**1. Introduction**

400 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

Abidi, M. A. and R. C. Gonzales (1992). Multi-sensor Image Fusion. *Data Fusion in Robotics* 

Beetz, M., T. Arbuckle, et al. (2001). Integrated, Plan-based Control of Autonomous Robots

Bellotto, N. and H. Hu (2009). Multisensor-based Human Detection and Tracking for Mobile Service Robots. *IEEE Trans. System, Man, and Cybernetics-B* 39(1): 167-181. Brown, R. G. (1983). *Introduction to Random Signal Analysis and Kalman Filtering*. New York,

Ciftcioglu, Ö. (2008). Multiresolutional Filter Application for Spatial Information Fusion in Robot

A. R. Trevino (Eds.), ISBN 78-953-7619-16-9, I-Tech Publishing, Vienna, Austria. Ciftcioglu, Ö. (2008). Shaping the Perceptual Robot Vision and Multiresolutional Kalman

Ciftcioglu, Ö., M. S. Bittermann, et al. (2007). Visual Perception Theory Underlying

Grewal, M. S. and A. P. Andrews (2001). *Kalman Filtering Theory and Practice Using MATLAB*.

Hong, L. (1991). Adaptive Distributed Filtering in Multi-coordinated Systems. *IEEE Trans. on* 

Hong, L. (1992). Distributed Filtering Using Set Models. *IEEE Trans. on Aerospace and* 

Hong, L. (1993). Multiresolutional Filtering using Wavelet Transform. *IEEE Trans. on* 

Hsin, H. C. and A. C. Li (2006). Wavelet-based Kalman Filtering in Scale Space for Image

Jazwinski, A. H. (1970). *Stochastic Processes and Filtering Theory*. New York Academic Press. Kailath, T. (1981). *Lectures on Wiener and Kalman Filtering*. New York, Springer Verlag. Mallat, S. G. (1989). A theory for multiresolution signal decomposition:the wavelet

Maybeck, P. S. (1982). *Stochastic Models, Estimation and Control*, Vol II. New York, Academic Press. McKendall, R. and M. Mintz (1992). Data Fusion Techniques using Robust Statistics. *Data* 

Richardson, J. M. and K. A. Marsh (1988). Fusion of Multi-Sensor Data. *Int. J. Robotics* 

Sorenson, H. W. (1985). *Kalman Filtering: Theory and Application*. New York, IEEE Press. Wang, M. and J. N. K. Liu (2004). Online Path Searching for Autonomous Robot Navigation.

*Fusion in Robotics and Machine Intelligence* Academic Press: 211-244. Mendel, J. M. (1987). *Kalman Filtering and Digital Estimation Techniques*. New York, IEEE. Oriolio, G., G. Ulivi, et al. (1998). Real-time Map Building and Navigation for autonomous

Simon, D. (2006). Optimal State Estimation. New Jersey, Wiley Interscience.

Fusion. *Pattern Recognition and Computer Vision.* C. H. C. a. P. S. P. Wang. Singapore,

representation. *IEEE Trans. on Pattern Analysis and Machine Intelligence*. 11(7): 674-693.

robots in unknown environments. *IEEE Trans. on Systems, Man and Cybernetics -* 

*IEEE Conf. on Robotics, Automation and Mechatronics*, 1-3 December, Singapore: 746-

Navigation. In: *Advances in Robotics, Automation and Control*, 355-372, J. Aramburo and

Filtering Implementation. *Int. Journal Factory Automation, Robotics and Soft Computing(3)*: 62-75, ISSN 1828-6984, International Spociety for Advanced Research,

Perceptual Navigation. *Emerging Technologies, Robotics and Control Systems* 

*and Machine Intelligence*. R. S. Blum and Z. Liu, Academic Press.

in Human Environments. *IEEE Intelligent Systems* 16(5): 56-65.

International Society for Advanced Research: 139-153. Gelb, A. (1974). *Applied Optrimal Estimation*. Cambridge, MA, MIT Press.

*Aerospace and Electronic Systems* 27(4): 10.

*Aerospace and Electronic Systems* 29(4): 1244-1251.

**8. References** 

John Wiley & Sons.

*www.internationalsar.org*.

New York, Wiley.

World Scientific.

*Electronic Systems* 28(4): 10.

*Part B*: Cybernetics 28(3): 316-333.

751, vol.2, ISBN 0-7803-8645-0

*Research* 7(6): 78-96.

Parallel manipulators have the advantages of high stiffness and low inertia compared to serial ones (Merlet, 2006). Most pick-and-place operations, including picking, packing and palletizing tasks; require four-degree-of-freedom (DOF), i.e. three translations and one rotation around a vertical axis (Company et al, 2003). A new family of 4-DOF parallel manipulator being called H4 that could be useful for high-speed, pick-and-place applications is proposed by Pierrot and Company (Pierrot & Company, 1999). This manipulator offers 3-DOF in translation and 1-DOF in rotation about a given axis. The H4 manipulator is useful for highspeed handling in robotics and milling in machine tool industry since it is a fully-parallel mechanism with no passive chain which can provide high performance in terms of speed and acceleration (Wu et al, 2006). Its prototype, built in the Robotics Department of LIRMM, can reach 10g accelerations and velocities higher than 5 m/s (Robotics Department of LIRMM). Pierrot et al. proved the efficiency of H4 serving as a high-speed pick-and-place robot (Pierrot et al, 2006). Corradini et al. evaluated the 4-DOFs parallel manipulator stiffness by two methods and compared the results (Coradini & Fauroux, 2003). Renaud et al. presented the kinematic calibration of a H4 robot using a vision-based measuring device (Renaud et al, 2003). Tantawiroon et al. designed and analyzed a new family of H4 parallel robots (Tantawiroon & Sangveraphunsiri, 2003). Poignet et al. estimated dynamic parameters of H4 with interval analysis (Poignet et al, 2003).

Parallel manipulators suffer from smaller workspaces relative to their serial counterparts; therefore, many researchers addressed the optimization of their workspaces (Boudreau & Gosselin, 1999; Laribi et al, 2007). But optimization for such a purpose might lead to a manipulator with poor dexterity. To alleviate this drawback some others considered both performance indices and volume of workspace, simultaneously (Li & Xu, 2006; Xu & Li, 2006; Lara et al, 2010).

This chapter deals with an optimal design of H4 parallel manipulator aimed at milling and Rapid-Prototyping applications with three degrees of freedom in translation and one in rotation. The forward and inverse kinematics of the manipulator are solved. The forward kinematics analysis of H4 leads to a univariate polynomial of degree eight. The workspace of the manipulator is parameterized using several design parameters. Some geometric constraints are considered in the problem, as well. Because of nonlinear discontinuous behaviour of the

Corresponding Author

Optimization of H4 Parallel Manipulator Using Genetic Algorithm 403

 The parameters **Mi**, d and h are the length of the rods, the offset of the revolute-joint from the ball-joint, and the offset of each ball-joint from the center of the traveling plate,

The pose of the EE is defined by a position vector *<sup>T</sup>* **<sup>B</sup>** *<sup>x</sup> <sup>y</sup> <sup>z</sup>* and an angle θ,

a) Robot with four lines drives and *<sup>2</sup> (S S)* chains

b) Robot CAD model

 .

One can effectively analyze the mobility of a H4 parallel manipulator by resorting to screw theory, which is a convenient tool to study instantaneous motion systems that include both

A screw is called a twist when it is used to describe the motion state of a rigid body and a wrench when it is used to represent the force and moment of a rigid body. If a wrench acts on a rigid body in such a way that it produces no work, while the body is undergoing an infinitesimal twist, the two screws are said to be reciprocal (Li & Xu, 2007). In a parallel

*i ii* **<sup>P</sup>** *ab0* for simplicity, Qz is

Without losing generality, in this chapter we consider *<sup>T</sup>*

rotation and translation in three dimensional spaces (Zhao et al, 2004).

respectively.

representing its orientation.

Fig. 2. H4 parallel manipulator

the offset of {B} from {A} along the direction of *<sup>z</sup> k*

problem, Genetic Algorithm (GA) Method is used here to optimize the workspace. Finally, using GA, the manipulator is optimized based on a mixed performance index that is a weighted sum of global conditioning index and its workspace. It is shown that by introducing this measure, the parallel manipulator is improved at the cost of workspace reduction.
