Dynamically Stable Legged Locomotion Progress Report: October 1982 – October 1983

Abstract

This report documents our recent progress in exploring active balance for dynamic legged systems. The purpose of this research is to establish a foundation of knowledge that can lead both to the construction of useful legged vehicles and to a better understanding of legged locomotion as it exists in nature. We have made progress in five areas: Balance in 3D can be achieved with a very simple control system. The control system has three separate parts, one that controls forward running velocity, one that controls body attitude, and one that controls hopping height. Experiments with a physical 3D machine that hops on just one leg show that it can hop in place, travel at a specified rate, follow simple paths, and maintain balance when disturbed. Top recorded running speed was 2.2 m/sec (4.8 mph). The 3D control algorithms are direct generalizations of those used earlier in 2D, with surprisingly little additional complication. Computer simulations of a simple multi-legged system suggest that many of the concepts that are useful in understanding locomotion with one leg can be used to understand locomotion with several legs. A planar model with two legs trots and bounds with the same three part control decomposition used for the one-legged systems. Our most exciting result was to find a particular case for which the model bounds with each leg controlled independently, and without the need for active control of body attitude. We have designed a four-legged running machine in order to experiment with balance in systems with more than one leg. The machine is arranged like a large dog, with narrow hips, and a long body. While the leg design for this system is more complicated than our previous designs, the machine is very much like four 3D hopping machines connected by a common frame. Our intention is to study the trot, the rack, the gallop and the bound, and a number of gaits that are not normally used by natural quadrupeds. We have begun to study gait in terms of coupled oscillations. The question is, "Are gait transitions the result of explicit changes in control, or are they changes in the modal behavior of an oscillating mechanical system?" We do not have an answer yet, but we have made progress in exploring this question with a planar model. We have found that changes in the ratio of leg stiffness to hip stiffness change the pattern of rocking and swaying motions. For legged systems to be maneuverable, they must be able to traverse arbitrary paths in the horizontal plane. A useful component in accomplishing this goal is the ability for a legged system to travel a path of arbitrary curvature. We describe simple methods that permit a simulated 3D one-legged system to travel along paths of varying curvature. They depend on jointly manipulating the placement of the foot on each step, and the speed of forward motion. The report closes with a collection of partially formulated ideas that should stimulate more thinking and lead to further work.