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Passive Dynamic Walking
Human Power and Robotics Lab, Theoretical and Applied Mechanics, Cornell Univ. (lab of Andy Ruina)

For an informal introduction to our lab, see the article about our lab in the Fall 1996 issue of Cornell Engineering Magazine.

News flash (August 2003): We now have a biped that walks on level ground with power. Contact Steve Collins or Andy Ruina if you want to see
a video or preprint. It is not online because it is not yet published and some journals are wary of pre-publicity for such possibly high-publicity items.

Video Collection
Walking and Locomotion Papers
Very Basic Reference List
Other Sites


The human body, like anything else that is large enough and slow enough, is bound by the laws of Newtonian mechanics. Our research is centerred on understanding of how humans walk from a Newtonian mechanics point of view. If we can gain better insight into how humans walk, perhaps we could improve prosthetics for the gait-impaired, help correct neuro-muscular deficiencies, or build better two-legged walking robots. Our approach, which picks up on the ideas and inventions of Tad McGeer, is to focus on what aspects of coordination can be largely explained by mechanics.
Our first of two near duplicates of one of McGeer's machines is shown walkingdownhill and to the left in this photo. The machine is meant to vaguely resemble a set of human legs in two dimensions. This so-called passive dynamic walker has no actuation except gravity, and no control system, except for mechanical knee stops that prevent the shanks from hyperextending with respect to the thighs. Inner and outer legs are paired to constrain it from falling over sideways, but it can still fall forward or backward or buckle at the knees. Curiously enough, as Tad McGeer first showed, this robot and others like it are capable of stable, human-looking walking. This visual appearance alone suggests that passive dynamic effects play a big role in the mechanics of human gait, that Nature takes major advantage of these passive stability and efficiency mechanisms in its designs.

Of course, many people have worked on gait synthesis. Most of the approaches arecentered neuro-physiological or computor-motor issues, emphasizing the role of control and actuation in producing locomotion. Following McGeer, further than he intended perhaps, we are taking the approach toward understanding walking that de-emphasizes the roles of the brain, the nervous system, and muscles in walking. Why take this approach?

1) Simple models tend to give better insight into the underlying mechanics of complicated systems. The art, of course, as Einstein said, is to "make the model as simple as possible but no simpler!" not to throw the baby out with the bath water. By leaving brains and muscles out of people we think there are useful insights to be gained.

2) Compared to classical mechanics, neurological control is a poorly- understood subject. No one knows what the brain's feedback loops look like and no one really knows what sort of control algorithm is used to generate and maintain gait.

3) Evidence exists that a minimal amount of control and actuation is necessary for some basic human motions, including gait. (References include Kelso, Basmajian, Yamaguchi).

Generally our work involves developing mechanically complete models of walking that emphasize the passive interaction of gravity, inertia, and collisions and minimize the roles of control and actuation. To get some feeling for this concept, imagine a slinky `walking' down stairs. A slinky is a device driven only by gravity down a slope that seems to enter into a limit cycle- a "repeatable" or steady periodic motion (at least on the right stairs with the right initial conditions) that is inherent to the mechanism - much like rolling is inherent to a round object. Once such models are understood, then small amounts of power could be added in efficient ways to allow them to walk on level ground or up a hill and simple control mechanisms can be introduced to increase the stability of the motion. In the same way, we can study the inherent effects of mass distributions and geometry on stability and efficiency of gait.

McGeer motivated his work by making an analogy to the development of powered flight. The first successful flying devices were unpowered, uncontrolled gliders, little models and paper-airplane-like things. Once gliders were perfected, then engines and control systems were added. Of course, another approach to achieving stable and efficient flying might have been to start with arbitrary amounts of control and actuation and then to gradually minimize their role. But this does not reflect the history of flight or our present approach to locomotion modeling. But, to be frank, gliders are fun in their own right and so are these walking gadgets.


Following McGeer, we have several 2D kneed walking simulations. The first two were done more or less at the same time, one by Mario Gomes in C (developing the equations with Mathematica) and the other by Mariano Garcia using MATLAB (developing the equations with Maple).

Dan Jung, and undergraduate in our lab at Cornell, created a Working Model simulation based on the parameters and initial conditions that had yielded stable walking in the first two simulations. Art Kuo in Michigan cleaned up the graphics on Dan's simulation.

Click on the picture to see a simulation. Gravity points slightly to the right. (430kB).
Passive_Walk/passive_walking.html/Passive Walker Movie

If you have WORKING MODEL, here is the walker: or model.sit.
       (Get a demo version of Working Model from Knowledge Revolution.)

Compare the simulation above with Cornell's 4 leg McGeer walker: video

MATLAB code to simulate some walking models is available on Mariano Garcia's homepage.


Mike Coleman with others has analyzed a 3D version of McGeer's rimless wheel, has invented the first walking toy that can't stand still, and has post-predicted on the computer that such a device should work. We have also built the first two-legged passive dynamic walker with knees.

We are attempting various walking devices with minimal power: one a straight legged machine with four legs and another a two leg machine with knees.

Walking and Locomotion Papers: click here.

Video Collection

The best walking robot in the world (2 legs, knees, slaved arms), Collins
We think this robot has as natural looking a steady walking gait as any other robot in the world (Compare, for example to the Honda Humanoid. Let us know of other comparison videos or if you disagree.) In the summer of 2000, undergraduate Steven Collins worked on improving Martijn Wisse's passive walker. The resulting walking device combines 4 ideas to try to lift kneed 2D passive-dynamic walking to 3 dimensions. The ideas are: 1) Use wide feet that guide the motion (as in the 1912 Bechstein patent), 2) Use soft heels that kill the instability from indeterminacy at the collision of a line of contact, 3) counter-swing the arms to reduce angular momentum effects about the vertical axis (as per the 1888 Fallis patent), 4) Swing the arms side to side at appropriate times to reduce side-to-side rocking.
photo (20K)     photo (20K)       photo (20K (3.8meg)        SteveAngle.mpg (1.6meg) (3.6meg)       SteveBehind.mpg(1.8meg)

Kneed Walker (2 legs), Wisse
In the fall 0f 1998 Martijn Wisse visited the Cornell lab and, inspired by the 1912 Bechstein patent, built this most remarkable machine.
mov (4 meg)

Original Tinkertoy walker
Video recording of the original Tinkertoy walker (subject of our PRL paper, "An Uncontrolled Toy That Can Walk But Cannot Stand Still") and a newer design too: movie (8 meg)             Schematic (.eps 70k)        Photo (.gif 200k)


Kneed Walker Movie (4 legs)
Video recording of our lab's physical kneed walker pictured a few paragraphs above.
.mov (499k) .avi (148k)

Dan Jung's Walker Movie  (Cornell HP lab undergrad project)
Animation of Working Model version of 2D kneed walker (same as above picture).
mov (372k)
   avi (693k)

Point Mass Brachiation animation: Videos by Mario Gomes: mpg(88K), gif(400K)

A collection of old patents of walking toys
(scanned .pdf files, about 2 meg each):  Fallis 1888,   Bechstein 1912 ,   patent 3,   patent 4,   Wilson 1938 ,   patent 6

An Incomplete Reference List

T. McGeer. Principles of walking and running. In Advances in Comparative and Environmental Physiology 11: Mechanics of Animal Locomotion. R. McN. Alexander, ed. Berlin: Springer-Verlag 1992.

T. McGeer. Dynamics and control of bipedal locomotion. J. Theoretical Biology 16 3, 277-314, 1993.

Other Places of Interest

Art Kuo At Michigan has done much work closely related to passive dynamics.
BioRobotics Lab at Washington (Glenn Klute).
Biomechanics World Wide
Delft Biped Laboratory (van der Linde, Wisse ...)
Martin Buehler's Ambulatory Robotics Lab at McGill
The Biomechanics Laboratory at UC Berkeley.
The Poly-Pedal Laboratory at UC Berkeley, where Mariano Garcia pursued post-doctoral research on cockroach locomotion.
Georgia Tech Animation Lab (Hodgins et. al.)
Yildirim Hurmuzlu at SMU.
Ton van den Bogert at the Cleveland Clinic.
The UNH Robot Lab.
Eric Dunn at Harvard.
Human Engineering Lab at UC Berkeley (Kazerooni).
Ambarish Goswami.
Hans De Man's multibody mechanics group at the Free University of Brussels.
Aarne Halme's group at the Helsinki University of Technology, (where Andy Ruina spent the 1997-98 academic year).
Robotics group at INRIA, (they also do work on passive models).
Michael T. Rosenstein at U Mass, an excellent biped bibliography among other things.
Matthew Berkemeier at Utah State.
Shuji Kajita, with links to biped researchers around the world.
Tad McGeer's current work (building small autonomous planes, one crossed the Atlantic in the summer of 98, the pacific is next).
Walking Machines Catalogue (Karsten Berns, Germany. An attempt to catalogue all walking robots)
Robot Books
Knowledge Revolution, where you can get a demo version of Working Model Software.
Working Model files to simulate our passive walker can be downloaded below. There are two versions: one is a raw file, and one is MacBinary encoded (needs Stuffit to open). Neither file seems to work with all systems/setups/versions; so far, we have not found a robust way to allow people to download Working Model files. If you have trouble downloading, contact Working Model passive kneed walker (raw file)
Working Model passive kneed walker (needs Stuffit to open)
MATLAB code to simulate a few different walking models is available on Mariano Garcia's homepage.

Any Other Ideas? Let us know if you want to be on our list.

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