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In
creasin
g
Ban
d
w
id
th
Robot 1
commercial robot controller
Robot 1 Trajectory
Generator
Robot 2
Robot 2 Trajectory
Generator
commercial robot controller
FTS 1
WP Trajectory
Generator
WP
Trajectory
Comp/Imp
Controller 1
Gravity
Compensation 1
FTS 2
Comp/Imp
Controller 2
Gravity
Compensation 2
Environment
WP Gravity
Compensation
Geometrical
Constraints
Comp/Imp
Controller 1
Gravity
Compensation 1
ravity
nsation
Robot 1
commercial robot controller
Robot 1 Trajectory
Generator
Robot 2
Robot 2 Trajectory
Generator
commercial robot controller
FTS 1
Comp/Imp
Controller 1
Gravity
Compensation 1
FTS 2
Comp/Imp
Controller 2
Gravity
Compensation 2
Environment
WP Gravity
Compensation
commer
Robot 1
rcial r
Robot 1 Trajectory
Generator
Robot 2
Robot 2 Trajectory
Generator
rcial r
FTS 1
WP Trajectory
Generator
WP
Trajectory
Controller 1
pensation 1
F
Comp/Imp
Controller 2
Gravity
Compensation 2
Environment
WP G
Compe
Geometrical
Constraints
commer
Robot 1
commercial robot controller
Robot 1 Trajectory
comm
comm
o
Generator
Robot 2
Robot 2 Trajectory
comm
comm
o
Generator
commercial robot controller
ot c
FTS 1
TS 2
Com
Comp/Imp
Controller 1
Gravity
Compensation 1
FTS 2
Comp/Imp
Controller 2
Gravity
Compensation 2
2
Environment
n
r
WP Gravity
vity
Compensation
pensation
a
Robot 1
commercial robot controller
Robot 1 Trajectory
Generator
Robot 2
Robot 2 Trajectory
Generator
commercial robot controller
WP Trajectory
Generator
WP
Trajectory
Environment
Geometrical
Constraints
Control Modes
Switch1
Switch2
Switch3
Trigger2
Trigger1
Control Strategy
Control Architecture
Task Specification
Control Structures
Control Layers
Figure 5.1: The di
fferent definitions in a control architecture
It is imperative to note that this chapter mainly discusses the undermost level i.e. the
control structures. Nevertheless the information with the other layers is also outlined and
will be thoroughly discussed in the next chapter.
55
5 Control Architecture
5.2 Modeling
Modeling serves to understanding relations between the di
fferent components of the system
in light of kinematic and dynamic analysis. This assists in designing the required control
architecture. Furthermore it facilitates decreasing the design complexity of the controllers
by incorporating assumptions to simplify the analysis.
5.2.1 Coordinate systems
In this section the di
fferent coordinate systems encountered in the analysis of cooperative
manipulation will be introduced (Figure 5.2).
World frame (
W)
The world frame, also termed the ’global frame’ is a fixed coordinate system which is
usually set in an arbitrary location somewhere in the vicinity of the manipulators. To
aid the mathematical description of the system, the frame is usually positioned so as to
simplify the derivation of equations. A common practice is to adjust it to coincide with
the initial position of the work-piece frame. All or most of the other coordinate systems
are at some point defined w.r.t the world frame.
Robot frame (
R)
The robot frame is a coordinate system attached to the base of a given robot. It is usually
considered fixed w.r.t the world frame unless the robot is capable of moving i.e. mobile or
installed on a linear motor. In industrial robots, it is usual to have the z-axis of the frame
coincide with the axis of the first joint, thus simplifying kinematic analysis.
Tool frame (
T )
This frame is attached to the TCP of a given robot. In industrial practice and sometimes
in the research literature it is commonly
/interchangeably termed the TCP frame. It is
imperative to point out that this frame does not lie at the robot’s flange, but is directly
attached in the middle of the gripper. In most cases, the gripper is not flexible in a manner
that the mathematical transformation between both the tool frame and the flange frame is
constant, hence the interchangeable nature of the term. Additionally, the posture of this
frame in practice is defined w.r.t the robot frame.
Work-piece frame (
O)
This frame is usually attached to the work-piece’s center of gravity. The initial orientation
thereof is usually aligned to that of the World Frame.In this work only one work-piece is
considered at any given time. Therefore, only one work-piece frame exists through this
ongoing analysis.
Generalized coordinates
In dealing with rigid bodies, sometimes it is more advantageous to describe the system in
a set of generalized coordinates which are independent from a fixed frame or coordinate
system. This eliminates the variables needed to express constraints between the variables.
56
5.2 Modeling
W
2
nd
Robot
i
th
Robot
R
1
R
2
R
i
O
T
1
T
i
T
2
1
st
Robot
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