Page 74 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Closed Loop Controls, Rabbits and Hounds

A common problem with applying standard control theory is that the required para-
meters are often either unknown at design time, or are subject to change during
operation. For example, the inertia of a robot as seen at the drive motor has many
components. These might include the rotational inertia of the motor’s rotor, the
inertia of gears and shafts, rotational inertia of its tires, the robot’s empty weight,
and its payload. Worse yet, there are elements between these components such as
bearings, shafts and belts that may have spring constants and friction loads.
Not withstanding the wondrous advances in CAD (computer aided design) systems,
dynamically modeling such highly complex systems reliably is often impractical be-
cause of the many variables and unknowns. For this reason, when most engineers are
confronted with such a task, they seek to find simpler techniques.

Flashback…
As a newly minted engineer, my first design assignment was a small box that mounted
above the instrument panel of a carrier borne fighter plane. The box had one needle and
three indicator lights that informed the pilot to pull the nose up or push it down as the
multi-million dollar aircraft hurtled toward the steel mass of the ship. As I stood with all
of the composure of a deer caught in the landing lights of an onrushing fighter, I was told
that it should be a good project to “cut my teeth on!”

The design specification consisted of about ten pages of Laplace transforms that de-
scribed the way the control should respond to its inputs, which included angle-of-attack,
air speed, vertical speed, throttle, etc. Since microprocessors did not yet exist, such com-
puters were implemented using analog amplifiers, capacitors, and resistors, all configured
to perform functions such as integration, differentiation, and filtering. Field effect switches
were used to modify the signal processing in accordance to binary inputs such as “gear-
down.”
My task was simply to produce a circuit that could generate the desired mathematical
function. The problem was that the number of stages of amplifiers required to produce
the huge function was so great that it would have been impossible to package the correct
mathematical model into the tiny space available. Worse yet, the accumulation of toler-
ances and temperature coefficients through so many stages meant the design had no
chance of being reproducible. With my tail between my legs, I sought the help of some of
the older engineers.

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