Page 62 - Introduction to Autonomous Mobile Robots

3 Mobile Robot Kinematics

3.1 Introduction

Kinematics is the most basic study of how mechanical systems behave. In mobile robotics,
we need to understand the mechanical behavior of the robot both in order to design appro-
priate mobile robots for tasks and to understand how to create control software for an
instance of mobile robot hardware.
Of course, mobile robots are not the first complex mechanical systems to require such
analysis. Robot manipulators have been the subject of intensive study for more than thirty
years. In some ways, manipulator robots are much more complex than early mobile robots:
a standard welding robot may have five or more joints, whereas early mobile robots were
simple differential-drive machines. In recent years, the robotics community has achieved a
fairly complete understanding of the kinematics and even the dynamics (i.e., relating to
force and mass) of robot manipulators [11, 32].
The mobile robotics community poses many of the same kinematic questions as the
robot manipulator community. A manipulator robot’s workspace is crucial because it
defines the range of possible positions that can be achieved by its end effector relative to
its fixture to the environment. A mobile robot’s workspace is equally important because it
defines the range of possible poses that the mobile robot can achieve in its environment.
The robot arm’s controllability defines the manner in which active engagement of motors
can be used to move from pose to pose in the workspace. Similarly, a mobile robot’s con-
trollability defines possible paths and trajectories in its workspace. Robot dynamics places
additional constraints on workspace and trajectory due to mass and force considerations.
The mobile robot is also limited by dynamics; for instance, a high center of gravity limits
the practical turning radius of a fast, car-like robot because of the danger of rolling.
But the chief difference between a mobile robot and a manipulator arm also introduces
a significant challenge for position estimation. A manipulator has one end fixed to the envi-
ronment. Measuring the position of an arm’s end effector is simply a matter of understand-
ing the kinematics of the robot and measuring the position of all intermediate joints. The
manipulator’s position is thus always computable by looking at current sensor data. But a