机器人建模,规划和控制

In all robot applications, completion of a generic task requires the execution of a specific motion prescribed to the robot. The correct execution of suchmotion is entrusted to the control system which should provide the robot’s actuators with the commands consistent with the desired motion. Motion control demands an accurate analysis of the characteristics of the mechanical structure, actuators, and sensors. The goal of such analysis is the derivation of the mathematical models describing the input/output relationship characterizing the robot components. Modelling a robot manipulator is therefore a necessary premise to finding motion control strategies.

在所有机器人应用中，通用任务的完成需要执行机器人规定的特定运动。将这种运动的正确执行委托给控制系统，该控制系统应该为机器人的执行器提供与期望运动一致的命令。运动控制需要对机械结构，执行器和传感器的特性进行准确的分析。这种分析的目的是描述表征机器人组件的输入/输出关系的数学模型的推导。因此，建模机器人操纵器是找到运动控制策略的必要前提。

Significant topics in the study of modelling, planning and control of robots which constitute the subject of subsequent chapters are illustrated below.

构成后续章节主题的机器人建模，规划和控制研究中的重要课题如下所示。

1. Modelling

1. 建模

Kinematic analysis of the mechanical structure of a robot concerns the description of the motion with respect to a fixed reference Cartesian frame by ignoring the forces and moments that cause motion of the structure. It is meaningful to distinguish between kinematics and differential kinematics.With reference to a robot manipulator, kinematics describes the analytical relationship between the joint positions and the end-effector position and orientation.Differential kinematics describes the analytical relationship between the joint motion and the end-effector motion in terms of velocities, through the manipulator Jacobiann.

机器人的机械结构的运动学分析涉及通过忽略导致结构运动的力和力矩来描述相对于固定的基准笛卡尔坐标系的运动。区分运动学和微分运动学是有意义的。参考机器人末端执行器，运动学描述了关节位置和末端执行器位置和方向之间的解析关系。微分运动学通过雅克比在速度方面描述了关节运动和末端执行器运动之间的解析关系。

The formulation of the kinematics relationship allows the study of two key problems of robotics, namely, the direct kinematics problem and the inverse kinematics problem. The former concerns the determination of a systematic,general method to describe the end-effector motion as a function of the joint motion by means of linear algebra tools. The latter concerns the inverse problem; its solution is of fundamental importance to transform the desired motion, naturally prescribed to the end-effector in the workspace, into the corresponding joint motion.

运动学关系的形成允许研究机器人的两个关键问题，即正运动学问题和逆运动学问题。前者涉及通过线性代数工具来描述作为关节运动的函数的末端执行器运动的系统一般方法的确定。后者涉及到逆向问题，这个问题的解决很重要，其解决方案对于将所期望的运动（在工作空间中指定末端执行器）转换成相应的关节运动。

The availability of a manipulator’s kinematic model is also useful to determine the relationship between the forces and torques applied to the joints and the forces and moments applied to the end-effector in static equilibrium configurations.

机械手的运动学模型的可用性也可用于确定施加到关节的力和扭矩之间的关系以及在静态平衡构型中施加到末端执行器的力和力矩之间的关系。

Chapter 2 is dedicated to the study of kinematics. Chapter 3 is dedicated to the study of differential kinematics and statics, whereas Appendix A provides a useful brush-up on linear algebra.

第二章专门研究运动学。第3章致力于微分运动学和静力学的研究，附录A回顾了线性代数。

Kinematics of a manipulator represents the basis of a systematic, general derivation of its dynamics, i.e., the equations of motion of the manipulator as a function of the forces and moments acting on it. The availability of the dynamic model is very useful for mechanical design of the structure, choice of actuators, determination of control strategies, and computer simulation of manipulator motion. Chapter 7 is dedicated to the study of dynamics, whereas Appendix B recalls some fundamentals on rigid body mechanics.

机械手的运动学代表了其动力学系统的一般推导的基础，即机械手的运动方程作为作用在其上的力和力矩的函数。动力学模型的获得对机械结构设计，执行器的选择，控制策略的确定以及机械手运动的计算机模拟非常有用。第7章致力于研究动力学，而附录B回顾了刚体力学的一些基础知识。

Modelling of mobile robots requires a preliminary analysis of the kinematic constraints imposed by the presence of wheels. Depending on the mechanical structure, such constraints can be integrable or not; this has direct consequence on a robot’s mobility. The kinematic model of a mobile robot is essentially the description of the admissible instantaneous motions in respect of the constraints. On the other hand, the dynamic model accounts for the reaction forces and describes the relationship between the above motions and the generalized forces acting on the robot. These models can be expressed in a canonical form which is convenient for design of planning and control techniques. Kinematic and dynamic analysis of mobile robots is developed in Chap. 11, while Appendix D contains some useful concepts of differential geometry.

移动机器人的建模需要对轮子的存在所产生的运动学约束进行初步分析。根据机械结构，这种约束可以是可积分的; 这对机器人的移动性有直接的影响。移动机器人的运动学模型基本上是关于约束的容许瞬时运动的描述。另一方面，动力学模型反映了反作用力，并描述了上述动作与作用于机器人的广义力之间的关系。这些模型可以用规范形式表达，便于规划和控制。移动机器人的运动和动力学分析在第 11，附录D包含微分几何的一些有用的概念。

2. Planning

2. 规划

With reference to the tasks assigned to a manipulator, the issue is whether to specify the motion at the joints or directly at the end-effector. In material handling tasks, it is sufficient to assign only the pick-up and release locations of an object (point-to-point motion), whereas, in machining tasks, the endeffector has to follow a desired trajectory (path motion). The goal of trajectory planning is to generate the timing laws for the relevant variables (joint or endeffector) starting from a concise description of the desired motion. Chapter 4 is dedicated to trajectory planning for robot manipulators.

考虑分配给机械手的任务，问题是指定关节处的运动还是直接在末端执行器处的运动。在材料处理任务中，仅分配对象的拾取和释放位置（点对点运动）就足够了，而在加工任务中，任务必须遵循所需的轨迹（路径运动）。轨迹规划的目标是从对所需动作的简明描述开始，为相关变量（关节或末端执行器）生成时间律。第4章专门用于机器人操纵器的轨迹规划。

The motion planning problem for a mobile robot concerns the generation of trajectories to take the vehicle from a given initial configuration to a desired final configuration. Such a problem is more complex than that of robot manipulators, since trajectories have to be generated in respect of the kinematic constraints imposed by the wheels. Some solution techniques are presented in Chap. 11, which exploit the specific differential structure of the mobile robots’kinematic models.

移动机器人的运动规划问题涉及生成将车辆从给定的初始配置带到期望的最终配置的轨迹。这种问题比机器人操纵器的问题更为复杂，因为必须根据车轮施加的运动学约束产生轨迹。一些解决技术在第 11章，利用移动机器人运动模型的具体微分结构。

Whenever obstacles are present in a mobile robot’s workspace, the planned motions must be safe, so as to avoid collisions. Such a problem, known as motion planning, can be formulated in an effective fashion for both robot manipulators and mobile robots utilizing the configuration space concept. The solution techniques are essentially of algorithmic nature and include exact, probabilistic and heuristic methods. Chapter 12 is dedicated to motion planning problem, while Appendix E provides some basic concepts on graph search algorithms.

每当移动机器人的工作空间中存在障碍物时，规划的动作必须是安全的，以免发生碰撞。这种问题，称为运动规划，可以用有效的方式为利用配置空间概念的机器人操纵器和移动机器人制定。解决方案技术本质上是算法性质，包括精确的，概率的和启发式的方法。第12章专门针对运动规划问题，附录E提供了图形搜索算法的一些基本概念。

3. Control

3. 控制

Realization of the motion specified by the control law requires the employment of actuators and sensor
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s. The functional characteristics of the most commonly used actuators and sensors for robots are described in Chap. 5.

由控制法规定的运动的实现需要使用执行器和传感器。最常用的机器人执行器和传感器的功能特征在第 5章介绍.

Chapter 6 is concerned with the hardware/software architecture of a robot’s control system which is in charge of implementation of control laws as well as of interface with the operator.

第6章涉及机器人控制系统的硬件/软件架构，负责控制律的执行以及与操作人员的接口。

The trajectories generated constitute the reference inputs to the motion control system of the mechanical structure. The problem of robot manipulator control is to find the time behaviour of the forces and torques to be delivered by the joint actuators so as to ensure the execution of the reference trajectories. This problem is quite complex, since a manipulator is an articulated system and, as such, the motion of one link influences the motion of the others.Manipulator equations of motion indeed reveal the presence of coupling dynamic effects among the joints, except in the case of a Cartesian structure with mutually orthogonal axes. The synthesis of the joint forces and torques cannot be made on the basis of the sole knowledge of the dynamic model, since this does not completely describe the real structure. Therefore, manipulator control is entrusted to the closure of feedback loops; by computing the deviation between the reference inputs and the data provided by the proprioceptive sensors, a feedback control system is capable of satisfying accuracy requirements on the execution of the prescribed trajectories.

生成的轨迹构成了这个机械结构体的参考输入。机器人控制器控制的问题是得到在不同时间节点上传递到各个关节执行器的力和扭矩，以确保参考轨迹的执行。这个问题是相当复杂的，因为操纵器是关节系统，因此，一个关节的运动影响其他关节的运动。除了笛卡尔结构的具有相互正交的轴的情况，机械臂的运动方程确实揭示了关节之间耦合动态效应的存在。关节力和扭矩的合成不能仅在动态模型的基础上进行，因为这并不能完全描述实际结构。因此，操纵器控制被委托给闭合反馈回路; 通过计算参考输入和传感器提供的数据之间的偏差，反馈控制系统能够满足执行规定轨迹的精度要求。

Chapter 8 is dedicated to the presentation of motion control techniques, whereas Appendix C illustrates the basic principles of feedback control .

第8章专门介绍运动控制技术，而附录C则说明了反馈控制的基本原理。

Control of a mobile robot substantially differs from the analogous problem for robot manipulators. This is due, in turn, to the availability of fewer control inputs than the robot has configuration variables. An important consequence is that the structure of a controller allowing a robot to follow a trajectory (tracking problem) is unavoidably different from that of a controller aimed at taking the robot to a given configuration (regulation problem). Further, since a mobile robot’s proprioceptive sensors do not yield any data on the vehicle’s configuration, it is necessary to develop localization methods for the robot in the environment. The control design problem for wheeled mobile robots is treated in Chap. 11.

移动机器人的控制与机器人操纵器的类似问题大不相同。这反过来又归功于具有比机器人配置变量更少的控制输入。一个重要的结果是允许机器人跟踪轨迹（跟踪问题）的控制器的结构与旨在使机器人处于给定配置（调节问题）的控制器的结构不可避免地不同。此外，由于移动机器人的传感器在车辆的配置上不产生任何数据，因此有必要开发环境中机器人的定位方法。第二章讨论了轮式移动机器人的控制设计问题。11。

If a manipulation task requires interaction between the robot and the environment, the control problem should account for the data provided by the exteroceptive sensors; the forces exchanged at the contact with the environment, and the objects’ position as detected by suitable cameras. Chapter 9 is dedicated to force control techniques for robot manipulators, while Chap. 10 presents visual control techniques.

如果操纵任务需要机器人与环境之间的交互，则控制问题应该解释由外部感应传感器提供的数据; 与环境接触交换的力量以及由适当摄像机检测到的物体的位置。第9章专门用于机器人操纵器的力控技术。10展示了视觉控制技术。