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...)
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.
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
These properties are:
The eight classes are the 2^3 combinations of these properties:
motion of g-feet
- rolling (net rotation) vs swinging (no net rotation)
- continuity of g-foot/ground interaction
- continuous contact vs discrete contact
- 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)
Examples of these classifications with Polypod are shown
here. The classes are shown with the three letter abbreviation next
to each example.
- RCB: rolling continuous big-footed
- RCL: rolling continuous little-footed
- RDB: rolling discrete big-footed
- RDL: rolling discrete little-footed
- SCB: swinging continuous big-footed
- SCL: swinging continuous little-footed
- SDB: swinging discrete big-footed
- SDL: swinging discrete little-footed
There are three ways that gaits can be combined.
- articulated combination, a uniting by means of a joint, bodies which
could separately execute a gait. The classical example is a horse
- 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).
- 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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last updated November 1996, though this represents work from 1994