Skip to main content
main-content

Über dieses Buch

Furthering the aim of reducing human exposure to hazardous environments, this monograph presents a detailed study of the modeling and control of vehicle-manipulator systems. The text shows how complex interactions can be performed at remote locations using systems that combine the manipulability of robotic manipulators with the ability of mobile robots to locomote over large areas.

The first part studies the kinematics and dynamics of rigid bodies and standard robotic manipulators and can be used as an introduction to robotics focussing on robust mathematical modeling. The monograph then moves on to study vehicle-manipulator systems in great detail with emphasis on combining two different configuration spaces in a mathematically sound way. Robustness of these systems is extremely important and Modeling and Control of Vehicle-manipulator Systems effectively represents the dynamic equations using a mathematically robust framework. Several tools from Lie theory and differential geometry are used to obtain globally valid representations of the dynamic equations of vehicle-manipulator systems.

The specific characteristics of several different types of vehicle-manipulator systems are included and the various application areas of these systems are discussed in detail. For underwater robots buoyancy and gravity, drag forces, added mass properties, and ocean currents are considered. For space robotics the effects of free fall environments and the strong dynamic coupling between the spacecraft and the manipulator are discussed. For wheeled robots wheel kinematics and non-holonomic motion is treated, and finally the inertial forces are included for robots mounted on a forced moving base.

Modeling and Control of Vehicle-manipulator Systems will be of interest to researchers and engineers studying and working on many applications of robotics: underwater, space, personal assistance, and mobile manipulation in general, all of which have similarities in the equations required for modeling and control.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Vehicle-manipulator systems and mobile manipulators have the potential to bring advanced robotic technology out of the structured environment of the factory floor and into unstructured and possibly hostile plants at distant locations. Vehicle-manipulator systems are composed of two parts: the vehicle brings mobility and locomotion capabilities which allow the system to reach distant areas, while the manipulator arm allows for complex manipulation. This is a powerful combination, as advanced robotic solutions that previously only have been available in the structured environment of the factory floor can be utilized also in other areas, many of which are novel to robotics.
Vehicle-manipulator systems are an important class of mobile robots, which will bring with them advances in areas such as underwater and space manipulation, field robotics, service robotics, and several other areas. It is believed that mobile robotic technology will introduce several technological advances to novel application areas in the same way that industrial robots revolutionized factory automation a few decades ago. This chapter gives a short overview of the most important mobile robots discussed in this book, and describes how mobile robots will account for several of the most important advances in robotics over the next decades.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 2. Preliminary Mathematical Concepts

Abstract
This chapter presents the main mathematical tools used throughout the book. The necessary mathematical background is presented, which in turn will be used to develop mathematical models that accurately describe the mechanical behavior of our systems, which is the main goal of mathematical modeling. The models are derived so that they are well suited for analysis, simulation, and control of the mechanical system.
In this chapter the most important tools from Lie theory and differential geometry are presented in a brief but concise manner. The theory is presented in such a way that it can serve as an introduction to differential geometry for roboticists not familiar with the topic. We focus on the tools and properties required for modeling mechanical systems with focus on presenting the reader with a well-defined framework well suited to derive a singularity-free formulation of the kinematics and dynamics of complex mechanical systems. Even though the main mathematical tools are presented in this chapter, the readers that are not interested in a deep mathematical analysis of these systems, but rather a more practical approach, can go straight to Chap. 3 on rigid body modeling.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 3. Rigid Body Kinematics

Abstract
Rigid body kinematics is the study of the displacement, velocity, and acceleration of a rigid body with respect to a reference. We introduce the notion of reference frames and associate each reference frame with a rigid body. We thus achieve a mathematical framework for describing how rigid bodies move with respect to each other and with respect to the inertial reference frame.
Single rigid body motion serves as the basis for multibody motion. In addition to describe the configuration and motion space of vehicles and mobile robots, single rigid body kinematics is also the basis of robotics, i.e., multibody motion with additional kinematic constraints imposed on the motion space. Based on the concepts introduced in Chap. 1, the location, velocity, and acceleration of single rigid bodies are described in terms of well-defined mathematical entities. This chapter thus serves as an introduction to rigid body modeling as a part of an introductory robotics course.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 4. Kinematics of Manipulators on a Fixed Base

Abstract
Fixed-base manipulators are composed of several rigid bodies attached together in a chain in such a way that the relative motion between two consecutive rigid bodies is restricted by the admissible motions of the joints, often to a very simple one degree of freedom linear or rotational motion. The main objective of the kinematics study is to find the position and velocity of the last link given the position and velocity of each joint in the robotic chain. The inverse of this problem is also important in robot modeling and control.
This chapter serves as an introduction to robotic manipulators. Readers not previously familiar with this topic can use this chapter, together with the previous chapters, as an introductory course to robotic manipulator modeling. It is written so that it can be used as course literature in an introductory course on robotic manipulators. For readers already familiar with robotics the chapter gives a mathematical robust treatment using important results from Lie theory and differential geometry, normally not found in robotics textbooks.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 5. Kinematics of Vehicle-Manipulator Systems

Abstract
This chapter studies in detail the kinematics of vehicle-manipulator systems, which is the main topic of this book. Kinematically, the vehicle and the robotic manipulator are quite different in nature. While the manipulator’s motion space can be written in terms of a simple Euclidean (flat) configuration space, the vehicle’s state space is curved and defined on manifolds. We describe in detail how to find the kinematic relations of these two systems in terms of one unified theory. The formulation describes the vehicle’s state space as embedded in a manifold while it maintains the simplicity of the Euclidean space of the manipulator arm.
The kinematics of vehicle-manipulator systems is derived in detail with focus on obtaining a well-defined formulation. The chapter will give the reader a deeper understanding of the underlying spaces and in particular help to understand the difference between Euclidean and non-Euclidean spaces. This will give the reader the necessary background to model complex mechanical systems, including multibody systems with both simple Euclidean transformations and complex transformations described using matrix Lie groups.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 6. Rigid Body Dynamics

Abstract
Dynamics is the study of how forces affect the motion of rigid bodies. In this chapter we introduce the fundamental topics required to derive the dynamic equations for rigid bodies with the results obtained in the previous chapters on rigid body kinematics as a starting point. In this way we obtain a well-defined formulation of the dynamics without singularities and other artifacts. The formulation can be used to derive the dynamics of bodies with different configuration spaces, i.e., both flat Euclidean spaces and non-Euclidean configuration spaces on manifolds. The equations are well suited for simulation and controller design.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 7. Dynamics of Manipulators on a Fixed Base

Abstract
Manipulator dynamics tells us how the manipulator responds to joint torques and external forces. Each joint is normally equipped with an actuator which generates either linear forces or torques in the direction or around a fixed axis. The relatively simple joint torques and forces applied at each joint result in a complex overall motion of the robotic manipulator. One of the most important questions in robotics is thus how to find the joint torques that give the desired robot motion.
In this chapter we present the dynamic equations of a robotic manipulator in a well-defined but simple way. The chapter can be used in an introductory course to robotics and will give the reader a good understanding of how to model manipulator arms. Furthermore, as the formulation is based on the mathematically rigid formulations presented in the previous chapters, this chapter may also be interesting for readers already familiar with robotics and would like a mathematically more robust treatment than the one normally found in textbooks on robotics.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 8. Dynamics of Vehicle-Manipulator Systems

Abstract
This chapter presents the dynamic equations of vehicle-manipulator systems, which is the principal topic of the book. Because the configuration space of the vehicle and the manipulator are different in nature we need to use the well-defined formulation of the state space presented in the previous chapters to obtain a singularity-free set of dynamic equations. The configuration space of the manipulator is Euclidean, so standard formulations of Lagrange’s equations can be used. For the vehicle, however, the configuration space is a manifold, so we need to modify Lagrange’s equations to be valid also on matrix Lie groups, which are in fact manifolds.
This chapter will give the reader a deep understanding of how the underlying configuration spaces affect the modeling of mechanical systems and the reader will be able to derive the dynamics of complex mechanical systems with different configuration spaces, both Euclidean and non-Euclidean. Emphasis is put on obtaining well-defined and singularity-free dynamic equations by using the results from differential geometry and Lie theory presented in the previous chapters.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 9. Properties of the Dynamic Equations in Matrix Form

Abstract
When deriving the dynamic equations of mechanical systems it is common to present the equations in matrix form in such a way that the different matrices, in particular the inertia and Coriolis matrices, possess certain properties. These properties are very useful when deriving control laws and in the stability proofs of these. The most important properties in robotics are the boundedness property of the inertia matrix and the skew symmetry property of the Coriolis matrix.
For both these properties vehicle-manipulator systems need to be treated differently from standard fixed-base manipulators or single rigid bodies. This has led to several misconceptions in the robotics literature, because these properties are often taken for granted for vehicle-manipulator systems based on the proofs of other systems. This chapter therefore shows when these properties are in fact true for vehicle-manipulator systems, and for what formulations of the dynamics they are not.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 10. Underwater Robotic Systems

Abstract
Underwater robotics represents one of the most promising application areas of vehicle-manipulator systems. Due to the extremely hostile environment found under water and the dangers exposed to human divers, the underwater environment is believed to benefit greatly from this technology. In fact, there are already several underwater robotic systems available that are both able to locomote freely under water and carry a manipulator arm for interaction with objects under water.
As of today most underwater robots are used in the oil and gas industry to monitor and operate underwater fields. This is an area that will benefit greatly from robotic solutions as an increasingly high number of fields are being developed on the seabed. Other underwater applications include surveillance and exploration of the seabed, exploration of ship wrecks and coral reefs, and search missions in case of airplane or ship accidents.
This chapter discusses the modeling and control of underwater vehicle-manipulator systems and shows how the free-floating base and submerged bodies affect the dynamic equations. Properties such as added mass and buoyancy forces and moments are included in the dynamics. We also look at other considerations that need to be made when mechanical and electrical systems are submerged in water.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 11. Spacecraft-Manipulator Systems

Abstract
Due to the extreme costs of transporting humans to space, the use of robotic arms has been proposed as a safer and more cost-efficient solution to several tasks. Some remotely controlled robotic arms are operating in space, for example on the International Space Station, and several more will probably find their way into space in the very near future, on both space stations and satellites.
This chapter discusses the kinematics and dynamics of free-floating vehicle-manipulator systems in a free-fall environment. There are several challenges related to introducing manipulators in space that are not present in fixed-base manipulators on Earth. Firstly, there is no natural way to choose the inertial frame; because the base is floating we cannot simply choose the inertial frame to coincide with the base in the normal way. Secondly, the free-floating base complicates the kinematic modeling as the forward kinematics map is not only position dependent and non-holonomic behavior arises.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 12. Field Robots

Abstract
Several mobile robots have been developed to operate in distant fields with low accessibility, and robotic solutions have now become imperative to the monitoring and surveillance of many of these fields. By adding manipulator arms to the robot base we can bring another dimension to these robots as they will be able to perform interaction tasks and manipulation in the field. Agricultural robotics is one important area where robots with manipulator arms and advanced sensory systems can revolutionize today’s technology with more efficient pruning and harvesting, surveillance and monitoring, and precision farming in general.
This chapter discusses the most important aspects of field robotics, including efficient locomotion found in for example wheeled robots. The dynamic equations of field robots with manipulator arms are found with particular focus on robots that operate on land, either on Earth or in space such as the moon and distant planets.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Chapter 13. Robotic Manipulators Mounted on a Forced Non-inertial Base

Abstract
As other vehicles, such as airplanes and cars, ships are also believed to become partially or completely unmanned in the next decade or so. This calls for more automation and increased use of robots for monitoring, surveillance, and operation of these ships.
Ships are influenced by waves, ocean currents, and wind. In particular the wave forces make the ship move with a high-frequency motion which will affect the dynamics of any robot that is mounted on the ship. In this chapter we show how the motion of the ship adds non-inertial forces to the robot dynamics. These forces need to be considered in order to obtain accurate mathematical models and robust control laws. We study how to accurately and efficiently control robotic manipulators when non-inertial forces enter the manipulator dynamics.
Pål Johan From, Jan Tommy Gravdahl, Kristin Ytterstad Pettersen

Backmatter

Weitere Informationen