一种变直径球形机器人结构设计与控制
Structure Design and Control of a Variable-diameter Spherical Robot
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摘要: 为给球形机器人增加变直径功能, 设计了一种由20个六边形单元、12个五边形单元及其连接件组成的变直径球壳机构, 在其表面覆盖一层弧面元件, 以确保球壳在滚动中的平顺性。为确保球壳内部机构始终处于球壳球心位置, 设计了差动式对中机构。分析差动式对中机构中结构尺寸与球壳直径的关系, 采用PID(比例-积分-微分)控制器, 使球形机器人能够控制自身直径在220~329 mm之间改变。在机器人坠落触地时, 利用球壳直径的改变与对中机构中电机的抵抗扭矩减小冲击, 保护机器人内部结构。为使球形机器人具备在水平面内的全向运动能力, 将机器人的运动分解为直线运动和转向运动。采用拉格朗日动力学方程对机器人直线前进运动进行分析, 对前进电机旋转角速度进行闭环控制, 使得机器人能够较为准确地跟踪基于高斯函数的目标速度曲线。采用牛顿-欧拉法对转向运动进行分析, 对质心在机器人内部的侧向偏置进行闭环控制, 实现了半径约为1 m的匀速圆周运动。Abstract: To add a variable-diameter function to the spherical robot, a variable-diameter spherical shell mechanism consisting of 20 hexagonal cells, 12 pentagonal cells and their connectors is designed, with a layer of curved elements covering the surface of the spherical shell to ensure the smoothness of the spherical shell during rolling. In order to ensure that the internal mechanism is always in the center of the spherical shell, a differential centering mechanism is designed. The relationship between the structure size of the differential centering mechanism and the diameter of the spherical shell is analyzed, and a PID (proportional-integral-derivative) controller is used to enable the spherical robot to control its diameter within 220 \sim 329 mm. In case of a fall to the ground, the change in diameter of the spherical shell and the resistance torque of the motors in the centering mechanism are used to reduce the impact and protect the internal structure of the robot. In order to equip the spherical robot with omnidirectional motion in the horizontal plane, the motion of the robot is decomposed into linear and steering motions. The Lagrangian dynamics equation is used to analyze the linear forward motion, and the closed-loop control of the rotational angular velocity of the forward motor enables the robot to more accurately track the target velocity curve based on the Gaussian function. The Newton-Euler method is used to analyze the steering motion, and the closed-loop control is applied to the center-of-mass lateral bias inside the robot to achieve a uniform circular motion with a radius of about 1 m.