Page 244 - Autonomous Mobile Robots

230 Autonomous Mobile Robots

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
[7,8]. Using the special algebraic structures of the canonical forms, various
feedback strategies have been proposed to stabilize nonholonomic systems in
the literature [9–12]. The majority of these constructive methods have been
developed based on exact system models. However, it is more practical to design
the controller against possible existence of modeling errors and external dis-
turbances. A hybrid feedback algorithm based on supervisory adaptive control
was presented to globally asymptotically stabilize a wheeled mobile robot
[13]. Output feedback tracking and regulation controllers were presented in
Reference14forpracticalwheeledmobilerobots. Robustnessissueswithregard
to disturbances in the kinematic model have also been investigated.
In practice, however, it is more realistic to formulate the nonholonomic
system control problem at the dynamic level, where the torque and force are
taken as the control inputs. In actual applications, however, exact knowledge of
the robot dynamics is almost impossible. Adaptive control strategies were pro-
posed to stabilize dynamic nonholonomic systems [15]. Sliding mode control
was applied to guarantee the uniform ultimate boundedness of tracking error
in Reference 16. In Reference 17, stable adaptive control was investigated for
dynamic nonholonomic chained systems with uncertain constant parameters.
Using geometric phase as a basis, control of Caplygin dynamical systems was
studied in Reference 18, and the closed-loop system was proved to achieve the
desired local asymptotic stabilization of a single equilibrium solution. Thanks
to the research in References 19 and 20, the motion control part of the problem
can be reduced to a problem similar to the free-motion control of a robot with
less degrees of freedom. Robust adaptive motion controllers were proposed in
References 21 and 22 using the linear-in-the-parameter property of the system
dynamics and the bound of the robot parameters.
The difficulty in precise dynamic modeling has invoked the development
of approximator-based control approaches, using Lyapunov synthesis for the
general nonlinear system [23–28]. Neural networks (NNs) are well known for
its ability to extend adaptive control techniques to systems in nonlinear-in-the-
parameters. The universal approximation properties of NNs in the feedback
control systems successfully avoid the use of regression matrices, and assump-
tions such as certainty equivalence. It requires no persistence of excitation
conditions by using the robustifying terms. For a comprehensive study of
the subject, readers are referred to Reference 29 and the references therein.
For fuzzy logic systems, it provides natural and linguistic representation of
human’s (or expert’s) knowledge, reasoning about vague rules that describe
the imprecise and qualitative relationship between the system’s input and out-
put. The combination of NNs and fuzzy logic systems can overcome some
of the individual weaknesses and offer some appealing features. It offers an

© 2006 by Taylor & Francis Group, LLC

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