Global tracking for an underactuated ships with bounded feedback controllers

In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable (GAS). It has been designed using a 3 Degree of Freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observers and can be used as an output feedback controller. Simulation results demonstrate the effectiveness of this method

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

Underactuated leader-follower synchronisation for multi-agent systems with rejection of unknown disturbances

Author preprintIn this paper leader-follower synchronization is considered for underactuated followers in an inhomogeneous multi-agent system. The goal is to synchronise the motion of a leader and an underactuated follower. Measurements of the leader's position and velocity are available, while the dynamics and trajectory of the leader is unknown. The leader velocities are used as input for a constant bearing guidance algorithm to assure that the follower synchronises its motion to the leader. It is also shown that the proposed leader-follower scheme can be applied to multi-agent systems that are subjected to unknown environmental disturbances. Furthermore, the trajectory of the leader does not need to be known. The stability properties of the complete control scheme and the unactuated internal dynamics are analysed using nonlinear cascaded system theory. Simulation results are presented to validate the proposed control strategy.Preprint version. © IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

Normal forms for underactuated mechanical systems with symmetry

We introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms include three classes of cascade systems, namely, nonlinear systems in strict feedback form, feedforward form, and nontriangular quadratic form (to be defined). In each case, the transformation to cascade systems is provided in closed-form. We apply our results to the Acrobot, the rotating pendulum, and the cart-pole system

Prescribed performance control of underactuated surface vessels' trajectory using a neural network and integral time-delay sliding mode

summary:To tackle the underactuated surface vessel (USV) trajectory tracking challenge with input delays and composite disturbances, an integral time-delay sliding mode controller based on backstepping is discussed. First, the law of virtual velocity control is established by coordinate transformation and the position error is caused to converge utilizing the performance function. At the same time, based on the estimation of velocity vector by the high-gain observer (HGO), radial basis function (RBF) neural network is applied to compensate for both the uncertainty of model parameters and external disturbances. The longitudinal and heading control laws are presented in combination with the integral time-delay sliding mode control. Then, on the basis of Lyapunov - Krasovskii functional and stability proof, virtual velocity error is guaranteed to converge to 0 in finite time. Finally, the outcomes of the numerical simulation demonstrate the reliability and efficiency of the proposed approach

Adaptive neural network control of underactuated surface vessels with guaranteed transient performance: Theory and experimental results

In this paper, an adaptive trajectory trackingcontrol algorithm for underactuated unmanned surfacevessels (USVs) with guaranteed transient performance isproposed. To meet the realistic dynamical model of USVs,we consider that the mass and damping matrices are notdiagonal and the input saturation problem. Neural Networks(NNs) are employed to approximate the unknown externaldisturbances and uncertain hydrodynamics of USVs. Moreover,both full state feedback control and output feedbackcontrol are presented, and the unmeasurable velocities ofthe output feedback controller are estimated via a highgainobserver. Unlike the conventional control methods,we employ the error transformation function to guaranteethe transient tracking performance. Both simulation andexperimental results are carried out to validate the superiorperformance via comparing with traditional potential integral(PI) control approaches

NONLINEAR ADAPTIVE HEADING CONTROL FOR AN UNDERACTUATED SURFACE VESSEL WITH CONSTRAINED INPUT AND SIDESLIP ANGLE COMPENSATION

In this paper, a nonlinear adaptive heading controller is developed for an underactuated surface vessel with constrained input and sideslip angle compensation. The controller design is accomplished in a framework of backstepping technique. First, to amend the irrationality of the traditional definition of the desired heading, the desired heading is compensated by the sideslip angle. Considering the actuator physical constrain, a hyperbolic tangent function and a Nussbaum function are introduced to handle the nonlinear part of control input. The error and the disturbance are estimated and compensated by an adaptive control law. In addition, to avoid the complicated calculation of time derivatives of the virtual control, the command filter is introduced to integrate with the control law. It is analysed by the Lyapunov theory that the closed loop system is guaranteed to be uniformly ultimately bounded stability. Finally, the simulation studies illustrate the effectiveness of the proposed control method