Contents 1 Introduction
In an underactuated dynamical system, the dimension of the space spanned by the control vector is less than the dimension of the configuration space. Con-sequently, systems of this kind necessarily exhibit constraints on accelerations. See (11) for a survey of these concepts. The motivation for the study of controllers for underactuated systems, namely mobile robots is manifold and includes the following:
Practical applications. There isan increasing number of real-life underactuated mechanical sys-tems. Mobile robots, walking robots, spacecraft, aircraft, helicopters, missiles, surface vessels, and underwater vehicles are representative examples.
Cost reduction. For example, for underwater vehicles that work at large depths, the inclusion of a lateral thruster is very expensive and represents large capital costs.
Weight reduction. This issue is of critical importance for aerial vehicles.
Thruster efficiency. Often, an otherwise fully actuated vehicle may become underactuated when its speed changes. This happens in the case of AUVs that are designed to maneuver at low speeds using thruster control only. As the forward speed increases, the efficiency of the side thrusters decreases sharply, thus making it impossible to impart pure lateral motions on the vehicle.
Reliability considerations. Even for fully actuated vehicles, if one or more actuator failures occur, the system should be capable of detecting them and engaging a new control algorithm specially designed to accommodate the respective fault, and complete its mission if at all possible.
Complexity and increased challenge that this class of systems bring to the control area. In fact,. most underactuated systems are not fully feedback linearizable and exhibit nonholonomic constraints.
