Passive dynamic walking of compass-like biped robot with dynamic absorbers

Abstract

This paper investigates the roles and effects of dynamic absorbers attached to the leg frames on the gait properties of passive dynamic walking. First, we model a passive compass-like biped robot that consists of two identical leg frames with passive dynamic absorbers that represent micromechanical vibration or human flesh dynamics. We then conduct gait analysis through numerical simulations to observe how small oscillation of the leg frames affects the gait prop- erties, and show that speeding-up is achieved by utilizing the indirect softness produced by the dynamic absorbers. Second, we investigate the dominant effect of small oscillation using the same model. The simulation results show high nonlinearity in the generated walking gait. I. INTRODUCTION Limit cycle walkers generate energy-efficient walking gaits by using the inherent natural dynamics (1). Recently, the studies on legged robots focusing on the leg stiffness have been conducted in the area of limit cycle walking. Kawamoto and Asano clarified that adaptability to uneven terrain can be improved by using leg viscoelasticity through numerical simulation and experiments (2). They also showed that viscoelastic-legged walkers have advantages to overcome steps and continue stable walking on various road conditions without changing the walking speed so much. They also showed that rigid-legged walkers have an advantage to gener- ate faster walking gaits than viscoelastic-legged ones but are less adaptive to uneven terrain. The leg viscoelasticity tends to create non-instantaneous double-limb support motion and this significantly decreases the walking speed. The center of mass (CoM) trajectory, however, becomes smoother and this would make the walker overcome the potential barrier at mid-stance easily. Similar results are also reported in (3). The above facts imply that soft leg-frames are important for improving the adaptability and maneuverability of the generated gait in return for high-speed movement. We hu- mans have both advantages of the leg stiffness and softness, and can easily generate high-speed and highly adaptive walking gaits. We should reconsider how the robot leg- frames should be designed to reproduce the high performance of human walking. The basis of the leg frames should be made of a solid material to achieve high-speed walking motion, while soft- ness should be added indirectly so that the period of non- instantaneous double-limb support motion becomes short. The importance of robot's internal softness reproduced as an wobbling motion has also been reported by Hanazawa et al. (4) and Ackerman et al. (5). The authors also found the validity of a 2-DOF wobbling mass in a passive rimless wheel (6). In these early works, however, the indirect softness was given as an additional linkage to the robot's body frame. Based on the observations, in this paper we propose a novel limit-cycle walker that have dynamic absorbers on the leg frames. We add dynamic absorbers parallel to the rigid leg frames for the purpose of indirectly reproducing the dynamical effect of viscoelastic legs while keeping high- stiffness of the legs. It is then expected that efficient passive or underactuated walking gaits can be generated without decreasing the walking speed. We introduce the model of a compass-like biped robot (7) that added dynamic absorbers parallel to the leg frames and numerically analyze the gait properties according to the change in the viscoelastic coefficients. We show that speeding-up of passive compass gait can be achieved by the effect of the dynamic absorbers during motion. We discuss the speeding-up mechanism mainly from the viewpoint of flattening of the CoM trajectory. In addition, we also show that some strange gaits are generated where the dynamic absorber motion is more dominant.