Stability Analysis And Control Studies On The Passive Dynamic Walking Biped Robot

For the biped robot's potential application and practical value, related researches have aroused much attention by many researchers. Though research on biped robot has acquired remarkable achievements, the developmental level achieves far from the expectation of human being. One of the critical reasons is that movement capability is very poor. It mainly reflects that the biped walking is slow and inefficient. Passive biped robots without external inputted torque can successfully walk down an inclined slope in a natural,efficient and steady gait. The motive power of such robots comes from the conversion of the robot's gravitational potential energy as it descends down the slope. But the stable passive gaits can be found on shallow slopes, and are sensitive to large disturbance and chaning slopes. Therefore, the passive gaits have some limitations. Based on the research on the passive dynamic walking, the key of this dissertation covers the stability analysis and design of control laws for the passive dynamic walking biped robot. These control laws can make the biped robot walk naturally with high speed,high efficiency. Its main contents are presented as follows:Local stability of the passive walking robot with knees is analyzed with Poincarémapping method. Since one walking cycle of the passive walking robot with knees is separated into two swing phases and two impact phases, the construction of poincarémapping and the calculation of floquet multiplier are critical to analyze the local stability of biped robot. Since the swing phase of motion can be described by the nonlinear differential equation, and impact phase can be described by the discrete algebraic mapping, the model of the walking cycle of the biped robot can be described as a hybrid system. Semi-analytical method to compute the Jacobian matrix of the poincarémap for the hybrid system is proposed on the basis of the disturbance theory and the linearization method. Then the floquet multiplier is obtained. Jacobian matrix of the poincarémap for the passive walking robot with knees is calculated with the semi-analytical method. The effects of slope angle,model parameters on the floquet multiplier is studied, and the optimal slope angle and model parameters are obtained.Method to calculate the basin of attraction of the limit cycle is proposed. And the global stability of the passive dynamic walking robot with knees is analyzed by the means of calculating the basin of attraction. In order to decrease the computation, poincarécell mapping method is putted forward, which is the combination of poincarémapping and cell mapping method. And the basin of attraction of the passive biped robot with knees is computed with poincarécell mapping method. Based on the Poincarécell mapping method, poincaré-like-alter-cell-to-cell mapping method is presented to calculate the basin of attraction of the passive biped robot with knees. Poincaré-like-alter-cell-to-cell mapping method needs less computation and has higher accuracy. Numerical experiment results show that poincaré-like-alter-cell-to-cell mapping method can not only compute the basin of attraction of limit cycle, but also can compute the fixed point of poincarémapping. Randomness of selecting the initial value for the Newton-Raphson interation is avoided with this method. The influence of the model parameters on the global stability is studied with poincaré-like-alter-cell-to-cell mapping method.The effects of the normalized parameters include slopes,mass ratio between the thigh and shank,length ratio between the thigh and the shank on the arising of period-doubling and chaos are analyzed with simulations. The simulation results of period-doubling and chaos of gait descriptors for passive biped robot with knees, including period,initial state of stance leg are presented with increasing the slope angle. Based on the delay feedback control theory and the principle of bionics, bionic walking control for biped robot using adaptive constant torque and sensor feedback is proposed to make the chaotic gait converge to a stable cycle gait. Since the structure of controller is simple, the controller is used easily in practice. Simulation results verify the effectiveness of this control algorithm for the biped robot with knees. And the control algorithm can enhance the stability and robustness.How to design the control strategy to enlarge the ground slope range for the passive walking robot and make the stable walking gaits on varying slopes exist has been studied. Switching control strategy between different slopes is presented based on Lyapunov stabitity theory and robust control theory. And stability of the closed loop system is analyzed. Simulation results demonstrated that the switching controller between different slopes can make the passive walking robot realize switching smoothly between different passive walking gaits for different slopes with low energy dissipation in finite time, and the switching process has strong robustness for the disturbances and the model errors. Comparative experimental results show that the switching controller is superior to the energy based control, and it can increase the limit cycle convergence rate and improve the system stability easily. A wide range of stable walking control strategy is proposed to make the biped robot have stable gaits on flat ground or downhill slopes or uphill slopes. Simulation results verify the effectiveness of the control algorithm.The gravity field parameter is proportional to the walking speed, when the biped robot with knees is simplified to be an inverted pendulum. A control strategy based on gravity compensation is developed to enlarge the walking speed range. By adjusting the gravity field parameter of controller, the biped robot can achieve the desired walking speed and have high-speed walking. Simulation results show that the walking speed is accelerated with increasing the gravity field parameter, and the mechanical energy and kinetic energy are increased too. The limit cycles of the gaits at the target speed is taken as the tracking trajectory, and speed switching control strategy is proposed to make the walking speeds converge to the target value. Then the biped robot can walk stably at the different walking speeds. Simulation results show that the speed switching controller makes the gaits at different walking speeds switch smoothly, and the switching process has strong robustness.Finally, the main content of this dissertation is summarized, and the further researches are discussed.