同轴双偏心质量驱动球形机器人系统建立及运动控制研究
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摘要
球形机器人是一种以滚动方式行走的新型移动机器人,与传统的轮式、足式移动机器人相比,球形机器人具有运动灵活、自我保护能力强、环境适应能力强等特点,独特的机械结构和运动原理使其能够应用于多尘、潮湿、崎岖的复杂环境。球形机器人在军事、工业、生活等方面都具有广泛的应用前景,是目前智能机器人领域的研究热点之一。
在总结现有球形机器人构型的基础上,本文将球形机器人中应用最广泛的偏心质量驱动构型进行改进,提出一种同轴双偏心质量驱动球形机器人构型。在对同轴双偏心质量驱动球形机器人运动原理分析的基础上,对机器人进行了机械结构设计。针对所设计的球形机器人运动学特性,为了避免求解过程中出现奇点,采用卡尔丹角描述机器人的位置和姿态,对同轴双偏心质量驱动球形机器人进行运动学分析。利用平面几何关系得到了机器人运动过程中球壳倾角与轨迹半径之间的对应关系,通过球壳与地面之间的纯滚动约束条件建立了球心位置坐标的约束方程,通过位置变换矩阵建立了球壳及偏心质量在相对坐标系与惯性坐标系之间的速度映射关系,为进一步的动力学建模及控制系统研究奠定了基础。
本文将球形机器人的运动分为直线运动、原地转向运动和圆弧轨迹运动分别进行运动控制研究。为了使球形机器人直线运动能够平稳启停且速度可控,将直线运动模型简化为平面内单输入两自由度的欠驱动系统,利用拉格朗日方程建立了机器人直线运动的动力学模型,在此基础上提出了一种基于高斯函数的直线运动控制方法,通过仿真验证了控制方法的有效性。为了补偿外界扰动对机器人运动速度的影响,提出了一种基于参数调整的直线运动控制策略,在特殊的时间点根据机器人速度误差调整高斯函数,通过改变机器人的加速度实现了速度补偿。
针对球形机器人特有的原地转向运动,分析了同轴双偏心质量驱动球形机器人原地转向运动的运动原理,利用动量矩定理建立了原地转向运动的动力学模型,在此基础上提出一种基于粘滑原理的原地转向运动控制方法,通过余弦控制函数对两个偏心质量进行运动规划,利用偏心质量运动产生的惯性力矩实现原地转向运动。分析了余弦控制函数中各参数值对机器人运动的影响,并通过仿真验证了原地转向运动控制方法的有效性。
为了使球形机器人圆弧轨迹运动速度与轨迹半径均可控,研究了同轴双偏心质量驱动球形机器人圆弧轨迹运动原理,利用动量矩定理建立了圆弧轨迹运动动力学模型,提出一种基于单摆运动与随动控制相结合的控制策略,机器人圆弧轨迹运动分解为前向滚动与侧向滚动分别进行控制,采用正弦控制函数对偏心质量进行运动规划产生适当的惯性力,通过控制球壳相对于地面的倾角控制轨迹半径;采用位置随动控制实现机器人前向滚动速度控制。设计了圆弧轨迹运动控制器,并通过仿真验证了该控制策略的有效性。
最后搭建了同轴双偏心质量驱动球形机器人样机实验系统,介绍了球形机器人硬件及软件系统构成,对球形机器人样机进行了直线运动实验研究,实验结果表明球形机器人能够在高斯控制函数作用下做速度可控的直线运动,基于参数调整的控制策略能够补偿外界干扰对机器人速度的影响;开展了同轴双偏心质量驱动球形机器人原地转向运动实验研究,实验结果表明机器人能够在余弦控制作用下做原地转向运动;在室内和室外相对平坦的地面进行了圆弧轨迹运动实验研究,实验结果表明机器人速度和转弯半径均可控,验证了圆弧轨迹运动控制策略的有效性。
Spherical robot, which moves by the way of rolling, is a new kind of mobile robot. Compared with traditional wheeled and legged robots, the spherical robot features movement agility, good self-protection ability and strong environmental adaptability. The unique mechanism and motion principle assure spherical robot can be applied in dusty, damp and rugged environment. Spherical robot has extensive application prospect in military, industry and everyday life, which is one of the research focuses in the intelligent robot field.
Based on the mechanism analysis of the existing spherical robots, the pendulum driven mechanism which is widely used in spherical robot is improved, and a new two coaxial pendulums driven mechanism is proposed. Based on the analysis of motion principle, the mechanical structure of two pendulums driven spherical robot is designed. Aimed at the kinematic characteristics of spherical robot, in order to avoid computing singular point, Cardano angle is adopted to describe the position and attitude and to analyze the kinematics of spherical robot. The relationship between pitch angle of ellipsoidal shell and radius of motion trajectory is built based on plane geometry. The constraint equation is deduced according to the rolling constraints between shell and ground. The velocity map of shell and pendulum between relative coordinate system and inertial coordinate system is built based on the position transformation matrix, which laid the foundation for dynamics modeling and motion control.
The motion of the spherical robot is divided into linear motion, turning in place motion and circular trajectory motion which are studied separately in this paper. In order to assure the smooth start-stop and the controllabe velocity, the model of linear motion is simplified as a plane underactuated system which has single input and two degrees of freedom. The dynamics model of linear motion is built with Lagrange equation; the linear control method based on Gaussian function is proposed, and the control method is validated by simulation. In order to compensate the motion velocity which is disturbed by the environment, a parameter adjustment based linear control strategy is proposed. The Gaussian function is adjusted at special time according to the velocity error of spherical robot, and the velocity compensation is realized by the regulation of acceleration.
Aimed at the turning in place motion of spherical robot, the motion principle of the two coaxial pendulums driven spherical robot is analyzed. The dynamics model of turning in place motion is built by the theorem of moment of momentum. On this basis, a turning in place motion control method is proposed. The turning in place motion is realized by the inertia moment which is generated by the two pendulums controlled by cosine function. The effect of the parameters of cosine function on the motion of robot is analyzed, and the control method of turning in place motion is validated by simulation.
In order to acquire the controllable velocity and radius of circular trajectory motion, the motion principle of the motion is studied, and the dynamics model of circular trajectory motion is built according to the theorem of moment of momentum. A control strategy based on the combination of pendulum motion and follow-up control is proposed. The circular trajectory motion of spherical robot is divided into forward roll and pitch roll. The motion of pendulum is planned by the sine function to generate appropriate initial force, so the radius of trajectory can be regulated by the tilt angle between shell and ground. The velocity control of forward roll is achieved by position servo control. The controller of circular trajectory motion is designed, and the control strategy is validated by simulation.
Finally, the prototype experiment system of two coaxial pendulums driven spherical robot is built. The hardware and software system is introduced. The prototype experiment of linear motion is carried out, which shows that the velocity of linear motion is controllable acted by the Gaussian function; the effect of environment on velocity can be compensated by the parameters adjustment control strategy. The prototype experiment of turning in place motion is performed to validate the effectiveness of the control method which is based on cosine control function. The prototype experiment of circular trajectory motion is carried out in indoor environment and relatively flat outdoor environment respetively. The result shown that the forward velocity and radius of circular trajectory is controllable, which validates the effectiveness of the control strategy of circular trajectory motion.
在总结现有球形机器人构型的基础上,本文将球形机器人中应用最广泛的偏心质量驱动构型进行改进,提出一种同轴双偏心质量驱动球形机器人构型。在对同轴双偏心质量驱动球形机器人运动原理分析的基础上,对机器人进行了机械结构设计。针对所设计的球形机器人运动学特性,为了避免求解过程中出现奇点,采用卡尔丹角描述机器人的位置和姿态,对同轴双偏心质量驱动球形机器人进行运动学分析。利用平面几何关系得到了机器人运动过程中球壳倾角与轨迹半径之间的对应关系,通过球壳与地面之间的纯滚动约束条件建立了球心位置坐标的约束方程,通过位置变换矩阵建立了球壳及偏心质量在相对坐标系与惯性坐标系之间的速度映射关系,为进一步的动力学建模及控制系统研究奠定了基础。
本文将球形机器人的运动分为直线运动、原地转向运动和圆弧轨迹运动分别进行运动控制研究。为了使球形机器人直线运动能够平稳启停且速度可控,将直线运动模型简化为平面内单输入两自由度的欠驱动系统,利用拉格朗日方程建立了机器人直线运动的动力学模型,在此基础上提出了一种基于高斯函数的直线运动控制方法,通过仿真验证了控制方法的有效性。为了补偿外界扰动对机器人运动速度的影响,提出了一种基于参数调整的直线运动控制策略,在特殊的时间点根据机器人速度误差调整高斯函数,通过改变机器人的加速度实现了速度补偿。
针对球形机器人特有的原地转向运动,分析了同轴双偏心质量驱动球形机器人原地转向运动的运动原理,利用动量矩定理建立了原地转向运动的动力学模型,在此基础上提出一种基于粘滑原理的原地转向运动控制方法,通过余弦控制函数对两个偏心质量进行运动规划,利用偏心质量运动产生的惯性力矩实现原地转向运动。分析了余弦控制函数中各参数值对机器人运动的影响,并通过仿真验证了原地转向运动控制方法的有效性。
为了使球形机器人圆弧轨迹运动速度与轨迹半径均可控,研究了同轴双偏心质量驱动球形机器人圆弧轨迹运动原理,利用动量矩定理建立了圆弧轨迹运动动力学模型,提出一种基于单摆运动与随动控制相结合的控制策略,机器人圆弧轨迹运动分解为前向滚动与侧向滚动分别进行控制,采用正弦控制函数对偏心质量进行运动规划产生适当的惯性力,通过控制球壳相对于地面的倾角控制轨迹半径;采用位置随动控制实现机器人前向滚动速度控制。设计了圆弧轨迹运动控制器,并通过仿真验证了该控制策略的有效性。
最后搭建了同轴双偏心质量驱动球形机器人样机实验系统,介绍了球形机器人硬件及软件系统构成,对球形机器人样机进行了直线运动实验研究,实验结果表明球形机器人能够在高斯控制函数作用下做速度可控的直线运动,基于参数调整的控制策略能够补偿外界干扰对机器人速度的影响;开展了同轴双偏心质量驱动球形机器人原地转向运动实验研究,实验结果表明机器人能够在余弦控制作用下做原地转向运动;在室内和室外相对平坦的地面进行了圆弧轨迹运动实验研究,实验结果表明机器人速度和转弯半径均可控,验证了圆弧轨迹运动控制策略的有效性。
Spherical robot, which moves by the way of rolling, is a new kind of mobile robot. Compared with traditional wheeled and legged robots, the spherical robot features movement agility, good self-protection ability and strong environmental adaptability. The unique mechanism and motion principle assure spherical robot can be applied in dusty, damp and rugged environment. Spherical robot has extensive application prospect in military, industry and everyday life, which is one of the research focuses in the intelligent robot field.
Based on the mechanism analysis of the existing spherical robots, the pendulum driven mechanism which is widely used in spherical robot is improved, and a new two coaxial pendulums driven mechanism is proposed. Based on the analysis of motion principle, the mechanical structure of two pendulums driven spherical robot is designed. Aimed at the kinematic characteristics of spherical robot, in order to avoid computing singular point, Cardano angle is adopted to describe the position and attitude and to analyze the kinematics of spherical robot. The relationship between pitch angle of ellipsoidal shell and radius of motion trajectory is built based on plane geometry. The constraint equation is deduced according to the rolling constraints between shell and ground. The velocity map of shell and pendulum between relative coordinate system and inertial coordinate system is built based on the position transformation matrix, which laid the foundation for dynamics modeling and motion control.
The motion of the spherical robot is divided into linear motion, turning in place motion and circular trajectory motion which are studied separately in this paper. In order to assure the smooth start-stop and the controllabe velocity, the model of linear motion is simplified as a plane underactuated system which has single input and two degrees of freedom. The dynamics model of linear motion is built with Lagrange equation; the linear control method based on Gaussian function is proposed, and the control method is validated by simulation. In order to compensate the motion velocity which is disturbed by the environment, a parameter adjustment based linear control strategy is proposed. The Gaussian function is adjusted at special time according to the velocity error of spherical robot, and the velocity compensation is realized by the regulation of acceleration.
Aimed at the turning in place motion of spherical robot, the motion principle of the two coaxial pendulums driven spherical robot is analyzed. The dynamics model of turning in place motion is built by the theorem of moment of momentum. On this basis, a turning in place motion control method is proposed. The turning in place motion is realized by the inertia moment which is generated by the two pendulums controlled by cosine function. The effect of the parameters of cosine function on the motion of robot is analyzed, and the control method of turning in place motion is validated by simulation.
In order to acquire the controllable velocity and radius of circular trajectory motion, the motion principle of the motion is studied, and the dynamics model of circular trajectory motion is built according to the theorem of moment of momentum. A control strategy based on the combination of pendulum motion and follow-up control is proposed. The circular trajectory motion of spherical robot is divided into forward roll and pitch roll. The motion of pendulum is planned by the sine function to generate appropriate initial force, so the radius of trajectory can be regulated by the tilt angle between shell and ground. The velocity control of forward roll is achieved by position servo control. The controller of circular trajectory motion is designed, and the control strategy is validated by simulation.
Finally, the prototype experiment system of two coaxial pendulums driven spherical robot is built. The hardware and software system is introduced. The prototype experiment of linear motion is carried out, which shows that the velocity of linear motion is controllable acted by the Gaussian function; the effect of environment on velocity can be compensated by the parameters adjustment control strategy. The prototype experiment of turning in place motion is performed to validate the effectiveness of the control method which is based on cosine control function. The prototype experiment of circular trajectory motion is carried out in indoor environment and relatively flat outdoor environment respetively. The result shown that the forward velocity and radius of circular trajectory is controllable, which validates the effectiveness of the control strategy of circular trajectory motion.
引文
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