by Daniel Albert
To recap last month’s article, this big walker uses an inverse pendulum
weight distribution as opposed to big heavy feet. An inverted pendulum has its
mass above its pivot point, so it is inherently unstable. The goal is to use the
three weight sensors (load cells) on each foot to feed back weight information
to dynamically balance the mass. Each leg has a micro control unit (MCU) that
controls the five servos of each limb to always keep the weight at the centroid.
This month, I will discuss the design details of the biped’s feet, ankles, and hips.
Balancing on Three Points
A tripod is an extremely stable structure. On a level
surface with three legs of identical length, a tripod will
center the weight of a mass that is set onto the point
where the legs intersect. Picture a camera on a tripod. If
the surface tilts up, down, or sideways, the weight will
move from the center.
By adjusting the length of one or two legs, we can re-center the mass, thus making the structure stable. With
the load cell measurements at each of the three points,
we can calculate the direction to adjust each leg length to
re-center the weight. We could also calculate the amount
to adjust the length. This design does not require the scale
of the error. Each adjustment is the minimum movement.
Calculations and adjustments happen every 50 mSecs ( 20
times a second). The system will dynamically stay in
balance as long as the angles of the surface do not
change too fast.
FIGURE 1. Centroid triangle.
(M1 X1) + (M2 X2) + (M3 X3)
M1 + M2 + M3
(M1 Y1) + (M2 Y2) + (M3 Y3)
M1 + M2 + M3
The three tripod points
on each foot distribute and
measure the weight of the
leg individually. These
correspond to the heel, the
ball of the first metatarsal
at the big toe, and the
fifth metatarsal at the
We use only two
lengths of the tripod to tilt
and roll the foot, so we
only need two servos.
To keep the weight
closer to the hip, the foot
56 SERVO 03.2011