Page 65 - Anatomy of a Robot

02_200256_CH02/Bergren 4/17/03 11:23 AM Page 50
50 CHAPTER TWO
HOW TO GET OPTIMUM PERFORMANCE
FROM THE ROBOT
The requirements for a second-order system might vary all over the place. We might
need a fast rise time; we might need a quiet system that does not oscillate much; we
might need to minimize mass or another design parameter. Don’t forget that v and d
are parameters derived from m, K, and B. We might be stuck with one or more of these
five parameters and have to live with them. For example, the mass m might be set by
the payload, the spring constant K might be inherent in the suspension, and the friction
B might be set by the environment.
In many systems, the requirements are often at odds with one another and compro-
mises must be struck. In such a design, it is often difficult to figure out what to do next.
So here’s a fairly safe bet. Take a close look at Figure 2-16. It shows four curves, includ-
ing the lowest curve at a damping figure of 0.99. A second-order system with a damp-
ing constant near 1 is called “critically damped” (see Figure 2-20). The system rises
directly to the level of 1. No overshoot or undershoot takes place. True, the rise time is
nothing to marvel about, but the system is very stable and quiet. Designing a system to
be critically damped is a good choice if no other definable target exists for its per-
formance. It tends to be a very safe bet. In practice, it makes sense to back off from a
damping constant of 1 a little bit, since an overly damped system is a little sluggish. If
you can afford some overshoot, consider a damping constant between .5 and .9.

Notes on Robot Design

There are a number of other considerations to take into account when designing a robot.
I’ve listed them here in no particular order. These are just tricks of the trade I’ve picked
up over the years.

DESIGN HEADROOM
Cars offer great examples of second-order system designs. A car designer might be
called upon to design a light car with a smooth ride. Ordinarily, a light car will bounce
around quite a bit simply because it’s smaller. Carrying this vision to an extreme, con-
sider a car so small it has to drive down into a pothole before it can drive up the other
side and get out of it. Certainly, a lighter car will suffer from road bumps more than a
heavier car, but there is more to it than this. When a car goes over a pothole, the springs
and suspension attempt to absorb the impact and shield the passengers from the jolt.
But if the springs reach the end of their travel (as they would with a deep pothole), they