued mapping. Also we generalize the generalized projection operator “$\pi _{K}: E^{*} \rightarrow K$ π K : E ∗ → K ” from reflexive Banach spaces to uniformly convex uniformly smooth countably normed spaces and study its properties in these spaces.

On the Lyapunov–Perron reducible Markovian Master Equation

We consider an open quantum system in [Formula: see text] governed by quasiperiodic Hamiltonian with rationally independent frequencies and under the assumption of Lyapunov–Perron reducibility of the associated Schrödinger equation. We construct the Markovian Master Equation and the resulting CP-divisible evolution in the weak coupling limit regime, generalizing our previous results from the periodic case. The analysis is conducted with the application of projection operator techniques and concluded with some results regarding stability of solutions and existence of quasiperiodic global steady state.

PATSQL

SQL is one of the most popular tools for data analysis, and it is now used by an increasing number of users without having expertise in databases. Several studies have proposed programming-by-example approaches to help such non-experts to write correct SQL queries. While existing methods support a variety of SQL features such as aggregation and nested query, they suffer a significant increase in computational cost as the scale of example tables increases. In this paper, we propose an efficient algorithm utilizing properties known in relational algebra to synthesize SQL queries from input and output tables. Our key insight is that a projection operator in a program sketch can be lifted above other operators by applying transformation rules in relational algebra, while preserving the semantics of the program. This enables a quick inference of appropriate columns in the projection operator, which is an essential component in synthesis but causes combinatorial explosions in prior work. We also introduce a novel form of constraints and its top-down propagation mechanism for efficient sketch completion. We implemented this algorithm in our tool PATSQL and evaluated it on 226 queries from prior benchmarks and Kaggle's tutorials. As a result, PATSQL solved 68% of the benchmarks and found 89% of the solutions within a second. Our tool is available at https://naist-se.github.io/patsql/.

Quantum theory of redshift in de Sitter expanding universe

The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying special attention to the conserved observables and defining the projection operator selecting the detected momenta it is shown that the expectation values of the energies of the emitted and detected photons comply with the Lemaître rule of Hubble’s law. Moreover, the quantum corrections to the dispersions of the principal observables and new uncertainty relations are derived.