**6. Discussion**

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

Figure 17 and 18 shows the estimations in the second linear trajectory. They are the enlarged form of figure 10 at this very period. Next to satisfactory MDF estimations, the figures show the

trajectory ref [o], MDF [.], EKF [+] and measurements [\*]

17.5 17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4

trajectory ref [o], MDF [.], EKF [+] and measurements [\*]

Fig. 17. Enlarged *measurement*, *reference*, *extended Kalman filtering(EKF)* and *multiresolutional distributed filtering* (*MDF)* estimation of robot trajectory in the second linear period. The **\*** sign is for measurement; **+** for EKF; **o** for reference; for *MDF* estimated trajectory.

17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18 18.1

Fig. 18. Enlarged *measurement*, *reference*, *extended Kalman filtering(EKF)* and *multiresolutional distributed filtering* (*MDF)* estimation of robot trajectory in the second linear period. The **\*** sign is for measurement; **+** for EKF; **o** for reference; for *MDF* estimated trajectory.













In this work the effectiveness of multisensor-based multiresolutional fusion is investigated by means of estimation errors of mobile robot position determination. The comparison is made offline but not real-time. By doing so, a clear view presented about at what conditions the multiresolutional multi-sensor fusion process is effective and also in which circumstances the fusion process may have shortcomings and why. However, the implementation can be carried on in real-time in the form of one block ahead prediction forming the data-sensor fusion, and one step-ahead prediction at the highest resolutional level i.e., for *i=3* without fusion process. These are illustrated in figure 4. In both cases, i.e., real-time and off-line operations, the merits of the multiresolutional multisensor fusion remains robust although some unfavorable deviation from the existing results in real-time may occur due to a block prediction compared to 1-step-ahead prediction, obviously. Investigations on real-time operation for the assessment of the robustness are interesting since the mobile robot is especially meant for this type of operation.

## **7. Conclusions**

Autonomous mobile robot navigation is a challenging issue where robot should be provided with accurate and reliable position information. Although reliable information can be provided by adding redundant sensors, the enhanced accuracy and precision information can be provided by synergistically coordinating the information from these sensors. In this respect, the present research introduced a novel information fusion concept by inverse wavelet transform using independent multiresolutional sensors. In the linear system description, the highest resolutional sensor provides enough information for optimum information processing by Kalman filtering where residual variance is minimum so that the information delivered by multiresolutional sensors can be redundant depending on the sensors's qualities and associated noises. In situations where system dynamics is non-linear, Kalman filter is still optimal in its extended formulation. However, the estimation errors in this case are dependent on the degree of the non-linearity of the system dynamics. The multiresolutional sensor fusion becomes quite effective in the non-linear case since the partial nonlinearity information of the system in different resolutional scales is available. Sensor quality is always an important factor playing role on the estimation. These features are demonstrated and the fusion process presented can easily be extended to consider realtime operation as well as some cases of probabilistic nature such as missing measurements, sensor failures and other probabilistic occurrences.

**20** 

*Iran* 

and S.M. Varedi

*Babol University of Technology* 

**Optimization of H4 Parallel** 

**Manipulator Using Genetic Algorithm** 

M. Falahian, H.M. Daniali

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

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,

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

**1. Introduction** 

analysis (Poignet et al, 2003).

2006; Lara et al, 2010).

Corresponding Author

 

### **8. References**

