Page 73 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

48 A QUICK SKETCH OF MAJOR ISSUES IN ROBOTICS

The reality is more complex than this simple scheme may suggest. First,
depending on the path’s initial and ending points, in general the deviation is
not necessarily symmetrical on both sides of the midpoint knot. This means that
obtaining the same deviation on both sides of the path midpoint may require
uneven distribution of knot points. In fact, minimizing the number of knot points
that satisfy a given threshold is a complex computational problem, and so is
the optimal choice of locations for knot points. Second, as Figure 2.14 demon-
strates, the tangents at endpoints of two curves that meet at a knot are not equal,
causing unhealthy accelerations and jerky motion when the arm manipulator is
passing through knot points. Third, every arm has degenerate points where var-
ious control and computational difficulties arise [7]. For example, as discussed
above (Figure 2.3), if the arm links are of the same length, l 1 = l 2 ,the arm’s
joint values are ill-defined when its endpoint is at the arm base. If a knot point
happened to be located in the base, the inverse kinematics procedure that turns
out joint angles for every proposed knot point may give solutions that are in
sharp contrast with the arm’s prior and future motion.
Various schemes have been considered to address those complications, such
as splines between the path curve segments or approximation of the curves with
more complex polynomials featuring desired characteristics.

2.7 COLLISION AVOIDANCE

Whatever robot application is considered—assembly, welding, cleaning, explor-
ing a new planet—for the robot’s own sake and for its environment, it is
paramount that the robot does not bump into surrounding objects. Of the issues
in robotics that we set out to review in this chapter, motion planning and col-
lision avoidance is perhaps the most universal robotic problem. It is also the
most “robotic” robotic problem: Whereas other issues and techniques considered
above are common to other areas of sciences and engineering, collision avoid-
ance—especially its branch that deals with partial input information (such as
from sensors)—is the monopoly of robotics. This is true for all robots and all
variations of the collision avoidance problem, from mobile robots operating in
a two-dimensional surface to multilink robot arm manipulators moving in three-
dimensional space among three-dimensional objects. This monopoly does not
imply, of course, that the problem of motion planning is harder or easier than
those other issues, but it does imply two things: (a) that robotics is a distinct
discipline, with its own problems and its own methodological apparatus, and
(b) that solving this problem is our full responsibility—there will be no help
from other disciplines.
To avoid collisions, the robot must know something about objects that it tries
to avoid. Knowledge carries a price, either in terms of sensing that is necessary
to acquire it, or in terms of the amount and speed of memory the robot needs to
store it, or in terms of computational power it needs to process this knowledge. In
fact, a complete information about the robot workspace is usually of tremendous