Page 87 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Chapter 5

Drive-brake asymmetry

There are two basic categories of drive gear reduction: back drivable and non-back
drivable. The first category includes pinion, chain, and belt reducers, while the sec-
ond includes worm and screw reducers. Servos using non-back drivable reducers are
easier to control because variations in the load are largely isolated from the motor.
Back-drivable reducers are much more efficient, but more difficult to control because
load fluctuations and inertial forces are transmitted back to influence the motor’s
position.

The response of either type servo is usually very nonlinear with respect to driving
and braking. To achieve a given acceleration may require very significant motor cur-
rent, while achieving the same magnitude of deceleration may require only a minute
reverse current. For this reason, asymmetric gains are usually required in both cases.

Quadrant crossing nonlinearity
Most drives are either two or four quadrant. A two-quadrant drive can drive in one
direction and brake. A four-quadrant drive can drive and brake in both directions.
The term quadrant thus comes from these four possible actions of the drive. A nasty
phenomenon that appears in the back drivable servos is that of nonlinear regions in
a servo’s load. A drive motor using a pinion gear box is an excellent example. When
the power transitions from forward to reverse (called changing quadrants), the servo
will cross a zero load region caused by the gear backlash. If the control does not take
this into account, it may become unstable after freewheeling across this region and
slamming into the opposite gear face. One trick for handling this discontinuity is to
sense that the control has crossed quadrants and reduce its total gain after the
crossing. This gain can then be smoothly restored over several ticks if the control
remains in the new quadrant.

Natural deceleration
Any servo will have its own natural deceleration rate. This is the deceleration rate
at which the servo will slow if power is removed. If the programmed deceleration is
lower than the natural deceleration, the servo never goes into braking and the re-
sponse is usually smooth.
Thus, during normal operation the ugly affects of quadrant crossing may not be no-
ticed. If, however, the robot must decelerate unexpectedly to avoid a collision, the
servo may react violently, and/or the robot may tip over forward. For this reason, a

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