Mathematical Modelling and Simulation of Combined Trajectory Paths of a Seven Link Biped Robot

Abstract

In this chapter, simulation of combined trajectory paths of a seven link biped robot over various surfaces has been presented. We have focused on generation of combined trajectory paths with the aid of mathematical interpolation. The inverse kinematic and dynamic methods have implemented for providing the robot combined trajectory paths in order to obtain a smooth motion of the robot. This procedure avoids the link's velocity discontinuities of the robot in order to mitigate the occurrence of impact effects and also helps to obtain a suitable control process. The sagittal movement of the robot has been investigated while 3D simulations of the robot are presented. From the presented simulations, one can observe important parameters of the robot with respect to stability treatment and optimum driver torques. The most important factor is the hip height measured from the fixed coordinate system. As can be seen from Fig. 7f, the support knee needs more actuator torque than the value of the non-nominal gait (with lower hip height measured from the fixed coordinate system). This point can be seen in Figs. 8f and 10f. This is due to the robot's need to bend its knee joint more at a lower hip position. The role of the hip height is considerable over the torso's modified motion for obtaining the desired fixed ZMP position. With respect to Figs. 10c and 11c, the robot with the lower hip height needs more modified motion of its torso to satisfy the defined ranges of ZMP by the users. The magnitude of the torso's modified motion has drastic effects upon the control process of the robot. Assuming control process of an inverse pendulum included a stagnant origin will present relatively sophisticated control process for substantial deflection angle of pendulum. Note that the torso motion in a biped (as an inverted pendulum) includes both the rotational