光学 精密工程, 2019, 27(8): 1800, 网络出版: 2019-08-01

轮-腿复合式移动机器人球面并联腿机构的动力学模型

Dynamic model of spherical parallel mechanism for wheel-leg hybrid mobile robot
作者单位

山东大学(威海) 机电与信息工程学院, 山东 威海 264209

摘要
为适应现代工程领域对移动机器人的新要求, 拓展移动机器人的作业场合, 该文提出了一种轮-腿复合式移动机器人球面并联腿机构。首先, 基于球面并联腿机构的闭环约束方程和旋转变换矩阵构建了其位置逆解数学模型; 接着, 采用代数消元法推导出了球面并联腿机构的位置正解的解析解; 然后, 运用影响系数法推导出了球面并联腿机构的速度和加速度影响系数矩阵; 在此基础上, 运用拉格朗日方法建立了球面并联腿机构的动力学模型。运用数值仿真对运动学和动力学模型进行了验证, 仿真得到了给定位姿数据与计算位姿数据之间的最大误差为0.012 7 rad, 误差不超过实际值的2.43%, 发现了球面并联腿机构驱动力的理论曲线和虚拟样机仿真曲线吻合, 两者之间的误差稳定在0~1 N的合理范围内, 验证了运动学和动力学模型的正确性。研究结果为轮-腿复合式移动机器人的步态规划和运动控制提供了理论参考。
Abstract
To meet the new requirements for mobile robots in the field of modern engineering and expand the working opportunities of mobile robots, a spherical parallel leg mechanism of a wheel-leg composite mobile robot was proposed in this study. First, based on the closed-loop constraint equation and rotation transformation matrix of the spherical parallel leg mechanism, a mathematical model of its inverse position solution was constructed. Next, an analytical solution of the forward position solution of the spherical parallel leg mechanism was deduced by the algebraic elimination method. Then, the influence coefficient matrix of the velocity and acceleration of the spherical parallel leg mechanism was derived from the influence coefficient method. On this basis, the Lagrangian method was used. Kinematics and dynamics models were validated by numerical simulation. The maximum error between the given and calculated position data was 0.012 7 rad, and the error did not exceed 2.43% of the actual value. It is also found that the theoretical curve of the driving force of the spherical parallel leg mechanism coincided with the simulation curve of the virtual prototype. The error between the two was stable within a reasonable range of 0-1 N. The correctness of the kinematics and dynamics model is proved. The results from this study provide a theoretical reference for gait planning and motion control of a wheel-leg hybrid mobile robot.
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