Robotics

Modelling, Planning and Control

verfasst von: Bruno Siciliano, Lorenzo Sciavicco, Luigi Villani, Giuseppe Oriolo

Verlag: Springer London

Buchreihe : Advanced Textbooks in Control and Signal Processing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Based on the successful Modelling and Control of Robot Manipulators by Sciavicco and Siciliano (Springer, 2000), Robotics provides the basic know-how on the foundations of robotics: modelling, planning and control. It has been expanded to include coverage of mobile robots, visual control and motion planning. A variety of problems is raised throughout, and the proper tools to find engineering-oriented solutions are introduced and explained.

The text includes coverage of fundamental topics like kinematics, and trajectory planning and related technological aspects including actuators and sensors.

To impart practical skill, examples and case studies are carefully worked out and interwoven through the text, with frequent resort to simulation. In addition, end-of-chapter exercises are proposed, and the book is accompanied by an electronic solutions manual containing the MATLAB® code for computer problems; this is available free of charge to those adopting this volume as a textbook for courses.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract

Robotics is concerned with the study of those machines that can replace human beings in the execution of a task, as regards both physical activity and decision making. The goal of the introductory chapter is to point out the problems related to the use of robots in industrial applications, as well as the perspectives offered by advanced robotics. A classification of the most common mechanical structures of robot manipulators and mobile robots is presented. Topics of modelling, planning and control are introduced which will be examined in the following chapters. The chapter ends with a list of references dealing with subjects both of specific interest and of related interest to those covered by this textbook.

2. Kinematics

Abstract

A manipulator can be schematically represented from a mechanical viewpoint as a kinematic chain of rigid bodies (links) connected by means of revolute or prismatic joints. One end of the chain is constrained to a base, while an end-effector is mounted to the other end. The resulting motion of the structure is obtained by composition of the elementary motions of each link with respect to the previous one. Therefore, in order to manipulate an object in space, it is necessary to describe the end-effector position and orientation. This chapter is dedicated to the derivation of the direct kinematics equation through a systematic, general approach based on linear algebra. This allows the end-effector position and orientation (pose) to be expressed as a function of the joint variables of the mechanical structure with respect to a reference frame. Both open-chain and closed-chain kinematic structures are considered. With reference to a minimal representation of orientation, the concept of operational space is introduced and its relationship with the joint space is established. Furthermore, a calibration technique of the manipulator kinematic parameters is presented. The chapter ends with the derivation of solutions to the inverse kinematics problem, which consists of the determination of the joint variables corresponding to a given end-effector pose.

3. Differential Kinematics and Statics

Abstract

In the previous chapter, direct and inverse kinematics equations establishing the relationship between the joint variables and the end-effector pose were derived. In this chapter, differential kinematics is presented which gives the relationship between the joint velocities and the corresponding end-effector linear and angular velocity. This mapping is described by a matrix, termed geometric Jacobian, which depends on the manipulator configuration. Alternatively, if the end-effector pose is expressed with reference to a minimal representation in the operational space, it is possible to compute the Jacobian matrix via differentiation of the direct kinematics function with respect to the joint variables. The resulting Jacobian, termed analytical Jacobian, in general differs from the geometric one. The Jacobian constitutes one of the most important tools for manipulator characterization; in fact, it is useful for finding singularities, analyzing redundancy, determining inverse kinematics algorithms, describing the mapping between forces applied to the end-effector and resulting torques at the joints (statics) and, as will be seen in the following chapters, deriving dynamic equations of motion and designing operational space control schemes. Finally, the kineto-statics duality concept is illustrated, which is at the basis of the definition of velocity and force manipulability ellipsoids.

4. Trajectory Planning

Abstract

For the execution of a specific robot task, it is worth considering the main features of motion planning algorithms. The goal of trajectory planning is to generate the reference inputs to the motion control system which ensures that the manipulator executes the planned trajectories. The user typically specifies a number of parameters to describe the desired trajectory. Planning consists of generating a time sequence of the values attained by an interpolating function (typically a polynomial) of the desired trajectory. This chapter presents some techniques for trajectory generation, both in the case when the initial and final point of the path are assigned (point-to-point motion), and in the case when a finite sequence of points are assigned along the path (motion through a sequence of points). First, the problem of trajectory planning in the joint space is considered, and then the basic concepts of trajectory planning in the operational space are illustrated. The treatment of the motion planning problem for mobile robots is deferred to Chap. 12.

5. Actuators and Sensors

Abstract

In this chapter, two basic robot components are treated: actuators and sensors. In the first part, the features of an actuating system are presented in terms of the power supply, power amplifier, servomotor and transmission. In view of their control versatility, two types of servomotors are used, namely, electric servomotors for actuating the joints of small and medium size manipulators, and hydraulic servomotors for actuating the joints of large size manipulators. The models describing the input/output relationship for such servomotors are derived, together with the control schemes of the drives. The electric servomotors are also employed to actuate the wheels of the mobile robots, which will be dealt with in Chap. 11. Successively, proprioceptive sensors are presented which allow measurement of the quantities characterizing the internal state of the manipulator, namely, encoders and resolvers for joint position measurement, tachometers for joint velocity measurement; further, exteroceptive sensors are presented including force sensors for end-effector force measurement, distance sensors for detection of objects in the workspace, and vision sensors for the measurement of the characteristic parameters of such objects, whenever the manipulator interacts with the environment.

6. Control Architecture

Abstract

This chapter is devoted to presenting a reference model for the functional architecture of an industrial robot’s control system. The hierarchical structure and its articulation into functional modules allows the determination of the requirements and characteristics of the programming environment and the hardware architecture. The architecture refers to robot manipulators, yet its articulation in levels also holds for mobile robots.

7. Dynamics

Abstract

Derivation of the dynamic model of a manipulator plays an important role for simulation of motion, analysis of manipulator structures, and design of control algorithms. Simulating manipulator motion allows control strategies and motion planning techniques to be tested without the need to use a physically available system. The analysis of the dynamic model can be helpful for mechanical design of prototype arms. Computation of the forces and torques required for the execution of typical motions provides useful information for designing joints, transmissions and actuators. The goal of this chapter is to present two methods for derivation of the equations of motion of a manipulator in the joint space. The first method is based on the Lagrange formulation and is conceptually simple and systematic. The second method is based on the Newton–Euler formulation and yields the model in a recursive form; it is computationally more efficient since it exploits the typically open structure of the manipulator kinematic chain. Then, a technique for dynamic parameter identification is presented. Further, the problems of direct dynamics and inverse dynamics are formalized, and a technique for trajectory dynamic scaling is introduced, which adapts trajectory planning to the dynamic characteristics of the manipulator. The chapter ends with the derivation of the dynamic model of a manipulator in the operational space and the definition of the dynamic manipulability ellipsoid.

8. Motion Control

Abstract

In Chap. 4, trajectory planning techniques have been presented which allow the generation of the reference inputs to the motion control system. The problem of controlling a manipulator can be formulated as that to determine the time history of the generalized forces (forces or torques) to be developed by the joint actuators, so as to guarantee execution of the commanded task while satisfying given transient and steady-state requirements. The task may regard either the execution of specified motions for a manipulator operating in free space, or the execution of specified motions and contact forces for a manipulator whose end-effector is constrained by the environment. In view of problem complexity, the two aspects will be treated separately; first, motion control in free space, and then control of the interaction with the environment. The problem of motion control of a manipulator is the topic of this chapter. A number of joint space control techniques are presented. These can be distinguished between decentralized control schemes, i.e., when the single manipulator joint is controlled independently of the others, and centralized control schemes, i.e., when the dynamic interaction effects between the joints are taken into account. Finally, as a premise to the interaction control problem, the basic features of operational space control schemes are illustrated.

9. Force Control

Abstract

One of the fundamental requirements for the success of a manipulation task is the capacity to handle interaction between manipulator and environment. The quantity that describes the state of interaction more effectively is the contact force at the manipulator’s end-effector. High values of contact force are generally undesirable since they may stress both the manipulator and the manipulated object. In this chapter, performance of operational space motion control schemes is studied first, during the interaction of a manipulator with the environment. The concepts of mechanical compliance and impedance are introduced, with special regard to the problem of integrating contact force measurements into the control strategy. Then, force control schemes are presented which are obtained from motion control schemes suitably modified by the closure of an outer force regulation feedback loop. For the planning of control actions to perform an interaction task, natural constraints set by the task geometry and artificial constraints set by the control strategy are established; the constraints are referred to a suitable constraint frame. The formulation is conveniently exploited to derive hybrid force/motion control schemes.

10. Visual Servoing

Abstract

Vision allows a robotic system to obtain geometrical and qualitative information on the surrounding environment to be used both for motion planning and control. In particular, control based on feedback of visual measurements is termed visual servoing. In the first part of this chapter, some basic algorithms for image processing, aimed at extracting numerical information referred to as image feature parameters, are presented. These parameters, relative to images of objects present in the scene observed by a camera, can be used to estimate the pose of the camera with respect to the objects and vice versa. To this end, analytical pose estimation methods, based on the measurement of a certain number of points or correspondences are presented. Also, numerical pose estimation methods, based on the integration of the linear mapping between the camera velocity in the operational space and the time derivative of the feature parameters in the image plane, are introduced. In cases in which multiple images of the same scene, taken from different viewpoints, are available, additional information can be obtained using stereo vision techniques and epipolar geometry. A fundamental operation is also camera calibration; to this end, a calibration method based on the measurement of a certain number of correspondences is presented. Then, the two main approaches to visual servoing are introduced, namely position-based visual servoing and image-based visual servoing, as well as a scheme, termed hybrid visual servoing, which combines the benefits of both approaches.

11. Mobile Robots

Abstract

The previous chapters deal mainly with articulated manipulators that represent the large majority of robots used in industrial settings. However, mobile robots are becoming increasingly important in advanced applications, in view of their potential for autonomous intervention. This chapter presents techniques for modelling, planning and control of wheeled mobile robots. The structure of the kinematic constraints arising from the pure rolling of the wheels is first analyzed; it is shown that such constraints are in general nonholonomic and consequently reduce the local mobility of the robot. The kinematic model associated with the constraints is introduced to describe the instantaneous admissible motions, and conditions are given under which it can be put in chained form. The dynamic model, that relates the admissible motions to the generalized forces acting on the robot DOFs, is then derived. The peculiar nature of the kinematic model, and in particular the existence of flat outputs, is exploited to devise trajectory planning methods that guarantee that the nonholonomic constraints are satisfied. The structure of minimum-time trajectories is also analyzed. The motion control problem for mobile robots is then discussed, with reference to two basic motion tasks, i.e., trajectory tracking and posture regulation. The chapter concludes by surveying some techniques for odometric localization that is necessary to implement feedback control schemes.

12. Motion Planning

Abstract

The trajectory planning methods presented in Chaps. 4 and 11, respectively for manipulators and mobile robots, operate under the simplifying assumption that the workspace is empty. In the presence of obstacles, it is necessary to plan motions that enable the robot to execute the assigned task without colliding with them. This problem, referred to as motion planning, is the subject of this chapter. After defining a canonical version of the problem, the concept of configuration space is introduced in order to achieve an efficient formulation. A selection of representative planning techniques is then presented. The method based on the notion of retraction characterizes the connectivity of the free configuration space using a roadmap, i.e., a set of collision-free paths, while the cell decomposition method identifies a network of channels with the same property. The PRM and bidirectional RRT techniques are probabilistic in nature and rely on the randomized sampling of the configuration space and the memorization of those samples that do not cause a collision between the robot and the obstacles. The artificial potential method is also described as a heuristic approach particularly suited to on-line planning problems, where the geometry of the workspace obstacles is unknown in advance. The chapter ends with a discussion of the application of the presented planning methods to the robot manipulator case.

Backmatter

Titel: Robotics
verfasst von: Bruno Siciliano
Lorenzo Sciavicco
Luigi Villani
Giuseppe Oriolo
Verlag: Springer London
Electronic ISBN: 978-1-84628-642-1
Print ISBN: 978-1-84628-641-4
DOI: https://doi.org/10.1007/978-1-84628-642-1