Page 296 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

CHAPTER 6

Motion Planning for Three-Dimensional
Arm Manipulators

The robot is going to lose. Not by much. But when the final score is tallied, flesh
and blood is going to beat the damn monster.
—Adam Smith, philosopher and economist, 1723–1790

6.1 INTRODUCTION

We are continuing developing SIM (Sensing–Intelligence–Motion) algorithms
for robot arm manipulators. The cases considered in Chapter 5 all deal with
arm manipulators whose end effectors (hands) move along a two-dimensional
(2D) surface. Although applications do exist that can make use of those algo-
rithms—for example, assembly of microelectronics on a printed circuit board is
largely limited to a 2D operation—most robot arm manipulators live and work
in three-dimensional (3D) space. From this standpoint, our primary objective
in Chapter 5 should be seen as preparing the necessary theoretical background
and elucidating the relevant issues, before proceeding to the 3D case. Sensor-
based motion planning algorithms should be able to handle 3D space and 3D
arm manipulators. Developing such strategies is the objective of this chapter. As
before, the arm manipulators that we consider are simple open kinematic chains.
Is there a fundamental difference between motion planning for two-dimensional
(2D) and 3D arm manipulators? The short answer is yes, but the question is not
that simple. Recall a similar discussion about mobile robots in Chapter 3. From the
standpoint of motion planning, mobile robots differ from arm manipulators: They
have more or less compact bodies, kinematics plays no decisive role in their motion
planning, and their workspace is much larger compared to their dimensions. For
mobile robots the difference between the 2D and 3D cases is absolute and dramatic:
Unequivocally, if the 2D case has a definite and finite solution to the planning
problem, the 3D case has no finite solution in general.
The argument goes as follows. Imagine a bug moving in the two-dimensional
plane, and imagine that on its way the bug encounters an object (an obstacle).
Sensing, Intelligence, Motion, by Vladimir J. Lumelsky
Copyright  2006 John Wiley & Sons, Inc.
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