Page 95 - Introduction to Autonomous Mobile Robots

Chapter 3
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Can the omnidirectional robot accomplish this trajectory? We assume that the robot can
achieve some arbitrary, finite velocity at each wheel. For simplicity, we further assume that
acceleration is infinite; that is, it takes zero time to reach any desired velocity. Under these
assumptions, the omnidirectional robot can indeed follow the trajectory of figure 3.15. The
transition between the motion of second 1 and second 2, for example, involves only
changes to the wheel velocities.
Because the two-steer has δ = 3 , it must be able to follow the path that would result
M
from projecting this trajectory into timeless workspace. However, it cannot follow this 4D
trajectory. Even if steering velocity is finite and arbitrary, although the two-steer would be
able to change steering speed instantly, it would have to wait for the angle of the steerable
wheels to change to the desired position before initiating a change in the robot chassis ori-
entation. In short, the two-steer requires changes to internal degrees of freedom and
because these changes take time, arbitrary trajectories are not attainable. Figure 3.16
depicts the most similar trajectory that a two-steer can achieve. In contrast to the desired
three phases of motion, this trajectory has five phases.

3.5 Beyond Basic Kinematics

The above discussion of mobile robot kinematics is only an introduction to a far richer
topic. When speed and force are also considered, as is particularly necessary in the case of
high-speed mobile robots, dynamic constraints must be expressed in addition to kinematic
constraints. Furthermore, many mobile robots such as tank-type chassis and four-wheel
slip/skid systems violate the kinematic models above. When analyzing such systems, it is
often necessary to explicitly model the dynamics of viscous friction between the robot and
the ground plane.
More significantly, the kinematic analysis of a mobile robot system provides results
concerning the theoretical workspace of that mobile robot. However to effectively move in
this workspace a mobile robot must have appropriate actuation of its degrees of freedom.
This problem, called motorization, requires further analysis of the forces that must be
actively supplied to realize the kinematic range of motion available to the robot.
In addition to motorization, there is the question of controllability: under what condi-
tions can a mobile robot travel from the initial pose to the goal pose in bounded time?
Answering this question requires knowledge – both knowledge of the robot kinematics and
knowledge of the control systems that can be used to actuate the mobile robot. Mobile robot
control is therefore a return to the practical question of designing a real-world control algo-
rithm that can drive the robot from pose to pose using the trajectories demanded for the
application.