基于U-K方法的多自由度串联/冗余驱动并联多刚体机构模糊动力学建模与最优鲁棒控制基础研究

This research proposal mainly aims at the problem of dynamic modeling and optimal robust control of complex multi-rigid-body mechanism which includes serial mechanism with large numbers of degrees of freedom and parallel mechanism with redundant actuation. Based on Udwadia-Kalaba approach, we propose the three-step modeling approach which is easy for automatic modeling and applicable to systems with large numbers of degrees of freedom. The second-order structural passive constraint equation is to be established, and considering the nonideal constraint of friction force, we try to obtain the closed-form friction model and closed-from fundamental equation of constrained motion. The mechanism’s parameter uncertainty is described by using fuzzy set theory, and by applying Udwadia approach of inverse dynamics (Moore-Penrose generalized inverse can deal with redundant actuation problem of parallel mechanism), the system performance requirement is converted to second-order servo constraint equation and deterministic (not if-then-rules-based) robust control is employed to assure practical stability (uniform ultimate boundedness). The trade-off between system performance and the cost suggests an interesting optimal gain design and the unique closed-form optimal gain is to be obtained. Simulation software system is to be developed and the 7 DOF snake robot and redundantly actuated parallel robot are employed to verify the theory’s feasibility and superiority. This research is devoted to providing a systematic new theoretical frame and realization tool for dynamic modeling and control of serial/parallel multi-rigid-body mechanism.

本项目针对多自由度串联及冗余驱动并联多刚体机构的动力学建模与控制基础问题开展研究。基于U-K建模法，提出自动化建模程度更高的适用多自由度系统的三步建模法，建立机构的二阶结构性被动约束方程，考虑非理想约束摩擦力，得到摩擦力解析模型及解析形式的约束运动基础方程。提出用模糊集理论去描述机构参数不确定性，基于Udwadia逆动力学方法(用M-P广义逆可处理并联机构的冗余驱动问题)，将性能要求写为二阶伺服约束方程，进行确定性(非基于if-then模糊规则)鲁棒控制设计，达到实际稳定(最终一致有界)；鲁棒控制参数大小权衡着系统的性能与控制的代价，为此将进行最优参数设计并力求得到解析解。开发仿真软件系统并搭建七自由度蛇形机器人与平面二自由度冗余驱动并联机构来验证理论的实际可行性与优越性。本项目为串/并联多刚体机构的动力学建模与智能控制提供系统的新理论框架与实现手段。

本项目针对多自由度串联及冗余驱动并联多刚体机构的动力学建模与控制基础问题开展了一系列科学研究。基于U-K建模法，提出了自动化建模程度更高的适用多自由度系统的三步建模法，建立了机构的二阶结构性被动约束方程，并考虑非理想约束摩擦力，得到了摩擦力解析模型及解析形式的约束运动基础方程。提出并研究了使用模糊集理论来描述机构参数不确定性，基于Udwadia逆动力学方法(用M- P广义逆可处理并联机构的冗余驱动问题)，将性能要求写成二阶伺服约束方程，设计了确定性( 非基于if-then模糊规则)鲁棒控制算法，达到了实际稳定(最终一致有界)；鲁棒控制参数大小权衡着系统的性能与控制的代价，并进行了最优参数设计得到解析解。本项目为串/并联多刚体机构的动力学建模与智能控制提供了系统的新理论框架与实现手段。在完成本项目的过程中，我们开发了仿真软件系统并搭建了七自由度蛇形机器人与平面二自由度冗余驱动并联机构平台，验证了理论的实际可行性与优越性。我们使用Matlab编写了仿真程序，并在实验平台进行了实验。基于仿真和实验我们发表录用了15篇论文（其中10篇SCI，1篇EI，3篇IEEE会议论文），4篇专利，4篇软著。我们研究理论方法的同时，常与同行进行沟通交流，参加了两次IEEE的会议汇报。参加了2018年度中国机器人学术年会。基于本项目我们还开发了一套cSPACE系统，可用于半硬件在环仿真。我们建立了自己的网站用于展示我们的研究成果。