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 algorithms—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 ...