Page 203 - Autonomous Mobile Robots

II

Modeling and Control

For robotic systems that are embodied, situated and mobile, intelligent inter-
action with the environment and the successful operation in response to
higher-level commands is crucial before such systems can qualify as autonom-
ous and intelligent. This implies the ability of each robot to, at least, be capable
of controlling the equipped hardware so as to take the action that is required of
the robot, which ranges from moving between points, to changing the pose of
equipment like robotic grippers and manipulators. Effective control of a robot’s
hardware faculties, and making use of sensor feedback, is therefore extremely
important.
Due to Brockett’s theorem, it is well known that nonholonomic systems with
restricted mobility cannot be stabilized to a desired configuration (or posture)
via differentiable, or even continuous, pure-state feedback. Therefore, different
approacheshavebeenproposed, whichincludesdiscontinuous, hybrid, andtime
varying control laws. Many elegant control strategies have been proposed for
various nonholonomic systems. Among them, research results can generally be
classified into two classes. The first class is kinematic control, which provides
the solutions only on a pure kinematic level, where the systems are represented
by their kinematic models and velocity acts as the control input. One commonly
used approach for the controller design of nonholonomic systems is to convert,
with appropriate state and input transformations, the original systems into some
canonical forms for which the design can be carried out more easily. Chapter 5
explores the use of discontinuous control laws for the kinematic control of
nonholonomic systems. The chapter also presents the design of a hybrid variable

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© 2006 by Taylor & Francis Group, LLC

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