Research on System Establishment and Motion Control of a Two Coaxial Pendulums Driven Spherical Robot 

Author  ZhaoBo 
Tutor  SunLiNing 
School  Harbin Institute of Technology 
Course  Mechanical and Electronic Engineering 
Keywords  spherical robot two coaxial pendulums kinematics model dynamics model linear motion control turning motion control 
CLC  TP242.6 
Type  PhD thesis 
Year  2011 
Downloads  142 
Quotes  0 
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 selfprotection 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 startstop 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 followup 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.