ROBOTLAB: A SOFTWARE FOR ROBOT GRAPHIC SIMULATION

ROBOTLAB: A SOFTWARE FOR ROBOT
GRAPHIC SIMULATION
Narpat s. Gehlot
Universidade Federal da Paraíba - Departamento de Engenharia Elétrica
58109 - 970 Campina Grande-PB-Brasil
E-mail: [email protected]
Pablo J. Alsina
Universidade Estadual da Paraíba - CCT - Departamento de Física
58100-000 Campina Grande - PB - Brasil
Abstract: The ROBOTLAB is a MATLAB based software package developed for robot
simulation and analysis. MATLAB users can analyze and simulate any arbitrary serial
link manipulator using ROBOTLAB by specifying robot kinematics, geometric and
dynamic parameters. The package incorporates an extensive library of functions of
transforrnations, kinematics, dynamics, control, trajectory and 3D animation of robots .
IIIustrative examples are presented to show the capability of the ROBOTLAB.
1. INTRODUCTION
The availability of powerful software packages such
as Mathematica, MATLAB and MAPLE, has
motivated the development of software tools for the
analysis and simulation of robotic systerns (Nethery
& Spong, 1994; Corke, 1996). Also, for Unix
operating systems a robot graphic simulator
(Marhefka & Orin, 1996) has been developed which
is portable over wide range of platforrns . The use of
software based tools for the simulation and analysis
of robotics systems provides a very attractive
solution of design problems & is ideal for
educational purposes, since the cost of experimental
setups is generally high. Moreover, the flexibility of
the software tools perrnits convenient training and
teaching aids (White, et al., 1989) as well as allows
the investigation of control strategies without the
need of an experimental prototype (McMillan, et aI.,
1995; Agba, 1995). In this paper, the ROBOTLAB:
A Graphic Robot Laboratory Simulator (Alsina,
1996) is described which consists of a versatile
robotics functions library , interactive graphic user
interfaces and forceful 3D animation tools .
ROBOTLAB was developed for personal computers,
running MATLAB 4.0 in Windows . Given an
appropriate description file of any arbitrary N-link
serial robot, the ROBOTLAB functions, like
MATLAB functions, are used in the analysis,
dynamics simulation and 3D animation to create a
Virtual Prototype. ROBOTLAB user interface is
described in Section 2. In Section 3, robot modeling
commands are discussed . Section 4 presents a
general
description
of
the
RüBOTLAB
environment, including details of the different
program modules and graphic output interface. An
iIIustrative example is given in Section 5 to show the
versatility of the package. A comparison with other
state-of-the-art packages is given in Section 6.
2. ROBOTLAB USER INTERFACE
J
465
ROBOTLAB is an interactive environment for robot
analysis , dynamic simulation and graphic 3D
animation. ROBOTLAB front end is a friendly
graphical user Interface, developed in MATLAB,
which provides an easy way of executing the
ROBOTLAB tasks. The ROBOTLAB command
functions (see Table I) are norrnally transparent to.
the user and are utilized for writing RÇ)BOTLAB
user programs. Figure 1 shows an example of the
Graphic user interface.
_ . -'f-diLWlndows
_. . .- - ::·_..lielp
_ _. ..... .
- '
file.
•...
.-
.
.. . .. "-- -
'
......
variables : one for the forrn and size and other for the
reiative positioning of the part in the link . The first
variable foIlows the forrnat: P<xx>L <yy>, where
<xx> is a two-digit number associated to the part
and <yy> is a two-digit number associated to the
corresponding link. This var iabIe must be initialized
by means of an appropriate graphic primitive
function in order to store the forrn and size of the
corresponding part oThe second variable defines the
relative positioning of the part with respect to the
link reference frame by means of a homogeneous
transformation. The general format of this variable
is TP<xx>L<yy>, where <xx> and <yy> were
defined above. For example, the part 3 of link 4
could be created as:
.... . . t,
..
,.
I.:
F·OBOTL.A.B
-]
r
;:".,
·1·
·1
Fig. 1 - ROBOTLAB Menu .
P03L04 = [2
3. ROBOT MODELING
0.5]
TP03L04 = [ I
O
O
O
Any serial robotics manipulator can be simulated in
ROBOTLAB. The manipulator is specified by the
user by a proper parameter file in the format
MATLAB "script-file". This file includes the
kinematics, dynamics and geometric parameters of a
robot to be simulated. The input data (from files or
keyboard) is written in the MATLAB language
forrnat: matrix between brackets, elements in a row
separated by blank spaces and each row separated by
a semicolon. The kinematics parameters are given in
a matrix named KINPAR. Each one ofthe N rows of
matrix KINPAR consists of tive elements that
describe completely the kinematics of one link: the
type of joint and the four Denavit-Hartenbeg
parameters
(ai, ai, di, ai) (Craig, 1986). For
example, for single-link system with a rotational
joint, the cinematic parameters.are specified as:
O
1
O
O
O
O
1
O
5
O
O
1];
The numb er 2 in part P03L04 is a code for a
hemispheric part and 0.5 is the radius length . The
variable TP03L04 indicates that the hemispheric
part is aligned with the reference frame ofthe link 4
(rotation matrix equal to identity matrix) and its
center is localized 5 units in the positiv e direction of
the x-axis of the frame . Using the geometri c
modeling form given above, user can specify any
robot of desired structural detai ls. Figur e 2 shows an
example ofrobot manipul ator geometric modeling.
1,
0.8
N
0.4
Similarly, the dynamics parameters are given in an
N row matrix named DYNPAR. Each row includes
the mass (m.), vector of center of mass (S = [S, S,
Sz]T), inertia tensor elements n, = n, Iyy I,z]T and
I, = [Iyz .Ixz Ixy]T), Coulomb friction coefficient (Ac)
and viscous friction coefficient (Av) of.one link. For
example, for single-link ' system with a rotational
joint, the dynamic parameters are specified as:
0.2
0.5
o
Y(m)
-o.
-0.5
X(m)
Fig. 2 - Example ofrobot geometric modelin g.
The geometric model of the robot is\ composed by
links, which are numbered sequentially, starting
from the base of the manipulator. Each link is
Cõmposed by several numbered parts (graphic
objects), which are created using some special
graphic primitive functions (prism, cone, cylinder,
sphere, hemisphere). Each part is specified by two
4. THE
PROGRAM
4. J General Characteristics
ROBOTLAB is structured in several module s, which
can be expanded accordin g to the user needs .
ROBOTLAB is divided: in . six main modules :
466
/
Homogeneous Transfonns, Trajectory Generation,
Kinematics, Dynamics, Graphics and Dynamics
Simulation. Each module consists of a set of
MATLAB functions, developed for each specific
problêrn, and, due to the open structure, they can be
utilized by the user in his own programs. A list of
the available ROBOTLAB functions is given in
Table I.
<,
4.2 Homogeneous Transforms
This module includes severaI functions to deal with
the homogeneous transfonns, which are used to
describe link translation and orientation.
4.3 Trajectory Generation
This ROBOTLAB module consists of a set of
function for trajectory generation (position, velocity
and acceleration) in joint space. The trajectory
generation is realized through a 5º order polynomial
interpolation between the initial and final point of
the path. This module includes functions to update
the polynomial coefficients and the state vector at
any instant ofthe trajectory. The generated trajectory
is stored in a file named trajdata.mat (Trajectory
generation results).
Table I ::.List ofROBOTLAB Functions
HomogeneousTransforms
rotmatx
Homogeneous transfonn about xaxis.
rotmaty
Homogeneous transfonn about yaxis.
rotmatz
Homogeneous transfonn about zaxis.
Trajectory Generation
5!h
order
coefiraj
Coefficients
of
polynomial
for
trajectory
interpolation.
traject
Trajectory generation.
trajpnt
Specific point of a trajectory.
Kinematics
transfor
Link homogeneous transfonns.
transfb
Link homogeneous transfonns in
base reference frame.
eulerang
Eu ler angles.
dirkin
Direct kinematics.
invkin
Inverse kinematics.
homepos
Home position.
Dynamics
dirdyn
Direct dynam ics.
invdyn
Inverse dynamics.
inermat
Inertia matrix.
inertorq
. Inertialload.
reactorq
Non-inertial load.
coritorq
Coriolis/Centrifugalload.
gravtorq
Gravitational load.
visctorq
Viscous Friction.
coultorq
Coulomb friction .
Dynamics Simulation
rgkrobot
Runge-Kutta solution of robot
dynamics.
State derivatives ofrobot dynamics.
robotdyn
Graphics
Cone-type graphic object.
pcone
Cylinder-type graphic object.
pcylind
Hemisphere-type graphic object.
phemis
Prism-type graphic object.
pprism
Sphere-type
graphic object.
pspher
ofa link .
Graphic
display
showlink
of a part ofa link .
Graphic
display
showpart
Graphic display ofa robot.
showrob
showunif
of unifilar
Graphic
display
diagram o
Transforms
position
and
transfpa
orientation of graphic object.
4.4 Kinematics
This module includes a set of functions related to the
kinematics of manipulators: Home Position, Link
Transfonnations,
Direct
Kinematics,
Inverse
Kinematics, Euler Angles, etc. Due to the
complexity of the inverse kinematics problem, a
"script-file", for computing the inverse kinematics of
its own robot, must be fumished by the user . This
file must update the vector of joint variables from a
given position and orientation of the tool. The user
has the option of 3D view of the manipulator in the
chosen spatial configuration.
4.5 Dynamics
This module includes several functions, based on the
Newton-Euler fonnulation (Featherstone, 1987), for
computation of the tenns of the dynamics equation:
Direct Dynamics, Inverse Dynamics, lnertia Matrix,
Coriolis/
CentrifugaI
Torques,
Gravitational
Torques, etc.
4.6 Dynamics Simulation
This module consists of a dynamics simulator for
serial manipulators based on numerical integration
through a fourth-order Runge-Kutta method. A
controller script-file must be fumished by the user to
implement his own robot control law, however, a
standard Computed Torque Controller is provided in
the ROBOTLAB. "Measured" values of position,
velocity and acceleration can be used for this file to
update the driving torque vector in a variable named
TORQ. The initial state and the simulation time are
interactively requested by the programo The
manipulator state is updated in the matrices THIST
(simulation time), QHIST (joint var iables), DQHIST
(joint velocities) , D2QHIST (joint accelerations) e
TORQHIST (driving torques). Beside these
var iables , the following variables are associated to
467
the reference trajectory: QRHIST, DQRHIST and
D2QRHIST. The simulation resuits are storedin a
file named simudata.mat (Dynamics simulation
response).
11
I
N
4.7 Graphic Results
II
0.4
As explained in Section 3, by using a set of graphic
. primitive functions, the user can construct a 3D
graphic model of its own manipulator, including as
many details as one wants. By means of this model ,
RüBüTLAB can be utilized to execute several kind
of graphic simulations, resuiting in a powerful 3D
animation tool for robotics. The RüBüTLAB
graphic output module includes time response
curves, 3D animation, 3D tool trajectory, unifilar
diagram, etc. Figures 3, 4 and 5 show the graphic
capabilities of the RüBüTLAB.
I
I
0.2
01I,
Y(m)
X(m)
Fig, 5 - 3D Animation with multiple poses .
5. APPLICATION EXAMPLE
RüBOTLAB can be used as an educational aid in
Robotics, as well as a design tool for off-line testing
of control strategies. Suppose, for example, that the
arm , shown in Fig. 2, is required to track a
circular trajectory in Cartesian space. üne way to
accomplish this is updating, through inverse
kinematics, the corresponding joint references frorn
the desired Cartesian trajectory, and then, computing
the driving torques by a computed torque control
law. Figure 6 shows the user file code needed for
this task. This file updates vector TORQ of driving
torques,
utilized by
RüBOTLAB for the
simulation .
% COMPUTED TORQUE CONTROLLER FILE
2
t(s)
t(s)
% Circular Trajectory Generation in Cartesian Space
Fig. 3 - Time Response graphic output.
t=2*pi* simtime/maxtime; % Time Interval
POSVEC=[R*cos(t); pycenter; di +R*sin(t));
ORIENTMAT=eye(3);
1,
O.
% Inverse Kinematics & Reference Trajectory
In.
N
Qr=invkin(ORIENTMAT,POSVEC);
DQr=(Qr-QrO)/samplingtime; QrO=Qr ;
D2Qr=(DQr-DQrO)/samplingtime; DQrO=DQr ;
O.
o.
o
% Tracking Error & Command Acceleration
<,
CID
"
Err=Qr-Q; DError=DQr-DQ;
D2Qc=D2Qr+Kd*DError+Kp* Error;
. <'
//' 0.5
% Computed Torque Controller
Y(m)
X(m)
TORQ=invdyn(Q,DQ,D2Qc);
Fig. 6 - Computed Torque Controller - User file
Fig. 4 - Unifilar Diagram
468
Note that vectors Q and DQ (joint trajectories and
joint velocities) are available "measured values", that
the user can utilize for controller feedback. Figure 7
shows
the
simulated time
response
and
corresponding driving torques for this example. It
can be noted the high torque required by joint 2, due
to the high gravitational load over this joint. Figure
8 shows the corresponding Cartesian trajectory
tracking.
.
(a)
1
educational purposes. Other simulators with the
same overall goal are Xanimate (Marhefka & Orin,
1996), Robotica (Nethery & Spong, 1994) and
Robotics Toolbox (Corke, 1996). Xanimate is a
powerful tool for graphical simulation of robotics
systems of any topological structure and is portable
on a wide range . of platforms. However, the
Xanimate does not include dynamics simulation,
whereas ROBOTLAB petforms both dynamics and
graphics simulations. Robotica is a computer aided
design package for serial manipulator, including
dynamics simulation, based on the Mathematica
package, Simnon and a C language front end .
Robotica is capable of generating symbolic solution
for robot kinematics and dynamics, whereas,
ROBOTLAB provides numeric solutions. Both
Robotics Toolbox as well as the ROBOTLAB are ao
extension of MATLAB language, although
ROBOTLAB also runs with a Windows front end .
The Robotics toolbox has a more complete set of
robotic
functions
than
ROBOTLAB,
but
ROBOTLAB is more versatile and realistic in
graphic animation capabilities. A MATLAB
compiled version will further improve this salient
features of the ROBOTLAB.
Joint Angles
.
2
-1f
O
0.2
0.6
0.4
0.8
(b) Driving
1
Torques
.
..
...
3
.. __. O
0.2
0.4
0.6
0.8
.
, .'
7. CONCLUSION
1
t ts)
The graphic robot simulator ROBOTLAB was
presented. This program, based on MATLAB
language, includes several open modules and can be
expanded and improved by the user. The
ROBOTLAB provides user friendly graphic interface
and graphic output with 3D animation. These
features make the ROBOTLAB a suitable tool for
research and teaching. The suggestions for future
work to enhance the functionality of ROBOTLAB
are : Simulation of any fixed topological robotic
structure, Inclusion of collision detect ion , Expansion
of GUI & CAD based generation of parameters.
Fig. 7 - Time response for tracking a circular path.
a) Joint Variables. b) Driv ing Torques.
1J
o.J
i
N I
I
I
OA
i
I
I
oi
APPENDIX
0.5
Dynamics Simulation by Newton-Euler Method
o
-0 .'5
Y(rn)
The robot dynamics simulation problem can be
stated as follows : given the vector of driving torques
and the initial state, update the time response of the
arm position. This can be attained by the numerical
integration of the direct dynamics of the Nvlink
manipulator, which is represented by the following
non-linear second order differential equation,
-0 .5
X(m)
Fig. 8 - Circular Trajectory Tracking.
6. COMPARISON WITH OTHER PACKAGES
q
Although powerful commercial robot simulation
packages such as SILMA are available, most of
them were developed for industrial needs. The
ROBOTLAB was developed for research and
=
(1)
were, t is the Nx 1 vector of driving torques, q is the
Nx 1 vector of joint positions, M( q) is the NxN
469
\
inertia matrix and '[ d (q, q) \is the Nx I vector of
coriolis, centrifugaI, gravitational and disturbance
torques. The computation of the driving torques
(inverse dynamics) can be realized in an efficient
recursive way by means ofthe Newton-Euler method
(Featherstone, 1987). This formulation method is
realized in two stages: the Forward and Backward
Recursions. In the Forward Recursion, the cinematic
variables are transformed recursively from the base
to the robot tool. In the Backward Recursion, forces
and torques are updated recursively from the tool to
the base of the robot, thus allowing the computation
of the joint driving torques:
- Forward Recursion:
utilized for the inertia matrix computation by an
indirect way (Walker & Orin, 1982). First, the vector
of coriolis, centrifugai and gravitational torques, 'td
is updated from :
(8)
where
'[(O)
is the solution of the Newton-Euler
(9)
where vector r
=
e
algorithm for the vector of joint accelerations
equal to zero. Then , each column M, of the inertia
matrix is obtained from:
(O)
is the solution of the Newton-Euler
algorithm obtained by imposing
(2)
e = o for j:t= i .
e = 1 for j = ·i e
j
j
REFERENCES
jT . j
j p. I )) +
A 1+. I (ro.X
p.1+ , + V. I· + ffi·1 x.(ffi·x
1
t
1+
=
(4)
- Backward Recursion:
f;
=
A;+1f;+1
XlTI;Si +ffi; X(ffij xmsj-r mv,
(5)
n
A;+l j+l + j'pj+l x(A:+,fj+l)+I jcO j +
+ffi j xl jffij
\
ZTn.+zTf
I
t
I
I
-i
m.s, XV.Y
(6)
(7)
where ffii , cOi are respectively the 3xl vectors of
angular velocity and acceleration the link i reference
frame; j is the 3xl vector of linear acceleration of
link i reference frame; f; and n, are the 3x 1 vectors of
force and torque applied on link-i-l)y link i-I; m, is
the mass of link i; Ij is the inertia tensor of link i
expressed in its own reference frame; Si is the 3x I
vector of position of the center of mass of link i. ipi+)
and À:+I are respectively the 3x 1 position vector
and 3x3 rotation matrix of frame i+ I in relation to
frame i. Zj = [O Ol]T, (Zj = [O OO]T) if joint i
v
is rotational and Zi
joint .i is prismatic.
= [O OO]T, (Zj = [O Olf)
if
The robot dynamics simulation problem
involves the numerical integration of Eq. (I), thus ,
the computation of the inverse of the inertia matrix
is necessary. The Newton-Euler formulation cannot
be used directly for the direct dynamics calculation,
because it only updates the vector of driving torques.
In spite of this , the Newton-Euler method can be
470
Agba , E. I. (1995). "SeaMaster: An ROVManipulator System Simulator". IEEE Computer
Graphics and App lications, pp. 24-31 .
AIsina,
P. J. (1996) . "Modular Adaptive
Neurocontrol of Robotic Manipulators" : Doctoral
Thesis (in portuguese), Federal Univ. of Paraíba,
Brasil.
Corke, P. I. (1996) . "A Robotics Toolbox for
MATLAB". IEEE Robotics and Automation
Magazine, Vol. 3, No. 1, pp. 24-32 .
Craig, 1. 1. (1986). "Introduction to Robotics Mechanics & Control". Addison-Wesley .
Featherstone, R. (1987).
"Robot
Dynam ics
Algorithms".
Boston
Kluwer
Academic
Publishers.
Marhefka, D. W. & D. E. Orin (1996) "Xanimate:
An
Educational TooI for Robot Graphical
Simulation". IEEE Robotics & Automation
Magazine. Vol. 3, No. 2, pp. 6-14.
McMil1an, S., D. E. Orin & R. 8. McGhee (1995) .
" Obj ect Oriented Design of a Dynamic
Simulation for Underwater Robotic Vehicles".
Proc. of IEEE Int. Conference of Robotics and
Automation, Nagoya , Japan , pp. 1886-1893 .
Nethery,1. F. & M. W. Spong (1994) " Robotica: A
Mathematica Package for Robot Analysis" . IEEE
Robotics and Automation Magazine, Vol. 1, No.
1, pp. 13-20.
Walker, M. W. & D. E. Orin (1982). " Efficient
Dynamic Computer Simulation of Rabot
Mechanisms" . ASME Joumal of Dvnamic
Systems , Measure. & Control 104, pp .205-21 I.
White, R. 8., R. K. Read, M. W. Koch & R. J.
Schil1ing (1989) "A Graphics Simulator for a
Robotic Arm". IEEE Trans. on Education, Vol.
32, No. 4, pp. 417-429.