Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rigid bodies globally and uniquely.We focus on the kinematic model of the underactuated vehicle,which features an underactuation form that has no sway and heave velocity.To compensate for the lack of these two velocities,we construct additional rotation matrices to generate a motion of rotation coupled with translation.Then,the state feedback is designed with the help of the logarithmic map,and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction.Later,the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance.Finally,simulation examples are provided to verify the effectiveness of the stabilization controller.

A nonlinear bottom-following controller for underactuated autonomous underwater vehicles

The bottom-following problem for underactuated autonomous underwater vehicles （AUV） was addressed by a new type of nonlinear decoupling control law. The vertical bottom-following error and pitch angle error are stabilized by means of the stem plane, and the thruster is left to stabilize the longitudinal bottom-following error and forward speed. In order to better meet the need of engineering applications, working characteristics of the actuators were sufficiently considered to design the proposed controller. Different from the traditional method, the methodology used to solve the problem is generated by AUV model without a reference orientation, and it deals explicitly with vehicle dynamics and the geometric characteristics of the desired tracking bottom curve. The estimation of systemic uncertainties and disturbances and the pitch velocity PE （persistent excitation） conditions are not required. The stability analysis is given by Lyapunov theorem. Simulation results of a full nonlinear hydrodynamic AUV model are provided to validate the effectiveness and robustness of the proposed controller.

Serret-Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties

The path following problem for an underactuated unmanned surface vehicle(USV) in the Serret-Frenet frame is addressed. The control system takes account of the uncertain influence induced by model perturbation, external disturbance, etc. By introducing the Serret-Frenet frame and global coordinate transformation, the control problem of underactuated system(a nonlinear system with single-input and ternate-output) is transformed into the control problem of actuated system(a single-input and single-output nonlinear system), which simplifies the controller design. A backstepping adaptive sliding mode controller(BADSMC)is proposed based on backstepping design technique, adaptive method and theory of dynamic slide model control(DSMC). Then, it is proven that the state of closed loop system is globally stabilized to the desired configuration with the proposed controller. Simulation results are presented to illustrate the effectiveness of the proposed controller.

Diving control of underactuated unmanned undersea vehicle using integral-fast terminal sliding mode control

The problem of diving control for an underactuated unmanned undersea vehicle(UUV) considering the presence of parameters perturbations and wave disturbances was addressesed.The vertical motion of an UUV was divided into two noninteracting subsystems for surge velocity control and diving.To stabilize the vertical motion system,the surge velocity and the depth control controllers were proposed using backstepping technology and an integral-fast terminal sliding mode control(IFTSMC).It is proven that the proposed control scheme can guarantee that all the error signals in the whole closed-loop system globally converge to the sliding surface in finite time and asymptotically converge to the origin along the sliding surface.With a unified control parameters for different motion states,a series of numerical simulation results illustrate the effectiveness of the above designed control scheme,which also shows strong robustness against parameters perturbations and wave disturbances.

Control for Underactuated Reentry Aircraft in Small Angle of Attack

The control problem for under-actuated reentry vehicle like HTV-2 is considered with small angle of attack.The control strategy for an aircraft with positive lateral control departure parameter relies on strong lateral stability,which declines with the decrease of the angle of attack.Thus,to control the lateral-directional motion in a stable state is hard and even impossible in some scenarios where the under-actuated reentry vehicle,like HTV-2,flies in a low angle of attack.To address this problem,the lateral-directional open-loop motion characteristics are analyzed.The results show that in an uncontrolled state,the lateral-directional motion can automatically converge to stabilization thanks to the aerodynamic damping effect.Therefore,a method of turning-off the lateral-directional control and inviting aerodynamic damping to control can achieve stability.The six-degree-of-freedom simulation show that the lateral-directional motion can be stabilized by the aerodynamic damping,and the lateral position error caused by the bank angle deviation is limited near the zero-rise angle of attack.The control strategy is effective.

Three-Dimensional Trajectory Tracking Control of Underactuated Autonomous Underwater Vehicles with Input Saturation

This paper addresses a three-dimensional(3D)trajectory tracking problem of underactuated autonomous underwater vehicles(AUVs)subjected to input saturation and external disturbances.The proposed controller can achieve practical convergence of tracking errors for general reference trajectories,including persistently exciting(PE)time varying trajectories and fixed points.At first,a modified error state formulation is introduced to tackle the situation that desired velocities do not satisfy PE condition.Then,on the basis of the backstepping technique and a Nussbaum-type even function,a saturated controller is designed so that the tracking errors can converge to a bounded neighborhood of the origin.The stability analysis based on Lyapunov theory shows that the tracking errors are globally ultimately uniformly bounded.Finally,some simulation results illustrate the effectiveness and robustness of the proposed control strategy.