# Taxonomy of Statically Stable Locomotion

## What is statically stable locomotion?

Locomotion is defined to be the act or power of moving from place to place. Statically stable locomotion has the added constraint that the moving body be stable at all times. In other words, if the body were to instantaneously stop all motion, the body would still be standing. More specifically, the vertical projection of the center of gravity will be contained within the convex hull of the body's points of contact with the ground at all times.

In this taxonomy we will look only at the statically stable locomotion that needs gravity to remain stable . e.g. climing in a chimney by pressing against the walls, or climbing in a tree don't count. (We will look at force closure exclusively, not form closure for you manipulation people...)

## Gaits

A gait is defined to be one cycle of a repeated pattern of motion that is used to move from one place to another.

Simple gaits are those which cannot be broken down into separate gaits. This is as opposed to compound gaits which are combinations of simple gaits.

One example of two simple gaits being combined into a compoud gait is a (1) person walking, (2) a small toy 4-wheeled car, (1+2) a person roller skating.

## Simple Gaits

Every land locomotion gait must make contact with land. We define these interactions with generalized feet (g-feet). More specifically: a generalized foot (g-foot) is defined to be one contiuous set of points of a locomoting body that comes into contact with the ground.

Simple gaits are divided into eight classes based on three properties of these generalized feet.

These properties are:

1. motion of g-feet
rolling (net rotation) vs swinging (no net rotation)
2. continuity of g-foot/ground interaction
continuous contact vs discrete contact
3. g-feet relating to body stability
little footed (g-feet can be point contact, therefore need at least three g-feet to maintain stability) vs. big-footed (g-feet must have some area, may have fewer than three g-feet)
The eight classes are the 2^3 combinations of these properties:
1. RCB: rolling continuous big-footed
2. RCL: rolling continuous little-footed
3. RDB: rolling discrete big-footed
4. RDL: rolling discrete little-footed
5. SCB: swinging continuous big-footed
6. SCL: swinging continuous little-footed
7. SDB: swinging discrete big-footed
8. SDL: swinging discrete little-footed
Examples of these classifications with Polypod are shown here. The classes are shown with the three letter abbreviation next to each example.

## Compound Gaits

There are three ways that gaits can be combined.
1. articulated combination, a uniting by means of a joint, bodies which could separately execute a gait. The classical example is a horse and buggy.
2. heirarchical combination, combining two gaits, one called the superior and one the inferior where the superior gait's "sits on top of" the inferior gait. Thus the superior gait's g-feet make contact with the inferior gait's body moving the inferior gait's body, and the inferior gait's g-feet still make contact with the ground. The two gait's motions are additive. The classical example is a person (superior) using roller skates (inferior).
3. morphological combination the merging of gaits such that each gait can act in a different direction. Each gait can still make contact with the ground when locomoting (not heirarchical) and cannot be separated by removing only a joint (not articulated). The simplest example is a rolling sphere, a morphological combination of an infinite number of wheels.

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Comments may be sent to Mark Yim at mark@flamingo.stanford.edu

last updated November 1996, though this represents work from 1994