两柔性机器人协调操作的动力学模型及其逆动力学分析

柔性机器人动力学是当前机器人研究的热点,而其协调操作问题目前仍为空白．本 文首次建立了柔性机器人协调操作刚性负载的动力学模型,利用有限元法和Lagrange方程, 在柔性机器人协调操作的运动学和动力学协调约束条件基础上,推导出系统的动力学方程, 提出了其逆动力学问题的解决方案,并成功给出了平面两3R柔性臂协调操作的数值算例．     

基于模态的柔性机器人协调操作系统的动力学分析

目前，对于柔性机器人协调操作动力学问题的研究已经取得了一定的研究成果，但 是这些研究大多采用有限元法来建立动力学模型，很难将这种模型应用到实际的控制中．本 文利用假设模态法和Lagrange方程，建立了柔性机器人协调操作系统的动力学方程，并给出 平面两3R柔性机器人协调操作刚性负载完成目标运动规划任务的数值仿真算例，从而验证本 方法的可行性和正确性．     

一类受限柔性机器人的鲁棒性力／位置控制方法*

本文研究受限柔性连杆机器人的力／位置控制问题，首先导出受限柔性机器人的动力学模型，然后借助于微分几何理论将动力学模型转化为仿射非线性形式，再使用非线性反使系统线性化，最后对线性子系统设计变结构补偿器，使控制方法具有较高的精度和强鲁棒性。     

柔性机器人协调操作闭链负载机构的一般模型

本文利用闭链刚性负载内部运动参数之间的微分关系,在单柔性机器人有限元动力 学模型基础上,建立了系统的运动学和动力学协调约束条件,首次导出了基于负载运动任务 参数的柔性机器人协调操作闭链刚性负载的动力学方程,并给出了两3R柔性机器人协调操作 刚性四杆机构的仿真算例．     

柔性臂漂浮基空间机器人建模与轨迹跟踪控制

利用拉格朗日法和假设模态方法建立了末端柔性的两臂漂浮基空间机器人的非线性动力学方程．通过坐标变换,推导出一种新的以可测关节角为变量的全局动态模型，并在此基础上运用基于模型的非线性解耦反馈控制方法得到关节相对转角与柔性臂的弹性变形部分解耦形式控制方程．最后，讨论了柔性臂漂浮基空间机器人的轨迹跟踪问题，并通过仿真实例计算,表明该模型转换及控制方法对于柔性臂漂浮基空间机器人末端轨迹跟踪控制的有效性．     

输入有界的自由漂浮柔性空间机器人轨迹跟踪控制

针对自由漂浮柔性空间机器人轨迹跟踪控制问题, 首先利用拉格朗日和假设模态法建立了动力学模型. 分析系统动力学模型, 综合考虑欠驱动、柔性振动等特点, 将其简化为一种带有柔性振动扰动完全可控的动力学模型; 在此基础上, 考虑控制输入受限, 提出一种自适应状态反馈控制策略. 该策略采用自适应技术实时在线学习柔性振动扰动参数, 从而保证控制律对柔性振动扰动具有良好的鲁棒性; 最后, 基于Lyapunov方法证明了该控制策略能够实现关节期望轨迹的跟踪. 仿真验证了该控制策略对控制输入受限系统轨迹跟踪控制的有效性和可靠性.     

柔性两轮直立式自平衡仿人机器人的建模及控制

研究了柔性两轮直立式自平衡仿人机器人的动力学建模问题．运用拉格朗日方法和动力学原理建立了柔性两轮自平衡仿人机器人的动力学模型．使用弹簧模仿人的腰椎,并考虑了机器人的柔性腰椎弯曲;这是与以前机器人的不同之处．对得到的动力学模型进行了线性化处理,并建立其状态空间方程;由此建立的动力学模型结构简单,易于对机器人进行有效控制．仿真实验验证了系统的稳定性,对其实验结果进行的详细分析验证了系统建模和LQR控制器设计的合理性和有效性．     

变长度柔性双足机器人行走控制及稳定性分析

针对传统双足机器人模型缺少脚质量和躯干的问题,提出考虑摆动腿动态及躯干影响的柔性双足机器人模型,并对其行走控制及稳定性进行研究。首先,建立系统的动力学模型并采用欧拉-拉格朗日法推导了系统的动力学方程;同时,在弹簧负载倒立摆（SLIP）模型的基础上添加刚性躯干、脚质量及采用变长度伸缩腿,充分考虑躯干及摆动腿动力学对机器人行走步态的影响;其次,设计基于变长度腿的反馈线性化控制器来跟踪目标轨迹,以及调节摆动腿和躯干的姿态;最后,利用Newton-Raphson迭代法和庞加莱映射分析机器人的不动点及轨道稳定性条件,并在理论分析的基础上进行仿真。仿真结果表明,所提控制器可以实现机器人的周期行走,对外界干扰具有良好的鲁棒性,且雅可比矩阵所有特征值的模均小于1,能形成稳定的极限环,证明系统是轨道稳定的。     

连续型机器人研究综述

连续型机器人是一种新型的仿生机器人,采用“无脊椎”的柔性结构,不具有任何离散关节和刚性连 杆．其弯曲性能优良,对障碍物众多的非结构环境和工作空间狭小的受限工作环境适应能力强,不仅可以像传统机 器人那样在其末端安装执行器以实现抓取和夹持等动作,还可以利用其整个机器人本体实现对物体的抓取．本文对 连续型机器人的仿生原理与结构特点进行了分析,介绍了连续型机器人的研究现状,并对其潜在应用领域和未来研 究工作进行了探讨和展望．     

柔性机器人的动力学建模及其控制*

本文首先综述了近年来在柔性机器人动力学建模方面所取得的进展，着重介绍了目前较常见的几种建模方法和模型，同时对柔性机器人的控制问题进行了评述，指出了今后研究的方向。     

柔性机械臂运动轨迹的鲁棒自适应控制

本文针对多连杆柔性机械臂的运动轨迹问题，讨论了动力学建模，控制系统结构设计以及鲁棒自适应控制法，运用假设模记方法得到了柔性机械臂动力学所似方程，通过对柔性机械臂动力学特性分析，建立了等价动力学模型，依此提出了一种鲁棒自适应控制算法，并给出仿真研究结果。     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

Adaptive control of single rigid robotic manipulators interacting with dynamic environment — An overview

This paper presents the current state of the art in the adaptive control of single rigid robotic manipulators in the constrained motion tasks. A complete mathematical model of a single rigid robotic manipulator in contact with dynamic environment is presented. The basic approaches in deriving the environment model are given. The significance of the dynamic environment in the scope of the stability problem of the whole system robot-dynamic environment is emphasized. A classification of the adaptive contact control concepts in manipulation robotics is presented. The main characteristics of the most important adaptive strategies in constrained manipulation are given. The advantages and the drawbacks of the presented methods are emphasized. The paper covers results published a few years ago, as well as some recent trends in this field. One important result in the stability analysis of robotic manipulators in the constrained motion tasks is reported. Finally, some concluding remarks are given and possible future investigation trends in adaptive control of robotic manipulators are indicated.     

Experimental Control of a Two-Dof Flexible Robot Manipulator by Optimal and Sliding Methods

This paper presents an experimental study of a robust control scheme for flexible-link robotic manipulators. The design is based on a simple strategy for trajectory tracking which exploits the two-time scale nature of the flexible part and the rigid part of the dynamic equations of this kind of robotic arms: A slow subsystem associated with the rigid motion dynamics and a fast subsystem associated with the flexible link dynamics. Two experimental approaches are considered. In a first test an LQR optimal design strategy is used, while a second design is based on a sliding-mode scheme. Experimental results on a laboratory two-dof flexible manipulator show that this composite approach achieves good closed-loop tracking properties for both design philosophies, which compare favorably with conventional rigid robot control schemes.     

Modeling and control of two constrained manipulators

The coordinated control of two manipulators in the presence of environment constraints is studied in this paper. Such a control method is needed in applications in which the two manipulators grasp a common object whose motion is constrained by environments. The two manipulators are not only constrained with each other, but also constrained by the environment in their workspace. It is realized that the motion and constraint equations obtained directly from mechanics are not suitable for the control purpose. A set of equivalent equations are derived, which are in the standard form of the nonlinear system representation with clear state equations and output equations. A nonlinear feedback is found which exactly linearizes and decouples the dynamic nonlinear system of the two constrained manipulators. The coordinated controller design is then carried out based on the linearized system by using linear system theory.     

Dynamic state feedback control of two cooperative manipulators

Dynamic coordinated control of two robot manipulators that rigidly grasp a common object is studied. A dynamic coordinated control model for the two manipulators is derived that is suitable for system analysis and design in state space. The model takes into account kinematic and dynamic constraints between the two manipulators, and is explicitly described by non-linear state equtions and non-linear output equations in the state space. Since coordinated control requires the control of forces applied to the object by manipulators, the output equations include both position components and force components. While robotic systems with position outputs can be linearized using a static state feedback, systems with force outputs, such as the present two robot system, require a dynamic non-linear state feedback for exact linearization. By using dynamic non-linear feedback, coordinated control of two robotic manipulators is converted into a control problem of linear systems.     

Symbolic modeling and dynamic simulation of robotic manipulators with compliant links and joints

The explicit, non-recursive symbolic form of the dynamic model of robotic manipulators with compliant links and joints are developed based on a Lagrangian-assumed mode of formulation. This form of dynamic model is suitable for controller synthesis, as well as accurate simulations of robotic applications. The final form of the equations is organized in a form similar to rigid manipulator equations. This allows one to identify the differences between rigid and flexible manipulator dynamics explixitly. Therefore, current knowledge on control of rigid manipulators is likely to be utilized in a maximum way in developing new control algorithms for flexible manipulators.

Computer automated symbolic expansion of the dynamic model equations for any desired manipulator is accomplished with programs written based on commercial symbolic manipulation programs (SMP, MACSYMA, REDUCE). A two-link manipulator is used as an example. Computational complexity involved in real-time control, using the explicit, non-recursive form of equations, is studied on single CPU and multi-CPU parallel computation processors.     

一种双连杆柔性臂动力学模型的研究

针对末端位置受约束的双连杆柔性机械臂,通过哈密顿原理得到系统的分布参数模型,推导了描述关节角,柔性杆振动和接触力之间关系的动力学模型.根据3个假设条件推导柔性臂简化的集中参数动力学模型及准静态方程,利用了计算力矩法设计的控制器对模型进行控制,通过Matlab进行仿真,利用Matlab的符号运算功能,编制M文件实现数学模型自动推导,整个建模和运算过程简单、直观和高效,并绘制了参数轨迹图像,验证了模型的有效性,已应用到小波神经网络控制算法研究中.     

Adaptive synchronised tracking control for multiple robotic manipulators with uncertain kinematics and dynamics

In this study, a new adaptive synchronised tracking control approach is developed for the operation of multiple robotic manipulators in the presence of uncertain kinematics and dynamics. In terms of the system synchronisation and adaptive control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other robotic manipulators. On the other hand, the developed approach can cope with kinematic and dynamic uncertainties. The corresponding stability analysis is presented to lay a foundation for theoretical understanding of the underlying issues as well as an assurance for safely operating real systems. Illustrative examples are bench tested to validate the effectiveness of the proposed approach. In addition, to face the challenging issues, this study provides an exemplary showcase with effectively to integrate several cross boundary theoretical results to formulate an interdisciplinary solution.