Trajectory Planning and Coordinated Control

轨迹规划与协调控制

• 批准号: 9705312
• 负责人: Clyde Martin
• 金额: $ 22.64万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-10-01 至 2001-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9705312&HistoricalAwards=false
• 关键词: Trajectory; Planning; Coordinated; Control

The problems that will be proposed here have to do with one of the basic problem of applied control theory: the problem of designing trajectories for controlled systems. These problems, as are discussed here, arose in response to the needs of air traffic control, but are more basic than any one application. The most basic of the problems is to be given a controlled system, The measurement y is to be thought of as measuring the position of the system. A set of way-points in the form (yi, ti) that must be attained by the plant is assumed to be given. The problem is to find a control law that will move the system in such a way that y(ti)=yi. For most systems there is no unique way of solving this problem so it is necessary to impose other conditions in order to ensure uniqueness. For the air traffic control problem there are d/dt x=f(x)+ug(x) with initial data x(O)=x-O and a measurement function y=h(x). obvious constraints concerning the dynamics of the aircraft and passenger comfort. One obvious condition that should be met is that the dynamics of x(t) be should be smooth. For passengers abrupt changes in velocity or acceleration are very noticeable and physically reality requires that x(t) be continuous. The additional conditions that are imposed make a great deal of difference on the final behavior of the system as does the nature of the system itself. The goal of this research is to develop a tool that will allow the design of trajectories that meet the needs within the context of general control design. In order to do this we must reexamine the basic problem as posed above and extend it to other more complicated tasks. The basic problem as posed here is intimately related to the construction of numerical splines. To extend this to more general problems in control theory it is necessary to enter the area of hybrid systems. Here the problem is related to the more general mathematical problem of Birkhoff splines and to a set of new problems which we choose to call problems of coordinated control. in Section 2 the basic assumptions which we impose on the system will be set forth and the solutions that have been obtained to the basic problem will be described. Here is outlined an elementary, but important basic procedure for solving this entire set of problems and will justify many of the assumptions which have been made. Here will also be described the contents of the several papers that have been published on this problem and they will be related to other work that is ongoing on the problem of trajectory design. In Section 3 there will be presented a set of new problems that will be related to classical problems of Birkhoff splines. These problems arise in aircraft control when it is desired to be able to set commanded velocities, accelerations, angular velocities etc. So in fact we have a set of measurements yk(t) and at various points in time some, but not all, of these must have prescribed values and the control must be designed in order to attain the required values. Here the problem is more basic than uniqueness and is related to the most basic of problems-existence. In Section 4 will be discussed what is really new ground. In many complicated systems the movement of the system is governed by subsystems that effect particular avenues of control. The basic example of this research is the muscular control of the human body. For the most part muscles occur in opposing pairs and only one of a pair can be active at any given time. In order to execute a movement a muscle contracts and causes one particular movement. To execute a complicated movement muscles are switched on and off in accordance with some higher control law and the body makes a smooth coordinated movement. One only need watch a professional gymnast to see the superb coordination that must be maintained for the body to move smoothly and quickly through a complicated maneuver as, for example, one would see on the pommel horse. There are no current plans to develop a control strategy for such a complicated maneuver, but control strategies will be developed that will perform other simpler tasks. Finally in Section 5 it is shown that there are basic problems in stability that must be considered with each of these problems. The problem of stability for systems which are being switched is relatively new. Here is discussed the current state of research and described a series of problems that must be solved to insure that the controls schemes that are being proposed are implementable.

这里提出的问题与应用控制理论的一个基本问题有关：受控系统的轨迹设计问题。 这些问题，如这里所讨论的，出现在空中交通管制的需要，但比任何一个应用程序更基本。 最基本的问题是给定一个受控系统，测量y被认为是测量系统的位置。 假设给定了一组必须由设备到达的形式为（yi，ti）的路点。 问题是找到一个控制律，使系统以y（ti）=yi的方式运动。对于大多数系统来说，没有唯一的方法来解决这个问题，因此有必要施加其他条件以确保唯一性。 对于空中交通管制问题，有d/dt x=f（x）+ug（x），初始数据x（0）= x-0，测量函数y=h（x）。 关于飞机动力学和乘客舒适性的明显限制。 应该满足的一个明显的条件是x（t）be的动态应该是平滑的。 对于乘客来说，速度或加速度的突然变化非常明显，物理现实要求x（t）是连续的。 附加的条件对系统的最终行为产生很大的影响，系统本身的性质也是如此。 本研究的目标是开发一种工具，将允许设计的轨迹，满足一般控制设计的背景下的需求。 为了做到这一点，我们必须重新审查上面提出的基本问题，并将其扩展到其他更复杂的任务。 这里提出的基本问题与数值样条的构造密切相关。 为了扩展到更一般的控制理论问题，有必要进入混合动力系统领域。 这里的问题涉及到更一般的数学问题的伯克霍夫样条和一组新的问题，我们选择调用问题的协调控制。在第二节中，我们将阐述我们对系统所作的基本假设，并将描述对基本问题所得到的解答。 这里概述了一个基本的，但重要的基本程序来解决这一整套问题，并将证明许多假设已经作出。 这里也将描述的内容的几篇论文已经发表在这个问题上，他们将涉及到其他工作，正在进行的问题上的轨迹设计。 在第3节中，将提出一组新的问题，这将涉及到经典问题的伯克霍夫样条。 当希望能够设定指令速度、加速度、角速度等时，这些问题出现在飞机控制中。因此，实际上我们有一组测量值yk（t），在不同的时间点上，这些测量值中的一些（但不是全部）必须具有规定的值，并且控制必须被设计为达到所需的值。 在这里，问题比唯一性更基本，并且与最基本的问题-存在有关。 第四节将讨论什么是真正的新基础。 在许多复杂的系统中，系统的运动是由子系统控制的，子系统实现特定的控制途径。 这项研究的基本例子是人体的肌肉控制。 在大多数情况下，肌肉出现在相反的对，只有一对可以在任何给定的时间活动。 为了执行一个动作，肌肉收缩并引起一个特定的动作。 为了执行一个复杂的运动，肌肉根据一些更高的控制规律打开和关闭，身体进行平滑的协调运动。 只要看一看专业体操运动员的动作，就能看出身体必须保持高超的协调性，才能在复杂的动作中平稳而迅速地移动，例如，人们在鞍马上看到的。 目前还没有计划为这种复杂的机动动作开发控制策略，但是将开发执行其他简单任务的控制策略。 最后，在第5节中，它表明，有基本的问题，稳定性，必须考虑与这些问题。 被切换系统的稳定性问题是一个相对较新的问题。 这里讨论了目前的研究状况，并描述了一系列必须解决的问题，以确保正在提出的控制方案是可实施的。