There have already been many studies of bipedal walking, but most of them have concentrated on building a good controller and have failed to utilize the dynamic properties of robots. Recently a new approach to bipedal walking has appeared. Using this new approach, a robot can walk down a shallow slope without any actuators or controllers. This walking mode is called Passive Dynamic Walking (PDW). Because of its simplicity in respect to both energy and control, PDW is thought of as a “glider” in walking (Pratt, 1999).
Since the appearance of the first paper on PDW by McGeer (McGeer, 1990), many researchers have studied various aspects of it. Previous studies, however, treat only the lower part of the body, not the torso. If the purpose of PDW studies is to make effective use of the body in a humanoid robot, it is natural to treat a robot with a torso. In this paper, we show the effects of the torso on PDW walking in two-dimensional computer simulation.
For the first PDW trial with a torso, we used a very simple mode consisting of three links: a torso and two legs. This is a simple extension of the simplest PDW robot. First we examined the possibility of PDW by this robot without adding any torque. The center of mass of the torso and the initial condition of walking were changed variously. We could not, however, find any suitable parameters or initial conditions for stable walking with the center of mass of the torso higher than the hip point.
We therefore added torque to support the torso and tried to suppress that torque. As we wanted to maintain simplicity of PDW, a simple feedback control scheme was applied as follows:
τ=−kvθw+k(θwd−θw)
Torque is applied only to the joint between the torso and the support leg. Given appropriate initial conditions, the robot can walk stably down a shallow slope. Moreover, the walking mode of this robot has the same properties as the original PDW robot suggested by McGeer. For certain parameter combinations, the PDW robot can walk with a stable limit cycle motion.
To suppress the torque needed to stand the torso up, four body parameters were changed variously: changing the posture of the torso, adding soft leg tips, changing the curvature of the sole, and adding passive joint resistance. From experimental results, four qualitative points were obtained: (1) as the torso inclines backward, the torque becomes small, (2) a shock absorber is useful to reduce the torque at heel contact, (3) the shape of the sole is important in suppressing torque in the supporting phase, and (4) passive joint resistance is effective in accelerating the speed and duration of walking, but it cannot suppress the torque. Simple analysis shows that the torque at the hip joint to stand the torso up is closely related to the acceleration of the hip. Moreover, the torque at the contact phase is determined by the vertical component of acceleration of the hip, and torque in the supporting phase is determined by the horizontal component. This analysis improves understanding of the simulation results.
