Kinematics velocity and dynamic modeling of biped robot

Abstract

In this paper, we have attempted to focus on the kinematics velocity and dynamic modeling of a biped robot with seven mechanical links, six actuators and 3 degree of freedom. The Jacobian matrix is used to represent the analytical expressions of the Cartesian speed of the hip in terms of the joint speed and vice-versa. We did not represent the forward and inverse kinematic velocity modeling of the other two legs points but it can be deduced by the same technique. The kinematic model was then injected into the dynamic model to calculate the kinetic energy of the entire robot. The Lagrange formalism was chosen in order to determine the inverse dynamic model. The walking gait cycle considered is the phase of simple support (SSP) followed by an impact then of the phase of double support (DSP) with rotation on the toes of the swing foot. The mathematical equations that model the constraints of the contact (contact with one foot or two feet) with the ground have been added to the initial dynamic model (flight phase). The resolution of the dynamic model at each phase allows us to determine the joint torques as well as the ground contact forces and the knowledge of the robot configuration during the walking gait cycle is very important in this case. We used the force parameterization method to resolute the dynamic model during the double support phase. The trajectories of the different joints are defined from the polynomial functions with a well-defined order and as a function of time (period of simple support Tss, double support Tds and step T). These functions have been implemented on Matlab to simulate the walking gait cycle.