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Based on the analysis of the mechanism of robot manipulators, a trajectory tracking controlling research model is first built up with ADAMS, and its mathematical model is formulated through the study of robot kinematics and dynamics. After the modeling errors are analyzed in practical robotic systems, a conception of centralized error is brought forward according to the theory of weighting functions. In the case of modeling errors' exist, the robotic uncertain model is derived by introducing an auxiliary control variable into inverse dynamic analysis. The control strategy of robust exponential convergence is applied to the robotic uncertain model, the applicable conditions and the applicable controller with this application are presented. The stable control effect under three main model uncertainties (parametric errors, joint disturbs, joint frictions) are systematically studied on the previously built research model. The problems of robust exponential convergence controller which often results in unstable output and so produces a large relative error when the input trajectory is in a small range are resolved by adjusting the control parameters based on the controller's structure.

本文在机械手的机械结构分析基础上，利用ADAMS建立了用于机械手轨线跟踪控制研究的机械手模型；通过对机器人运动学和动力学问题的研究，建立了机械手研究的数学模型；分析了机器人系统中模型误差的主要来源，根据加权函数法分析，提出了模型集中误差的概念；在存有模型误差的情况下，采用逆动力学结构并引入辅助控制量，由机器人误差模型推导了机器人非确定性模型；提出了采用鲁棒指数收敛法对上述机器人非确定性模型进行鲁棒镇定的控制策略，并给出了对机器人进行鲁棒指数收敛控制时系统不确定因素应满足的匹配条件；针对机械手研究模型，深入研究了鲁棒指数收敛控制器对机器人系统中常见的模型参数误差、关节扰动、关节摩擦等不确定因素的镇定控制效果；针对鲁棒指数收敛控制器易产生控制量振荡的问题以及在小范围内系统轨线跟踪的稳态误差过大问题，本文分别提出了基于控制器结构的控制参数调整法和基于轨线跟踪范围大小的控制参数分段切换法。

Based on this, a mathematical model of average error of localization is proposed.

通过算法比较和实验分析，证明了方案的有效性和可行性。

The mathematical model was simplified with the method of averaging ,and the closed-loop nonlinear feedback control scheme was presented.

用平均法对欠驱动机械臂的拉格朗日动力学模型进行了简化，并基于简化后的模型给出了闭环非线性反馈控制律。

The most important development in mathematical logic for the philosophy of mathematics was Godel's proof that any axiomatic system powerful enough to formalise arithmetic will be incomplete in the sense that there will be truths which are not provable within the system.

数理逻辑中最重要的数学哲学的发展是哥德尔的证明，任何公理系统足够强大以正式算术将在这个意义上不完全会有真理不属于系统内证明的。

Similarly it is important to see rationalists like Descartes and Spinoza, trying to formulate philosophy in terms of some kind of an axiomatic system, in a discursive and historical context characterized by the emerging natural sciences, formulated in a mathematical language.

同样，在看待象笛卡儿和斯宾诺莎这样设法用某种公理体系构造哲学的唯理论者时，也要将其置于以数学语言构造的新兴自然科学为特征的商谈和历史情境中。

The theory of quantum logic, which has developed during the course of the mathematical axiomatization of the quantum theory, is copious, with a history of 80 years.

量子逻辑是伴随着量子理论的数学公理化而发展起来的一种理论，有着80年的历史和丰富的内容。

When we teaches the Theory of Probability and Statistics, we must pay attention to the teaching of typical mathematical thinking, such as axiomatization thinking, matrix thinking, convergence according to probability, statistical deduction and so on.

在讲授《概率统计》时，要注重公理化思想、模型思想、依概率收敛、统计推断等典型思想方法的教学。

Applying the law of conservation of mass,movement theorem of steady flow , and applying the mathematical method of stream function with the consideration of the axis symmetry,the three components of velocity quantum of the flow are deduced in detail.

本文详细阐述了旋风分离器内流动在球坐标系中的数学表述和结果，应用质量守恒定律和定常流动的运动定律，在轴对称的考虑下，用流函数方法详尽推导了流动的三个速度分量。

A mathematical model of axisymmetric compression of semi-solid alloy slurry was described.

描述了一种轴向挤压的半固态合金浆料的数学模型。

The range and azimuth processing have the same mathematical modal, but have the different physical characteristics and meaning.

故距离成像及方位成像处理程序有相同的数学模型，却有截然不同的物理特徵及意义。

I can still vividly recall the impressive scenes you gave. You were among my friends and relatives who accompanied me from my house to the seaport and when the porters were slow to show up, you obligingly carried my suitcase for me.

你对我的种种感人情意，使我记忆犹新，那天你随着我的亲友从家里送我上轮船，搬运工迟迟不来，你毅然替我提着皮箱上船。

St. Nicholas became the patron saint of Russia, where he was famous for his red cape, flowing white beard, and bishop's mitre.

圣尼古拉成了俄罗斯人的守护神，在那里，他以身披红斗篷，留着飘逸的白胡须，戴着主教法冠而闻名。