主要针对多机器人协调吊运系统的工作空间和运动稳定性进行分析，首先根据吊运系统驱动配置情况将系统分为三类；其次应用牛顿欧拉方程建立了系统的广义动力学模型；随后，采用虚拟柔索法给出了该欠约束系统力旋量封闭的解决方案，并对系统工作空间进行了分析，依据广义逆矩阵理论给出了系统满足运动要求时柔索拉力的最优解；紧接着，根据克拉索夫斯基法给出了吊运系统的运动稳定性判据；最后根据实例参数，对三类系统的工作空间进行了数值仿真分析，并应用方阵特征值分解法对工作空间中所有点的稳定性进行了计算，结果表明，三类系统在各自工作空间内均是稳定的，并获得了三类系统的稳定程度关系，研究结果为后续优化系统运动轨迹规划和防摆控制打下基础。
Abstract
This paper major presents the workspace and dynamic stability of multi-robot collaboratively towing system. Firstly, the towing system was divided into three types of systems by drive configuration. Secondly, the generalized dynamic model of system was established by Newton-Euler equations. Next, the method to solve wrench enclosed of under-constrained system was given by using the method of virtual cables, and its workspace was analyzed, optimal result of the cables tension that satisfy the motion requirements of the system was given based on generalized inverse matrix theory. Subsequently, the criterion of dynamic stability was given by Krasovskii method. Finally, the system was parameterized by combination with practical example, numerical simulation and analysis of the workspaces of three types of systems were given. Stability calculations of all workspace’s spots were done by using method of square matrix eigenvalue decomposition. The results show that three types of systems were dynamic stability in themselves workspaces, and relationships for degree of stable of three kinds of system were obtained. The results have provided foundation for further research on optimization of motion trajectory planning and anti-sway control of towing system.
关键词
吊运系统 /
多机器人系统 /
广义动力学模型 /
工作空间 /
稳定性分析
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Key words
towing system /
multi-robots system /
generalized dynamic model /
workspace /
stability analysis
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