A solution to the path following problem for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty is proposed. For a general class of vehicles moving in 2D space, we demonstrated a path following control law based on multiple variable sliding mode that yields global boundedness and convergence of the position tracking error to a small neighborhood and robustness to parametric modeling uncertainty. An error integration element is added into the “tanh” function of the traditional sliding mode control. We illustrated our results in the context of the vehicle control applications that an underwater vehicle moves along with the desired paths in 2D space. Simulations show that the control objectives were accomplished. 1. Introduction The past few decades have witnessed an increased research effort in the area of motion control of autonomous vehicles. A typical motion control problem is trajectory-tracking, which is concerned with the design of control laws that force a vehicle to reach and follow a time parameterized reference (i.e., a geometric path with an associated timing law). The degree of difficulty involved in solving this problem is highly dependent on the configuration of the vehicle. For fully actuated systems, the trajectory-tracking problem is now reasonably well understood. For underactuated vehicles, that is, systems with fewer actuators than degrees-of-freedom, trajectory-tracking is still an active research topic. The study of these systems is motivated by the fact that it is usually costly and often not practical to fully actuate autonomous vehicles due to weight, reliability, complexity, and efficiency considerations. Typical examples of underactuated systems include wheeled robots, hovercraft, spacecraft, aircraft, helicopters, missiles, surface vessels, and underwater vehicles. The tracking problem for underactuated vehicles is especially challenging because most of these systems are not fully feedback linearizable and exhibit nonholonomic constraints. The reader is refereed to [1] for a survey of these concepts and to [2] for a framework to study the controllability and the design of motion algorithms for underactuated Lagrangian systems on Lie groups. The classical approach for trajectory-tracking of underactuated vehicles utilizes local linearization and decoupling of the multivariable model to steer the same number of degrees of freedom as the number of available control inputs, which can be done using standard linear (or nonlinear) control methods. Alternative approaches include the
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