Modeling And Stability Analysis Of Biped Robot

As a biped robot moves like a human, it is more flexible and adaptable than other types of robots. Besides, the study of biped robots has very important significance in academic research, so it becomes one of the hotspots of robotics technology. Because the biped robot is a nonlinear dynamic system with variable structure and strong coupling, its precise mathematical model and the analysis about its stability are the boundary of the depth research of a biped robot.In order to achieve the motion of the biped robot in roll, pitch and yaw direction, we set that the robot has 12DOF, then D-H method is used to obtain the forward kinematics model of biped robot, and the inverse kinematics model was derived by the method of solving algebraic geometry. Based on the kinematics model, the forward dynamic model of a bipedal robot was established by Lagrange equation, and the inverse dynamics model was obtained using Newton-Euler equation by recursive method. Finally, a gait of biped robot was planned, then the driving force of every joint was calculated based on the inverse dynamic model, and dynamic simulation of the biped robot was realized by the virtual prototype in the ADAMS software.In the process of biped walking, the swing leg has a collision with the ground, which causes the robot's state changing immediately. The collision was constrained in this article, thereby the hybrid dynamic model of the biped robot was established, and the notions of stability and asymptotic stability of its periodic orbits were defined. Let the state just before the swing leg impacting with the ground as the Poincarésection, then the Poincarémap of the hybrid model was define. According to the characteristic of a fixed point of the Poincarémap, we analyzed the periodicity and convergence of the bipedal's motion. Finally, the moment of a three-link planar bipedal was simulated, and was analyzed according to the criterion based on Poincarémap.