## Tracking and Regulation Control of an Underactuated Surface Vessel with Nonintegrable Dynamics## IntroductionOver the past ten years, the attitude control of rigid body systems has become an active area of research. Among its many applications are the attitude control of rigid aircraft and spacecraft systems (the interested reader is referred to [27] for a literature review of the many different types of applications). Rigid spacecraft applications are often required to perform highly accurate slewing and/or pointing maneuvers that force the spacecraft to rotate along a relatively large amplitude trajectory. These performance requirements mandate that the control design be predicated on the use of the nonlinear spacecraft model [1]. This nonlinear model is typically represented by: (i) Euler's dynamic equation which is used to describe the time evolution of the angular velocity vector, and (ii) the kinematic equation which relates the time derivatives of the orientation angles to the angular velocity vector. Several kinematic parametrizations exist to represent the orientation angles, including singular, three-parameter representationse.g., the Euler angles, Gibbs vector, Cayley-Rodrigues
parameters, and modified Rodrigues parameters) and the nonsingular,
four-parameter representation given by the unit quaternion
i.e., the Euler parameters). Whereas the three-parameter
representations always exhibit singular orientations i.e.,
the Jacobian matrix in the kinematic equation is singular for some
orientations), the unit quaternion globally represents the
spacecraft attitude without singularities; however, an additional
constraint equation is introduced through the use of the
four-parameter representation.
Several solutions to the attitude control problem have been
presented in the literature since the early 1970's [19]. In [27], the authors
presented a general attitude control design framework which
includes PD, model-based, and adaptive setpoint controllers.
Adaptive tracking control schemes based on three-parameter,
kinematic representations were presented in [23,25] to compensate for the unknown, spacecraft
inertia matrix. In [1], an adaptive attitude
tracking controller based on the unit quaternion was proposed that
identified the inertia matrix via periodic command signals. The
work of [1] was later applied to the angular
velocity tracking problem in [2]. A
suboptimal state feedback controller was developed for the
quaternion representation in [10]. In [15], the authors designed an inverse optimal
control law for attitude regulation using the backstepping method
for a three-parameter representation. Recently, [5] presented a variable structure tracking
controller using quaternions in the presence of spacecraft inertia
uncertainties and external disturbances. In [8], Costic All of the above control strategies assume that the spacecraft
is fully actuated ( In this paper, we propose a novel, continuous, time-varying,
nonlinear tracking controller for the kinematic model of an
axisymmetric as well as non-axisymmetric underactuated rigid
spacecraft. The control structure is motivated by the
Lyapunov-based dynamic oscillator presented in [12] for wheeled mobile robots. The proposed control
approach is novel in that several key characteristics of the
quaternion kinematic representation are exploited during the
redesign of the control structure originally proposed in [12]. Indeed, it is the fusion of the dynamic
oscillator-based approach ( ## Simulation Results:Select and click to view some of the simulation plots: ## Publication:For more information concerning this research, please refer to the following publication: |