Modeling and Control of Closed Kinematic Chains

闭合运动链的建模与控制

• 批准号: 9900194
• 负责人: Fathi Ghorbel
• 金额: $ 21万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9900194&HistoricalAwards=false
• 关键词: Modeling; Control; Closed; Kinematic; Chains

Abstract: Closed kinematic chain mechanical systems promise advantages over open chains in terms of less moving inertia, faster and stiffer motion, and much better force-to-weight ratio. However, derivation of dynamic equations of motion for closed chain mechanisms suitable for controller design is still a challenge because of the complexity of the kinematics, dynamics, and control analyses. This research identifies the central difficulties in the modeling and control of these systems and provides an analytical framework to derive dynamics models appropriate for advanced model-based control laws. Two modeling-for-control approaches are investigated. In the first approach, a formulation of the dynamics equations of closed chain mechanisms in terms of independent generalized coordinates (reduced model) is developed. Methods to extend the wealth of control laws of open chains to closed chains while taking into consideration the local and implicit nature of the reduced model are considered. The second approach is to transform the Differential Algebraic Equations (DAE) describing closed kinematic chains into a singularly perturbed differential equation system with asymptotically stable fast dynamics. It follows that when a proper control design is made for the singularly perturbed system, then for a small value of an artificially introduced small parameter, the response of the controlled singularly perturbed system would be quite close to that of the controlled DAE system (closed chain mechanism). The techniques developed in this research potentially have applications to many other systems described by DAE. The educational objective of this research is to help introduce dynamic modeling and control of complex closed chain dynamical systems in the traditional dynamics and control courses and laboratories. In particular, a robotic device will be made accessible for control experimentation over the World Wide Web for a more effective dissemination of the results of this research and integration in control education.

摘要：闭式运动链机械系统在运动惯性更小、运动速度更快、更硬、力重比更好等方面具有开式运动链机械系统的优点。然而，由于运动学、动力学和控制分析的复杂性，适合于控制器设计的闭链机构的动力学方程的推导仍然是一个挑战。本研究确定了这些系统建模和控制的主要困难，并提供了一个分析框架来推导适合于高级模型控制律的动力学模型。研究了两种控制建模方法。在第一种方法中，建立了独立广义坐标下的闭链机构动力学方程（简化模型）。考虑了简化模型的局域性和隐式性，将开链的控制律扩展到闭链的方法。第二种方法是将描述闭合运动链的微分代数方程转化为具有渐近稳定快速动力学的奇摄动微分方程组。由此可见，当对奇异摄动系统进行适当的控制设计时，对于人为引入的小参数的一个小值，被控奇异摄动系统的响应将与被控DAE系统（闭链机构）的响应非常接近。在这项研究中开发的技术有可能应用于DAE描述的许多其他系统。本研究的教学目的是帮助在传统的动力学与控制课程和实验室中引入复杂闭链动力系统的动力学建模和控制。特别是，将在万维网上提供一种机器人装置供控制实验使用，以便更有效地传播这项研究的结果并将其纳入控制教育。