Trajectory planning and simulation of Isoglide3 parallel robot.
Stan, Sergiu-Dan ; Maties, Vistrian ; Balan, Radu 等
1. INTRODUCTION
The 3 DOF Isoglide3 parallel robot and its structure is shown in
Fig. 1, where a mobile platform is coupled with the fixed base by three
legs of type PRRR (Prismatic Revolute Revolute Revolute). The fixed
coordinate frame originates at the point O. In Fig. 2, the reference
frame XYZ is attached to the fixed base.
The mobile platform can be visualized as a square whose side length
2L is defined by [B.sub.1], [B.sub.2], and [B.sub.3] points. The fixed
base is defined by three guide rods that passing through [A.sub.1],
[A.sub.2], and [A.sub.3] points, respectively (Stan, 2008).
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
The three revolute joint axes at each of these links are parallel
to the ground connected prismatic joint axis, and are located at points
[A.sub.i], [M.sub.i], and [B.sub.i], respectively. Also, the three
prismatic joint axes passing through points [A.sub.i], for i = 1, 2, 3,
are parallel to the X, Y, and Z axes, respectively.
The first prismatic joint axis lies on the X-axis; the second
prismatic joint axis lies on the Y axis; while the third prismatic joint
axis is parallel to the Z axis.
Consequently, the location of point P is determined by the
intersection of three planes. The forward and inverse kinematic analysis
is trivial. A simple kinematic relation can be written as (1).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
This robot architecture was also implemented and known in the
literature under the name of Isoglide3-T3 (Gogu 2004, 2008), Orthogonal
Tripteron (Gosselin et al. 2004), or CPM (Kim and Tsai 2002).
2. TRAJECTORY PLANNING AND SIMULATION RESULTS
The path is defined as sequence of robot configurations in a
particular order without regard for timing of these configurations while
trajectory is concerned about when each part of the path must be
obtained thus specifying timing.
The control of the robot is implemented using a joint-based control
scheme. In such a scheme, the end effecter is positioned by finding the
difference between the desired quantities and the actual ones expressed
in the joint space.
The first tests on the prototype encourage the direction of the
research: the chosen control algorithms emphasize the peculiar
characteristics of the parallel architecture and, in particular, the
good dynamic performance due to the limited moving masses, and
advantageous robot behaviour.
The interface is based on a virtual reality approach in order to
provide the user with an interactive 3D graphical representation of the
parallel robot.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
The interface was designed to give a novice user an intuitive tool
to control any kind of mechanical structure (serial, parallel or
hybrid), requiring no programming skills. Computer based simulation
allows mimicking of a real life or potential situations.
SimMechanics models, however, can be interfaced seamlessly with
ordinary Simulink block diagrams. For example, this enables user to
design the mechanical and the control system in one common environment.
In addition, Virtual Reality Toolbox for MATLAB makes possible a
more realistic rendering of bodies. Arbitrary virtual worlds can be
designed with Virtual Reality Modeling Language (VRML), and interfaced
to the SimMechanics model.
The sample trajectory of the end-effector is chosen to be a
circular path with the radius of 0.3 meters and its center is O(0,0,0).
This path is designed to be completed in 7 seconds when the
end-effector reaches the starting point P1 (0.3, 0, 0) again with
constant angular velocity [omega] = 0.5[pi] rad/sec. The end-effector
path is shown in figure 5.
The desired force obtained from the actuators to move the
end-effector of the Isoglide3 parallel robot along the desired
trajectory is shown in figure 6.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
3. CONCLUSION
The paper presents a Virtual Reality Interface for the 3 DOF
Isoglide3 parallel robot (IG3PR) control. An evaluation model from the
Matlab/SimMechanics environment was used for the simulation. An
interactive tool for dynamics system modeling and analysis was presented
and exemplified on the control in Virtual Reality environment of this
Isoglide3 parallel robot.
The main advantages of this parallel manipulator are that all of
the actuators can be attached directly to the base, that closed-form
solutions are available for the forward and inverse kinematics, and that
the moving platform maintains the same orientation throughout the entire
workspace.
By means of SimMechanics, the authors considered robotic system as
a block of functional diagrams. Besides, such software packages allow
visualizing the motion of mechanical system in 3D virtual space.
Especially non-experts will benefit from the proposed visualization
tools, as they facilitate the modeling and the interpretation of
results.
4. REFERENCES
Gogu, G., Structural synthesis of fully-isotropic translational
parallel robots via theory of linear transformations, European Journal
of Mechanics / A -Solids, vol. 23, pp. 1021-1039, 2004.
Gogu, G., Structural synthesis of parallel robots, Part 1:
Methodology, Springer, 2008.
Stan, S.-D, Manic, M., Maties, M., Balan, R., "Evolutionary
Approach to Optimal Design of 3 DOF Translation Exoskeleton and Medical
Parallel Robots", HSI 2008, IEEE Conference on Human System
Interaction, Krakow, Poland, May 25-27, 2008.
Stan, S.-D, Manic, M., Maties, M., Balan, R., "Kinematics
Analysis, Design, and Control of an Isoglide3 Parallel Robot
(IG3PR)", IECON 2008, The 34th Annual Conference of the IEEE
Industrial Electronics Society, Orlando, USA, November 10-13, 2008.
Kim, S.H., Tsai, L-W., "Evaluation of a cartesian parallel
manipulator", In: Lenarcic J, Thomas F (eds) Advances in robot
kinematics. Kluwer Academic Publishers, pp 21-28, 2002.
Gosselin, C.M., Kong, X., Foucault, S., Bonev, I.A., "A
fully-decoupled 3-dof translational parallel mechanism", In:
Parallel Kinematic Machines in Research and Practice, 4th Chemnitz
Parallel Kinematics Seminar, pp 595-610, 2004.
