Page 299 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

274 MOTION PLANNING FOR THREE-DIMENSIONAL ARM MANIPULATORS

As before with 2D arms, motion planning algorithms that we will design for
3D arms will depend heavily on the underlying arm kinematics. Each kinematics
type will require its own algorithm. The extent of algorithm specialization due to
arm kinematics will be even more pronounced in the 3D case than in the 2D case.
Let us emphasize again that this is not a problem of depth of algorithmic research
but is instead a fundamental constraint in the relationship between kinematics and
motion. The same is true, of course, in nature: The way a four-legged cat walks is
very different from the way a two-legged human walks. Among four-legged, the
gaits of cats and turtles differ markedly. One factor here is the optimization pro-
cess carried out by the evolution. Even if a “one fits all” motion control procedure
is feasible, it will likely be cumbersome and inefficient compared to algorithms
that exploit specific kinematic peculiarities. We observed this in the 2D case
(Section 5.8.4): While we found a way to use the same sensor-based motion
planning algorithm for different kinematics types, we also noted the price in
inefficiency that this universality carried. Here we will attempt both approaches.
This is not to say that the general approach to motion planning will be changing
from one arm to another; as we have already seen, the overall SIM approach is
remarkably the same independent of the robot kinematics, from a sturdy mobile
robot to a long-limbed arm manipulator.
As before, let letters P and R refer to prismatic and revolute joints, respec-
tively. We will also use the letter X to represent either a P or a R joint,
X = [P, R]. A three-joint robot arm manipulator (or the major linkage of an
arm), XXX, can therefore be one of eight basic kinematic linkages: PPP, RPP,
PRP, RRP, PPR, RPR, PRR,and RRR. As noted in Ref. 111, each basic linkage
can be implemented with different geometries, which produces 36 linkages with
joint axes that are either perpendicular or parallel to one another. Among these,
nine degenerate into linkages with only one or two DOF; seven are planar. By
also eliminating equivalent linkages, the remaining 20 possible spatial linkages
are further reduced to 12, some of which are of only theoretical interest.
The above sequence XXX is written in such an order that the first four linkages
in it are XXP arms; in each of them the outermost joint is a P joint. Those four
are among the five major 3D linkages (see Figure 6.1) that are commonly seen
in industry [111–113] and that together cover practically all today’s commercial
and special-purpose robot arm manipulators. It turns out that these four XXP
arms are better amenable to sensor-based motion planning than the fifth one
(Figure 6.1e) and than the remaining four arms in the XXX sequence. It is XXP
arms that will be studied in this chapter.
While formally these four linkages—PPP, RPP, PRP,and RRP—cover a half
of the full group XXX, they represent four out of five, or 80%, of the linkages
in Figure 6.1. Many, though not all, robot arm applications are based on XXP
major linkages. Welding, assembly, and pick-and-place robot arms are especially
common in this group, one reason being that a prismatic joint makes it easy to
produce a straight-line motion and to expand the operating space. The so-called
SCARA arm (Selective Compliance Assembly Robot Arm), whose major linkage