Near-Optimal Trajectory Generation of a Two-Legged Robot with Soft Sole on Staircase using PSO and ABC

1. Introduction

Biped robots are designed and developed to work in various man-made environments, such as staircases, sloping surface, obstacles and ditches etc. Many investigations were carried out on the gait generation and its optimization with respect to the energy consumption in the system. Asano et al. (2005) studied the passive dynamic walking performed by the compass-gait biped robot. They investigated the effectiveness of this algorithm through numerical simulations. A unified feedback control law for n-DOF biped robot with one degree of under actuation was proposed by Hu et al. (2011) on a sloping surface. The proposed method was tested with the help of two kinds of biped robots. Moreover, in (Wei In & Vadakkepat, 2004), the authors developed a hybrid controller for generating gaits of Robosapien robot. The controller developed uses a combination of dynamics –based approach with central pattern generator. It is important to note that the concept of zero moment point (ZMP) was proposed by Vukobratovic et al. (1970), and it had been used to verify the dynamic balance of the legged robots. Moreover, several mathematical models for walking on the flat surface (Pleaten et al., 2003; Yang et al., 2010), ascending staircase (Capi et al., 2001; Lim et al., 2014) and obstacle crossing (Lathan et al., 2012) were developed by various researches after assuming the hard foot ground interaction. Recently, Wang (2013) developed a biped robot balance control method based on force resistance preceptor mechanism and ZMP. The developed algorithm was tested on a real robot and obtained rapid and smooth motion. Later on, Lee and Ryoo (2014) tuned the walking gaits of the humanoid robot using the concept of ZMP. The developed algorithm was able to tune the intuitive parameters of the robot that help in improving the performance of the biped robot. Most of the works discussed above related to the gait generation of biped robots on various terrains are purely mathematical in nature and does not involve any optimization methodology. Therefore, the gait generated utilizing those methods may not be optimal in any sense. Later on, few researchers used non-traditional optimization methods for modeling and optimization of gait generation problems of biped robots on different terrains.