Optimal Biped Design Using a Moving Torso: Theory and Experiments

Legged robots have been studied and developed for a long time. The primary advantage of legged motion is that they can traverse terrains inaccessible to wheeled robots. Biped robots are probably the most complicated of legged robots. Despite their complexity there has been a substantial amount of work done in the field including different techniques that have been developed to model, design and control biped robots. There are primarily two kinds of biped robots: active and passive bipeds. Many sophisticated, intelligent bipeds have been built by major companies. Most of the bipeds built are based on active control techniques; these are typically complicated, require high energies and are expensive to build. Also, they are far frommimicking true human motion. Owing to this, reliable biped robots are still elusive even to this day. McGeer (1990) analyzed the natural dynamics of two-legged systems. He numerically and experimentally analyzed systems with concentrated masses on legs and hip. These bipeds did not have a torso and no external torques were applied. He showed that these systems could walk stably down small slopes and sustain the motion. This class of biped motion is known as Passive Dynamic Walking. The step length and the velocity of the passive biped depend on parameters such as the masses, lengths and the slope on which the biped is walking. A passive biped is much more efficient than active bipeds and mimics the human motion better. Goswami, Espiau & Keramane (1996); Goswami et al. (1993); Goswami, Thuilot & Espiau (1996); Goswami, Thuilotz & Espiauy (1996) describe the limit cycles and their stability in the passive gait of a biped without a torso. They obtained some numerical solutions of a system with known parameters. In Goswami et al. (1997) and Roussel et al. (98) bifurcation and chaos are studied and the dependence of the gait on the slope is explained. Asano, Luo & Yamakita (2004) use energy-based control laws to enable the biped to mimic the passive motion; they analyze a biped without torso and knees. Asano, Yamakita, Kamamichi & Luo (2004), Kim &Oh (2004), Paul et al. (2003), Silva &Machado (2001) and Goswami (1999) are some more of the innovative attempts to build a simple yet controllable walking machine. Although passive dynamic walking is efficient, simple to implement and analyze, the step length and the velocity of motion of the passive biped are greatly dependent on the system parameters. The path followed by the biped is uncontrollable and there is no control Karthik Kappaganthu1 and C. Nataraj2 1Principal Engineer, R&D Global, Strategic Solution, LLC Virginia, VA 20165 2Professor & Chair Department of Mechanical Engineering, Villanova University, Villanova, PA 19085 USA Optimal Biped Design Using a Moving Torso: Theory and Experiments 3