Minimum Energy Trajectory Planning for Biped Robots

Abstract

Biped robots have potential ability to elevate mobility of robotic system and they attract general attention in the last decade. Due to their form, it is easy to introduce them into our living space without preparing special infrastructure. There are many theoretical and experimental studies on the biped robots. Recently, several autonomous biped humanoid robots have been developed. In 1996, the first autonomous bipedal humanoid robot with battery power supply was developed by Honda Motor Co., Ltd. (Hirai, et al., 1998). Takanishi and his co-workers at Waseda University built a human-size bipedal humanoid robot and proposed a basic control method of whole body cooperative dynamic biped walking (Yamaguchi et al., 1999). Same group also developed a biped robot having two Stewart platforms as legs (Sugahara, et al., 2003). Kaneko and his colleagues at the National Institute of Advanced Industrial Science and Technology (AIST) also developed a bipedal humanoid robot of 1.54m height and 58kg weight mainly for the purpose of investigating fundamental techniques and applications (Kaneko et al., 2004). Same group also proposed a method of a biped walking pattern generation by using a preview control of the zeromoment point(ZMP) (Kajita, et al., 2003). The ZMP and its extension (FRI; foot-rotation indicator) are basic stability criteria for biped robots (Vukobratovic, et al, 2001, Goswami, 1999). Nishiwaki and his co-researchers at University of Tokyo studied a humanoid walking control system that generates body trajectories to follow a given desired motion online (Nishiwaki, et al. 2003). Loffler and his colleagues at Technical University of Munich also designed a biped robot to achieve a dynamically stable gait pattern (Loffler, et al., 2003). Generally, careful design is required for development of a bipedal robot. Selection of gears and actuators, taking their rate, power, torque, and weight into account, is especially important. Developments of power conversion technology based on semiconductor switching devices and rare-earth permanent magnet materials Nd-Fe-B in combination with optimal design of the electromagnetic field by the finite element method enable improvement of power/weight ratio of actuators. They contribute to the realization of such autonomous biped robots. However, they are still underpowered to achieve fast walking and running motions as the same that human does. There are several researches on running control of biped model (Raibert, 1986, Hodgins, 1996, Kajita, et al., 2002). The first humansize running robot was developed at AIST (Nagasaki, et al., 2004). In December 2005, Honda Motor Co., Ltd. announced their new bipedal humanoid robot that could run at 6km/h. Kajita, et al. proposed a method to generate a running pattern and reported that it requires