Professor has given a reference paper .based on which i have submitted a project proposal and he gave the feedback. we need to use MPC controller matlab .we need to submit the final project report in IEEE format (latex ).i need to get done from my previous expert who has done my assignment(order ID
118410.Model Predictive Control of an Autonomous Underwater Vehicle for Cable/Pipeline Tracking Lakshmi Kothuru∗, ID:101243905∗ Carleton University ∗, Ottawa, Canada Email:
[email protected] , Abstract—The inspection and monitoring of sub-sea cables and pipelines have become critical concerns in the modern world as any damage in sub-sea cables affects the internet which plays a pivotal role in everyday life. We will be using MPC (model control predictive control) to generate reference headings for autonomous underwater vehicles (AUVs) and minimize the error between vehicle path and pipeline. ROVs (Remotely operated vehicles) have limitations in their range of operation due to the length of their tether, and the need for a support vessel and operator increases the cost of monitoring operations. To address these issues, making the vehicle autonomous would allow it to perform tasks with minimal human intervention. Keywords—model control predictive control;autonomous under- water vehicles;Remotely operated vehicles; Application; Software I. INTRODUCTION Model predicative control (MPC) algorithms are designed to optimize the future behavior of a plant by computing a sequence of manipulated variable adjustments. While initially developed for power plants and refineries, this technology has found applications in a variety of fields such as chemicals, food processing, automotive, aerospace, metallurgy, and more [1]. II. OBJECTIVE The primary objective of this project is to develop an AUV capable of tracking underwater cables and pipelines using Model Predictive Control [2]. The project aims to design, simulate the results for the system that can operate autonomously and achieve accurate tracking of underwater cables and pipelines.In [3] The objective function is J = Hp∑ i=1 [ŷ(k + i)− w(k + i)]2 The components of the AUV velocity in the (x, y) plane can be stated as, • Vx = Vpcos(y)p • Vy = Vpsin(y)p III. PROPOSED SCHEDULE S.No Activity Timeline 1 Conduct a literature review and analyze existing systems and technologies for cable/pipeline 15 February, 2023 to 10 March, 2023 2 MPC MATLAB code and analysis 11 March, 2023 to 5 April, 2023 3 Documentation and Report 6 April, 2023 to 12 April, 2023 TABLE I. TIMELINE FOR THE PROJECT REFERENCES [1] H. W. Y. Shi, C. Shen and K. Zhang, Advanced Model Predictive Control for Autonomous Marine Vehicles, Springer Nature. ISBN 978-3-031- 19353-8: In Press, 2023. [2] A. S. M. Naeem W., Sutton R and B. R. S., “A review of guidance laws applicable to unmanned underwater vehicles,” The Journal of Navigation, vol. 56, no. 1, pp. 15–29, 2023. [3] W. Naeem, R. Sutton, and S. Ahmad, “Pure pursuit guidance and model predictive control of an autonomous underwater vehicle for cable/pipeline tracking,” in Proceedings-Institute of Marine Engineering Science and Technology Part C Journal of Marine Science and Environment. Cite- seer, 2004, pp. 25–35. Feedback 9/1 1. You have to explain clearly what the output y is in the cost function. What is w(k)? Are there any constraints? 2. In the model, you have to define what Vp, y, and p are. 3. The reference [2] was published in 2003. Please note the final report should be in a standard research paper format. The IEEE conference manuscript template can be found here. requirements), and proposed approaches (should be MPC or at least optimization-based approach) and timeline. Microsoft Word - IMarEST.doc 1 Pure Pursuit Guidance and Model Predictive Control of an Autonomous Underwater Vehicle for Cable/Pipeline Tracking W. Naeem, R. Sutton and S. M. Ahmad {wnaeem, rsutton, sahmad}@plymouth.ac.uk Marine and Industrial Dynamic Analysis Research Group Department of Mechanical and Marine Engineering The University of Plymouth, Plymouth, PL4 8AA, UK Abstract This paper investigates a new approach for the guidance and control of an autonomous underwater vehicle (AUV). An integrated system is developed and simulated involving a proportional navigation guidance (PNG) law and model predictive control (MPC). The classical PNG law for missile systems has been tailored to guide the AUV by generating reference headings. MPC is used to track the reference trajectory (guidance commands), which is optimised using a genetic algorithm (GA). The performance of the closed loop system is evaluated in simulations with and without sea current disturbance and imposing actuator constraints. Simulation results for the case of a cable tracking mission and waypoint following clearly shows the superiority of the proposed algorithm. 1. INTRODUCTION The technology and applications of unmanned underwater vehicles (UUVs) have been improving at a rapid pace. From missions such as cable/pipeline inspection to oil exploration and to mine clearing operations, they are routinely been deployed by the offshore and defence industry. This is mainly attributed to the fact that it does not require any human onboard thereby not jeopardizing any life. In addition, in cases such as deep-sea exploration, where human intervention is not possible, they are proved to be a viable tool. Although regular monitoring and inspection of cables/pipelines running in deep sea have emerged as an important issue, little attention has been paid to sub-sea cables or pipelines. This paper describes a novel approach to underwater vehicle cable tracking mission by employing an integrated guidance and control system using a PNG law for missile systems and MPC. The contemporary method to detect linear subsea objects is through active magnetic, 2 passive magnetic or electromagnetic detectors mounted on a remotely operated vehicle (ROV) [1]. These sensors provide lateral and longitudinal displacement of the ROV from the target pipeline, but no target direction. Additional sensor is needed to measure the target orientation. This information is then used by the ROV pilot to steer the vehicle over the pipeline. Although ROVs have been employed for detection and tracking, their range of operation is constrained by the length of the tether. Furthermore, the need for a support vessel and an ROV operator adds to the cost of monitoring operation. One way to circumvent these problems is to render the vehicle autonomous, that is, they execute the task with minimal human intervention. A variety of methodologies and concepts have been reported to perform object tracking by an underwater vehicle. An account of various AUV guidance schemes has recently been documented by Naeem et al. [2] while a comparison of classical and advance control strategies has been reported by Craven et al. [3]. In this paper, a modified PNG law is proposed for tracking underwater cables/pipelines employing a sonar system. MPC is used to track the reference commands generated by the PNG. The intent is to demonstrate the suitability of the integrated guidance and control scheme for detecting and tracking an undersea object, in this instance a pipeline, via simulation. The tracking of a pipeline by an AUV is first posed as an AUV-target interception problem. The classical PNG law is then employed to generate the guidance command signals to the AUV. Subsequently this is modified to achieve the desired target tracking trajectory objective. 1.1 Sonars Recent advances in sonar technology provides a sophisticated means of finding fibre optic cable, plastic, metal and other materials suspended in mid-ocean or buried in a seabed [4]. This strategy entails use of an active sonar system for target (pipeline) detection. Active sonars employ echo ranging to detect an object whereas passive sonars pick-up acoustic radiation of ships, submarines etc, by an array of hydrophones. Some of the several other factors that influence this choice are: 1. Active sonars echo-range and therefore are capable of detecting even a submerged pipeline in the background of clutter i.e., reverberations, in which it appears. Vision based systems will have severe limitations in such a scenario which is very 3 likely to occur at sea bed due to underwater current and various other natural disturbances. 2. They can provide both range and orientation of the target, unlike magnetometers, which are non-directional and can easily mislead the AUV in presence of subsea ferrous deposits. 3. Presence of onboard active sonar can also be employed for retrieval of an AUV back to the mother ship once mission is accomplished. This has been investigated by Ahmad et al. [5] and is an area of ongoing research. 4. Sonic signals are the only practical and efficient way of long-range undersea communication, for instance between the mother ship and the AUV [6]. The broader aim of the authors is to render a underwater vehicle truly autonomous, incorporating features such as smart launch, mid-course guidance, target tracking, area search and finally, return and dock to the mother ship autonomously on completion of a given task. 2. PROBLEM DEFINITION The following assumptions are made in order to formulate the guidance problem: i) The AUV-target engagement is planar i.e. in the same plane. ii) Although the pipeline is a continuous object, it is convenient to assume it as a point mass moving with a constant velocity. This condition can be ensured by considering only the latest value of echoed ping received by an onboard AUV sonar. The AUV is also considered as a constant velocity mass point. iii) Complete navigational information of the target is available to the AUV. Consider a two-dimensional engagement geometry in which the AUV and target are closing on each other at constant velocities pV and eV respectively as shown in Figure 1. An imaginary line joining the AUV and target is referred as the line of sight (LOS). The angle formed by the LOS with the fixed reference is λ and from the geometry is given as, r h1tan −=λ (1) 4 where, h and r are the relative separation between the AUV and target perpendicular and parallel to the fixed reference respectively. The relative movement between the AUV and target causes the LOS to rotate through a small angle λ , indicating a displacement h between AUV and target perpendicular to the fixed reference. The length of LOS is a range R and represents the initial AUV-target distance. The problem is then to develop an integrated system which will make the initial range R between the AUV and target as small as possible at the end of expected intercept time. It will be shown later in simulation that it is a good starting point for achieving the desired tracking objective, without actually intercepting the target. 3. GUIDANCE AND CONTROL Herein a PNG law is utilised to obtain the guidance commands. The guidance subsystem takes input from the sensors onboard the AUV. The sensors used could be global positioning system (GPS) for positioning on the surface, inertial navigation system (INS), compass etc. Information from the sensors is fused together and provided to the guidance system, which then generate commands to be followed by the AUV. A simple block diagram of the navigation, guidance and control system is depicted in Figure 2. MPC is used to track the reference commands from the guidance system. The selection of MPC for this paper is attributed to several factors, the most important being its ability to handle constraints in a natural and systematic way. The following subsections describe the PNG and MPC algorithms and their development. 3.1 Proportional navigation guidance law The ultimate objective of the guidance law is to steer the AUV so that it will chase a target using a constant AUV velocity pV and a controllable heading angle pψ . However, initially it will be regarded as an AUV-target interception problem and then subsequently modified to realise the desired “tail-chase” type AUV trajectory. The tail-chase type trajectory of interest is akin to that formed when a dog is chasing a cat. This type of trajectory will ensure that the AUV is always trailing behind the target and thus continuously monitor it at a close length. From the discussion of Section 2, it is intuitive that if the AUV is made to lie on the LOS and hold it there as well, a constant relative bearing between the AUV and target is ensured that is, the LOS of 5 sight does not rotate, and interception will occur. This mechanisation can be realised using a PNG law. Proportional navigation is a method of guidance, which generates command signals cu , proportional to the LOS angle λ , so that the pursuing vehicle remains on the LOS. This can be mathematically stated as: λ∝cu (2) λkuc = (3) Where, k is called the navigation constant and is an important design parameter. A judicious choice of k will ensure that the LOS does not rotate and hence no further input command is required. Thus, it influences both, the engagement trajectory as well as the command input. The proportional navigation guidance scheme is illustrated in Figure 3 and a good description on PNG can be found in [7]. 3.1.1 Guidance law application For implementing the guidance law of Equation 3, it is necessary to compute the LOS angle λ . This requires relative positions of the AUV and target in both the co- ordinates i.e., h = ye - yp (4) r = xe - xp (5) therefore, = − pe pe1 x- x y - y tanλ (6) The components of the AUV velocity in the ),( yx plane can be stated as, ppx cosVV ψ= (7) ppy sinVV ψ= (8) 6 Hence, the differential equation for the components of the AUV position can be expressed as: xp Vx =& (9) yp Vy =& (10) It is assumed that the AUV speed pV and heading angle pψ are available to the guidance logic from an onboard speed log and gyro compass respectively. In certain cases both components of the AUV speed i.e., Equations 9 and 10 can be obtained