Dynamically Stable Legged Locomotion: Second Report to DARPA, October 1,1981 – December 31,1982

Abstract

This report documents our recent progress in exploring balance and dynamic stability in legged systems. There have been five areas of progress, each described in a separate chapter in the pages that follow. Balance in 2D can be achieved with a surprising!y simple control system. The control system has three separate parts, one that controls hopping height, one that controls the velocity of forward travel, and one that controls body attitude. A physical 2D one-legged hopping machine that employs such a three-part control system hops in place, runs from place to place at speeds of up to 2.7 rnph, maintains its balance when disturbed, and leaps over small obstacles. Control of locomotion in 3D can build upon the results obtained in 2D. Simulations suggest that a 3D one-legged machine could run and balance using the same three-part controller developed for 2D, provided that additional extra-planar mechanisms operate to suppress roll, yaw, and lateral motions. We have designed and built a physical one-legged system that will permit experimentation in the control of balance in 3D. The device has a simple pneumatic leg that is positioncd by a hydraulic hip. It will hop on an open floor without a system of physical constraints. Last year we developed a method for obtaining balance that uses tabulated data. This year the method was extended by showing that the volumous tabular data can be approximated by a polygonal surface of moderate degree, without much loss of control precision. We refined our understanding of the mechanisms responsible for balance by simulating and comparing three differerent algorithms for horizontal control: one just places the foot during flight, one places the foot during flight and sweeps the leg during stance, and the third places the foot during flight and controls body attitude during stance. Each of the three methods elucidates a different principle of dynamic stability. The report closes with a bibliography on legged locomotion containing about 350 references.