基于差分进化算法的手眼标定方法

针对眼在手机器人视觉系统的手眼标定问题，提出了一种基于差分进化算法的手眼标定方法。首先建立了眼在手机器人视觉系统手眼标定的数学模型，通过李群李代数理论，将手眼标定问题转化为误差函数的优化问题，同时保证了优化问题的最优解落在特殊欧氏群ＳＥ（３）上。通过差分进化算法对优化问题进行求解，避免了求解过程中的局部最优问题。最后在实物平台上进行了手眼标定实验，实验结果验证了算法的可行性和有效性。     

A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle’s model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction. Later, the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance. Finally, simulation examples are provided to verify the effectiveness of the stabilization controller.      

带强迫项的KdV方程的非线性自伴随性和守恒律

应用非线性自伴随性的概念和伊布拉基莫夫的一般守恒律定理，研究了带强迫的KdV方程的非线性自伴随性和守恒律。首先讨论了自伴随性，结果表明这个方程具有非线性自伴随性，同时得到了这个方程的形式拉格朗日量。在对这个方程进行李对称分析之后，根据李对称的不同得到了这个方程的一些非平凡守恒律。     

Variational Bayesian data analysis on manifold

In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes: variational Bayesian expectation (VB-E) step and variational Bayesian maximum (VB-M) step. Moreover, the effective of different metrics for Bayesian analysis is discussed.     

Positively equicontinuous flows

Let G be a positively equicontinuous flow of homeomorphisms of a locally compact metric space E. We show how the dynamics of such a flow are rich. We study when regularly almost periodic elements in G are periodic and we describe orbits and their limit sets. In particular, we show that the limit set L(G?) of G is a closed subset on which G is equicontinuous and that if G moreover has closed orbits, then any w-limit set is a periodic orbit.     

Linearization through state immersion of nonlinear systems admitting Lie symmetries

In this paper, it is shown that if a nonlinear system admits a Lie symmetry that can be transformed into its Poincaré-Dulac normal form by a state diffeomorphism, then, under some technical conditions, such a nonlinear system can be immersed into a linear one. This allows us to compute in closed-form the flow, all algebraic invariant curves (through semi-invariants) of the nonlinear system, and Lyapunov functions to study stability properties.     

Complete and ready simulation semantics are not finitely based over BCCSP, even with a singleton alphabet

This note shows that the complete and the ready simulation preorders do not have a finite inequational basis over the language BCCSP when the set of actions is a singleton. Moreover, the equivalences induced by those preorders do not have a finite (in)equational axiomatization either. These results are in contrast with a claim of finite axiomatizability for those semantics in the literature, which was based on the erroneous assumption that they coincide with complete trace semantics in the presence of a singleton set of actions.     

Weak pseudo-Wajsberg and weak pseudo-MV algebras

 We introduce and study a generalization of pseudo-Wajsberg and pseudo-MV algebras. The weakening of the axioms leads to the existence of two lattice structures, and of two multiplicative monoid structures. Some categorical equivalences are established.     

A characterization of computable analysis on unbounded domains using differential equations

The functions of computable analysis are defined by enhancing normal Turing machines to deal with real number inputs. We consider characterizations of these functions using function algebras, known as real recursive functions. Since there are numerous incompatible models of computation over the reals, it is interesting to find that the two very different models we consider can be set up to yield exactly the same functions. Bournez and Hainry used a function algebra to characterize computable analysis, restricted to the twice continuously differentiable functions with compact domains. In our earlier paper, we found a different (and apparently more natural) function algebra that also yields computable analysis, with the same restriction. In this paper we improve earlier work, finding three function algebras characterizing computable analysis, removing the restriction to twice continuously differentiable functions and allowing unbounded domains. One of these function algebras is built upon the widely studied real primitive recursive functions. Furthermore, the proof of this paper uses our previously developed method of approximation, whose applicability is further evidenced by this paper.