An exact dynamic model for the Thomas-K biped robot: New simulator design

In this paper, the dynamic model of the Thomas-K biped robot, which was built at Ohnishi laboratory in Keio University, is derived, and a new efficient dynamic simulator is proposed. Although the dynamic model of bipedal locomotion is considered in this paper, the proposed model can be easily implemented any kind of floating point base robotic systems, such as mobile robots, space robots and so on. The Thomas-K biped robot has totally 16-degrees of freedom, in which 10 degrees of freedom can be controlled directly. Therefore, it is not an easy task to derive the conventional closed form dynamic model of the Thomas-K. Firstly, it is derived by using a Newton-Euler algorithm which is conventionally used to derive the dynamic models of biped robots. However, it does not give deep insight into the dynamics of bipedal locomotion. Besides, the Newton-Euler algorithm provides only inverse dynamics; therefore, it should be run recursively, which increases computational load, to derive the conventional closed form dynamic model, i.e., forward dynamics. Secondly, the inertia matrix and gravity vector are derived analytically. It simplifies the model and gives better insight into the dynamics of bipedal locomotion. However, the Coriolis and centrifugal forces are derived by using the Newton-Euler algorithm. A simple virtual spring-damper collision model is used to simulate the contact between the robot's soles and floor. The virtual spring-damper model makes the contact model easier than the plastic collision one and improves the performance of the simulation, significantly. Center of mass (CoM) of the robot is controlled in the single support phase in order to show the validity of the models.