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

The humanoid robot is designed like human for doing various tasks and adapting to human’s environment. Next generation humanoids are expected to successfully coexist within human environments. This imposes very difficult challenges to researchers to produce truly dynamic movements to maintain balance under unexpected changes of paths. There are vast majority of studies on single trajectory paths of the biped robot (Bagheri & Mousavi, 2007; Mousavi & Bagheri, 2007) while combined trajectory paths have not received much attention. In this chapter, we have hence focused on generation of combined trajectory paths with the aid of mathematical interpolation. Zarrugh and Radcliffe (1997) have considered a biped robot with respect to a walking pattern by recording human kinematic data while McGeer (1990) have focused on passive walking of a biped robot generated by gravitational and inertial components. Silva and Machado (1999) have focused on actuator power and energy by the adaptation of walking parameters. The stability of the robot is connected to the biped robot’s tendency to tip over. Zheng and Shen (1990) have considered a method of gait synthesis with respect to static stability while Chevallereau (1998) have focused on dynamic stability with the aid of a low energy reference trajectory definition. Takanishi et al. (1985), Shih et al. (1990), Hirai et al. (1998), and Dasgupta and Nakamura (1999) have considered the robot dynamic stability with respect to the walking process based on the zero moment point (ZMP) method. With respect to the various conditions of combined trajectory paths, Shih (1997, 1999), Huang et al. (2001) utilized methods to generate the trajectory paths of the robot where they carried out simulation of the combined trajectory paths. The current chapter focuses on the inverse kinematic and dynamic methods 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 main contribution of this work consists of a new method for simulation of a seven link biped robot over combined trajectory paths in order to study the effects of hip height over the torso’s modified motion. The process has been performed based on the system given breakpoints and either third-order spline or Vandermonde matrix interpolation method. 10