New simplified model for an under-actuated quadruped robot in bounding motion

In this paper, a quadruped robot is studied in bounding motion. A new simplified model of quadruped robot in bounding motion with four actuated and two unactuated joints is developed. The kinetic and potential energies of the under-actuated mechanical model of the quadruped robot are obtained and the dynamics of the robot model is derived using the Lagrangian method. It is shown that the dynamical equation of the proposed simplified model belongs to a class of second-order nonholonomic mechanical systems. The main motivation of this paper is to obtain quadruped model in bounding motion such that one can apply different control methods directly or after transformation in the obtained dynamic equations. Utilizing MATLAB, dynamics of the planar model has been simulated in backward and forward states. Physical parameters of the Little-Dog robot as an instance of the quadruped robot are considered in simulation The simulation is without control and therefore is unstable but it illustrates robot's manner in bounding motion before instability.