【摘要】：在控制理論中,路徑跟蹤(Path Following)是繼設(shè)定點(diǎn)鎮(zhèn)定、軌跡跟蹤之后一類重要的運(yùn)動控制問題。同軌跡跟蹤相比,路徑跟蹤控制器需要同時確定待跟蹤期望路徑的信息和控制運(yùn)動對象的系統(tǒng)動態(tài)。路徑跟蹤控制廣泛存在于數(shù)控機(jī)床跟蹤磨削、移動機(jī)器人運(yùn)動控制、飛機(jī)或輪船的航跡控制和智能車自主駕駛等領(lǐng)域,對路徑跟蹤及其分支問題進(jìn)行研究,不僅可以豐富運(yùn)動控制的理論成果,還可以滿足多領(lǐng)域?qū)\(yùn)動控制技術(shù)越來越高的要求,具有重大的理論和工程意義。輪式移動機(jī)器人是非線性約束系統(tǒng)的典型代表,本文將其選擇為運(yùn)動控制對象,對其路徑跟蹤控制問題進(jìn)行了研究。同其他控制方法相比,非線性模型預(yù)測控制(Nonlinear Model Predictive Control,NMPC)具有滾動優(yōu)化和反饋校正的機(jī)理,能夠處理系統(tǒng)的狀態(tài)約束和輸入約束。本文將NMPC控制方案應(yīng)用于輪式移動機(jī)器人的運(yùn)動控制,實(shí)現(xiàn)了機(jī)器人對期望路徑的跟蹤控制。本文按照如下的系統(tǒng)設(shè)計(jì)步驟完成了輪式移動機(jī)器人路徑跟蹤控制系統(tǒng)的設(shè)計(jì):問題描述、建立被控對象數(shù)學(xué)模型、依據(jù)控制目標(biāo)設(shè)計(jì)控制器、閉環(huán)系統(tǒng)穩(wěn)定性分析和仿真驗(yàn)證。本文首先對路徑跟蹤控制進(jìn)行了問題描述,推導(dǎo)并建立了輪式移動機(jī)器人的運(yùn)動學(xué)模型,確立了路徑跟蹤的控制任務(wù)。在本文中,存在路徑跟蹤任務(wù)的輪式移動機(jī)器人是Unicycle型機(jī)器人,它由兩個獨(dú)立驅(qū)動后輪和一個萬向輪構(gòu)成,機(jī)械結(jié)構(gòu)簡單,運(yùn)動形式靈活可控。分析所建立的數(shù)學(xué)模型,本文的運(yùn)動控制對象在本質(zhì)上屬于非線性、多輸入多輸出,同時具有狀態(tài)和輸入約束的系統(tǒng)。然后,針對具有非線性動態(tài)和約束條件的控制任務(wù),本文建立了基于NMPC方案的閉環(huán)控制結(jié)構(gòu),給出了開環(huán)優(yōu)化問題具體的數(shù)學(xué)形式和程序求解步驟,并對優(yōu)化問題的可行性和系統(tǒng)的性能進(jìn)行了分析。本文基于非線性多面體描述和線性矩陣不等式求解了保證NMPC方案可行性和收斂性的非零終端要素,并通過仿真實(shí)驗(yàn)對比分析了基于終端不等式約束的NMPC和基于終端等式約束的NMPC在系統(tǒng)動態(tài)和計(jì)算負(fù)擔(dān)方面的不同特點(diǎn)。仿真實(shí)驗(yàn)表明,基于終端不等式約束的NMPC和基于終端等式約束的NMPC均可使移動機(jī)器人在容許控制輸入的作用下跟蹤參考路徑。但基于終端不等式約束的NMPC控制方案只能解決光滑路徑的跟蹤問題,而基于終端等式約束的NMPC控制方案計(jì)算負(fù)擔(dān)重、在線求解時間長。另外,由于期望路徑是實(shí)時變化的,路徑跟蹤問題的本質(zhì)具有時變性。無論是基于非零終端的NMPC還是基于零終端NMPC,它們的終端域都是固定形式的,在整個優(yōu)化問題求解的過程中始終保持不變,這對于時變的路徑跟蹤問題而言具有保守性。因此本文最后設(shè)計(jì)了基于時變終端的NMPC方案,以解決上述問題。仿真結(jié)果表明時變終端不僅兼顧了路徑跟蹤問題的時變實(shí)質(zhì)和控制需求,并且系統(tǒng)的終端域得以擴(kuò)大。
[Abstract]:In control theory, path tracking (Path Following) is an important motion control problem after stabilization and trajectory tracking. Compared with the trajectory tracking, the path tracking controller needs to determine the desired path information and control the system dynamics of the moving object at the same time. Path tracking control is widely used in CNC machine tool tracking grinding, mobile robot motion control, aircraft or ship track control, intelligent vehicle autonomous driving and other fields. Path tracking and its branches are studied. It can not only enrich the theoretical results of motion control, but also meet the increasing requirements of motion control technology in many fields, which is of great theoretical and engineering significance. Wheeled mobile robot is a typical representative of nonlinear constrained system. In this paper, the path tracking control problem of wheeled mobile robot is studied by choosing it as a motion control object. Compared with other control methods, nonlinear model predictive control (Nonlinear Model Predictive Control,NMPC) has the mechanism of rolling optimization and feedback correction, and can deal with the state constraints and input constraints of the system. In this paper, the NMPC control scheme is applied to the motion control of wheeled mobile robot, and the desired path tracking control of the robot is realized. In this paper, the path tracking control system of wheeled mobile robot is designed according to the following system design steps: the problem description, the establishment of the mathematical model of the controlled object, and the design of the controller according to the control target. Stability analysis and simulation verification of closed-loop system. This paper first describes the problem of path tracking control, deduces and establishes the kinematics model of wheeled mobile robot, and establishes the control task of path tracking. In this paper, the wheeled mobile robot with path tracking task is Unicycle type robot. It consists of two independent driving rear wheels and one universal wheel. The mechanical structure is simple and the motion form is flexible and controllable. By analyzing the established mathematical model, the motion control object in this paper is in essence nonlinear, multi-input and multi-output system with state and input constraints at the same time. Then, for the control task with nonlinear dynamic and constrained conditions, a closed-loop control structure based on NMPC scheme is established, and the specific mathematical form and program solving steps of open-loop optimization problem are given. The feasibility of the optimization problem and the performance of the system are analyzed. Based on the description of nonlinear polyhedron and linear matrix inequality, the non-zero terminal elements which guarantee the feasibility and convergence of NMPC scheme are solved in this paper. The different characteristics of NMPC based on terminal inequality constraint and NMPC based on terminal equality constraint in the aspects of system dynamics and computational burden are compared and analyzed by simulation experiments. Simulation results show that both NMPC based on terminal inequality constraint and NMPC based on terminal equality constraint can track the reference path of mobile robot under the action of allowable control input. However, the NMPC control scheme based on terminal inequality constraints can only solve the tracking problem of smooth paths, while the NMPC control scheme based on terminal equality constraints has a heavy computational burden and takes a long time to solve on-line. In addition, because the desired path is real-time varying, the nature of the path tracking problem is time-varying. Whether NMPC based on non-zero terminal or NMPC, based on zero terminal, their terminal domain is fixed and remains the same in the whole optimization process, which is conservative for time-varying path tracking problem. Finally, this paper designs a NMPC scheme based on time-varying terminals to solve the above problems. The simulation results show that the time-varying terminal not only takes into account the time-varying nature and control requirements of the path tracking problem, but also expands the terminal domain of the system.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TP242

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