Robot Manipulators

Modeling, Performance Analysis and Control

Etienne Dombre, Wisama Khalil, Etienne Dombre, Wisama Khalil

• Publisher: Wiley-ISTE
• Year: 2013
• ISBN:
  9781118614105
• Edition: 1
• Topic: Technologie et ingénierie
• Subtopic: Robotique

This book presents the most recent research results on modeling and control of robot manipulators.

• Chapter 1 gives unified tools to derive direct and inverse geometric, kinematic and dynamic models of serial robots and addresses the issue of identification of the geometric and dynamic parameters of these models.
• Chapter 2 describes the main features of serial robots, the different architectures and the methods used to obtain direct and inverse geometric, kinematic and dynamic models, paying special attention to singularity analysis.
• Chapter 3 introduces global and local tools for performance analysis of serial robots.
• Chapter 4 presents an original optimization technique for point-to-point trajectory generation accounting for robot dynamics.
• Chapter 5 presents standard control techniques in the joint space and task space for free motion (PID, computed torque, adaptive dynamic control and variable structure control) and constrained motion (compliant force-position control).
• In Chapter 6, the concept of vision-based control is developed and Chapter 7 is devoted to specific issue of robots with flexible links. Efficient recursive Newton-Euler algorithms for both inverse and direct modeling are presented, as well as control methods ensuring position setting and vibration damping.

Chapter 1

Modeling and Identification of Serial Robots ¹

1.1. Introduction

The design and control of robots require certain mathematical models, such as:

– transformation models between the operational space (in which the position of the end-effector is defined) and the joint space (in which the configuration of the robot is defined). The following is distinguished:

- direct and inverse geometric models giving the location of the end-effector (or the tool) in terms of the joint coordinates of the mechanism and vice versa,

- direct and inverse kinematic models giving the velocity of the end-effector in terms of the joint velocities and vice versa,

– dynamic models giving the relations between the torques or forces of the actuators, and the positions, velocities and accelerations of the joints.

This chapter presents some methods to establish these models. It will also deal with identifying the parameters appearing in these models. We will limit the discussion to simple open structures. For complex structure robots, i.e. tree or closed structures, we refer the reader to [KHA 02].

Mathematical development is based on (4 × 4) homogenous transformation matrices. The homogenous matrix iTj representing the transformation from frame Ri to frame Rj is defined as:

[1.1]

where isj, inj and iaj of the orientation matrix iRj indicate the unit vectors along the axes xj, yj and zj of the frame Rj expressed in the frame Ri; and where iPj is the vector expressing the origin of the frame Rj in the frame Ri.

1.2. Geometric modeling

1.2.1. Geometric description

A systematic and automatic modeling of robots requires an appropriate method for the description of their morphology. Several methods and notations have been proposed [DEN 55], [SHE 71], [REN 75], [KHA 76], [BOR 79], [CRA 86]. The most widely used one is that of Denavit-Hartenberg [DEN 55]. However, this method, developed for simple open structures, presents ambiguities when it is applied to closed or tree-structured robots. Hence, we recommend the notation of Khalil and Kleinfinger which enables the unified description of complex and serial structures of articulated mechanical systems [KHA 86].

A simple open structure consists of n+1 links noted C0, …, Cn and of n joints. Link C0 indicates the robot base and link Cn, the link carrying the end-effector. Joint j connects link Cj to link Cj-1 (Figure 1.1). The method of description is based on the following rules and conventions:

– the links are assumed to be perfectly rigid. They are connected by revolute or prismatic joints considered as being ideal (no mechanical clearance, no elasticity);

– the frame Rj is fixed to link Cj;

– axis zj is along the axis of joint j;

– axis xj is along the common perpendicular with axes zj and zj+1. If axes zj and zj+1 are parallel or collinear, the choice of xj is not unique: considerations of symmetry or simplicity lead to a reasonable choice.

The transformation matrix from the frame Rj-1 to the frame Rj is expressed in terms of the following four geometric parameters:

– αj: angle between axes zj-1 and zj corresponding to a rotation about xj-1;

– dj: distance between zj-1 and zj along xj-1;

– θj: angle between axes xj-1 and xj corresponding to a rotation about zj;

– rj: distance between xj-1 and xj along zj.

Figure 1.1. A simple open structure robot

Figure 1.2. Geometric parameters in the case of a simple open structure

The joint coordinate qj associated to the jth joint is either θj or rj, depending on whether this joint is revolute o...