Page 141 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Chapter 8

First, we must determine the relative movement of the platform that probably resulted
from the drive tick. This action has two effects; it both drives and turns the platform.
We will assume that traction is evenly distributed across both treads, so the platform
pivots about the center of the stationary (right) tread. The center of the platform
moves forward by the distance D, which is equal to half the motion of the driven
tread:
D = d / 2

Note that D is actually an arc, but if the tick distance is small enough it can be as-
sumed to be a straight forward move. By approximating all moves as minute straight
vectors at a single heading, we are able to track any complex maneuver.

Because of this action, the platform steers clockwise by the angle α (remember we are
looking from below). This angle is simply the arcsine of the tick distance that the right
tread moved, divided by W, the distance between the treads. If the traction across
the treads is not even, then the platform may not pivot as shown, further demon-
strating the difficulty with skid steered odometry.

α = + Arcsine (d/W) for the left tread
α = – Arcsine (d/W) for the right tread

If this action by the left tread is followed by a tick of forward motion by the right
tread, then the angular changes will cancel and the platform will have moved
straight forward by the distance of a tread tick.
If instead, the forward movement of the left tread is followed by a reverse move of
the right tread, then the angular components will add while the linear motion
elements will cancel. In other words, the platform will turn on center (hopefully).
The next step is to add this relative motion to the vehicle’s current position and
heading estimate. The relative platform motion is a vector of D magnitude at the
current heading (θ) of the platform. This vector must be summed with the position
of the vehicle to produce the new Cartesian position estimate. The angle α is then
added to the heading of the platform to obtain the new heading.

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