基于模型预测控制的移动机器人路径跟踪控制

发布时间：2019-03-13 12:14

【摘要】：在控制理论中,路径跟踪(Path Following)是继设定点镇定、轨迹跟踪之后一类重要的运动控制问题。同轨迹跟踪相比,路径跟踪控制器需要同时确定待跟踪期望路径的信息和控制运动对象的系统动态。路径跟踪控制广泛存在于数控机床跟踪磨削、移动机器人运动控制、飞机或轮船的航迹控制和智能车自主驾驶等领域,对路径跟踪及其分支问题进行研究,不仅可以丰富运动控制的理论成果,还可以满足多领域对运动控制技术越来越高的要求,具有重大的理论和工程意义。轮式移动机器人是非线性约束系统的典型代表,本文将其选择为运动控制对象,对其路径跟踪控制问题进行了研究。同其他控制方法相比,非线性模型预测控制(Nonlinear Model Predictive Control,NMPC)具有滚动优化和反馈校正的机理,能够处理系统的状态约束和输入约束。本文将NMPC控制方案应用于轮式移动机器人的运动控制,实现了机器人对期望路径的跟踪控制。本文按照如下的系统设计步骤完成了轮式移动机器人路径跟踪控制系统的设计:问题描述、建立被控对象数学模型、依据控制目标设计控制器、闭环系统稳定性分析和仿真验证。本文首先对路径跟踪控制进行了问题描述,推导并建立了轮式移动机器人的运动学模型,确立了路径跟踪的控制任务。在本文中,存在路径跟踪任务的轮式移动机器人是Unicycle型机器人,它由两个独立驱动后轮和一个万向轮构成,机械结构简单,运动形式灵活可控。分析所建立的数学模型,本文的运动控制对象在本质上属于非线性、多输入多输出,同时具有状态和输入约束的系统。然后,针对具有非线性动态和约束条件的控制任务,本文建立了基于NMPC方案的闭环控制结构,给出了开环优化问题具体的数学形式和程序求解步骤,并对优化问题的可行性和系统的性能进行了分析。本文基于非线性多面体描述和线性矩阵不等式求解了保证NMPC方案可行性和收敛性的非零终端要素,并通过仿真实验对比分析了基于终端不等式约束的NMPC和基于终端等式约束的NMPC在系统动态和计算负担方面的不同特点。仿真实验表明,基于终端不等式约束的NMPC和基于终端等式约束的NMPC均可使移动机器人在容许控制输入的作用下跟踪参考路径。但基于终端不等式约束的NMPC控制方案只能解决光滑路径的跟踪问题,而基于终端等式约束的NMPC控制方案计算负担重、在线求解时间长。另外,由于期望路径是实时变化的,路径跟踪问题的本质具有时变性。无论是基于非零终端的NMPC还是基于零终端NMPC,它们的终端域都是固定形式的,在整个优化问题求解的过程中始终保持不变,这对于时变的路径跟踪问题而言具有保守性。因此本文最后设计了基于时变终端的NMPC方案,以解决上述问题。仿真结果表明时变终端不仅兼顾了路径跟踪问题的时变实质和控制需求,并且系统的终端域得以扩大。
[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.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP242

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