The Study of Dynamic Simulation of the Passive Dynamic Quasi-Quarupedal Walker
|School||Harbin Institute of Technology|
|Course||Mechanical and Electronic Engineering|
|Keywords||passive dynamic walking dynamic analysis domain of attraction period-doubling bifurcation dynamic simulation|
At present, the walking robot is a hot topic in the robot research field, especially the passive dynamic walking robot which has high efficiency and simple structure. This paper analyses the dynamic characters of the passive dynamic quasi-quadrupedal walker.Firstly, the three-dimensional model of the robot and its simplified structure of the multi-rigid body dynamics model are established. Through the analysis of the kinetic characteristic of the robot, the general differential equations of the swing stage and the transition stage follow immediately from the collision are deduced using Lagrange Equation and Moment of momentum theorem. Select the follow immediately from the collision of the phase plane as the Poincarésection. we select initial values which can make the robot walk steadily in the iterative solution according to the law of conservation of energy. Based on the given mathematics model, the forth order Runge-kutta method is used to draw their fixed point of the robot on the Poincarésection. We analyze the eigenvalues of Jacobi matrix to estimate the stability of the fixed point and take the stable fixed point as the initial conditions of the movement.Then, the center point cell mapping method is employed to obtain the finite steps domain of attraction of the fixed point. The size of the domain of attraction can measure the stability of the movement. Therefore by calculating the volume of the domain of attraction to analyze the effect of the stability of the robot by mass ratio, the ground slope and so on in this paper. And based on this, we choose the reasonable parameters to make the robot have a larger stability margin through the advisement of the effect of various parameters to the stability of the robot. The convert and evolution course of periodical motion, double-periodical bifurcation of the system response are opened out by branch chart, phase-plane diagram and so on. The bifurcation motion caused by parameters as mass ratio, the ground slope and so on are deeply studied. Investigate the effect of parametric variation on the stability by solving the fixed point when parameters changed.Finally, utilizing ADAMS to set up the virtual prototype, the analysis of dynamics is performed by taking the fixed point and the state parameters in the domain of attraction which are obtained in numerical simulation as initial conditions. Characteristic curves of the robot with time are given. By comparing with the preceding numerical simulation analysis results, verified dynamics building type and exactness of the analytical method. Find out that the robot has very good stability by analyzing the simulation of the movement of the robot which walks with eccentric load.