**4. Result analysis**

In this section, the analysis for the developed GWO based OTG method and GA for optimal planning of the trajectory for designing the 6 DOF Robotic manipulator. The applied methods are implemented by MATLAB.

A 3-degree-of-freedom (3-DOF) planar parallel manipulator performing highspeed, high-acceleration, and high-accuracy trajectory tracking as similar to the novel experimental pick-and-place manipulator is designed and constructed. At the time of trajectory tracking, multiple closed-loop performance specifications like tracking accuracy, settling time, control effort, and robustness to parameter uncertainty must be satisfied simultaneously. Commonly, closed loop requirement is clashing, i.e., when one requirement is improved, others may break down.

An Optimal Trajectory Generation Algorithm (OTGA) is created for producing least time smooth movement directions for 6 DOF equal controllers. The proposed OTGA utilizes the Gray Wolf enhancement procedure for the ideal direction age utilizing numerous goal capacities. Alongside this, to follow the smooth movement of mechanical controllers, the joint speed, joint increasing speed and joint jerks requires optimal value. At each cycle, the proposed Gray Wolf improvement method chooses the ideal directions utilizing the goal limitations.

The below graph 1 to 6 in **Figure 4** shows, the comparison of joint velocity for all active joints angles *θ*1, *θ*2, … , *θ*<sup>6</sup> of the manipulator between the proposed and existing methods. The below simulated results shows smooth motion with optimal velocity at each joints of the robotic arm (manipulator).

The below graph 1 to 6 in **Figure 5** shows, the comparison of joint acceleration for all active joints angles *θ*1, *θ*2, … , *θ*<sup>6</sup> of the manipulator between the proposed and existing methods. The below simulated results shows smooth motion with optimal acceleration at each joints of the robotic arm (manipulator).

The below graph 1 to 6 in **Figure 6** shows, the comparison of joint jerks for all active joints angles *θ*1, *θ*2, … , *θ*<sup>6</sup> of the manipulator between the proposed and existing methods. The below simulated results shows smooth motion with minimum jerks at each joints of the robotic arm (manipulator).

The above figures show that the comparison between projected GWO technique, existing GA and default methods for trajectory generation. We have taken

**Figure 4.** *Comparison plot for time segment vs. velocity for proposed and existing method.*

three measurements named as acceleration, jerk and velocity in which all these are going to be compare with different time segments. It is clearly shows that the proposed method achieves minimum effective value as compared to the exiting techniques.

with the GA (Genetic Algorithm) based trajectory generation method and a tradi-

*Comparison plot for time segment vs. acceleration for projected and existing method.*

The mean, maximum and minimum acceleration value is also less for the proposed OTG with GWO method when compared to the existing methods. The least acceleration value is attained for the joint angle. Finally, the Joint jerk value is also calculated for all the joint angles using proposed and exiting methods with 15

The comparison of joint velocity, joint acceleration and joint jerks for all active joints angles *θ*1, *θ*2, … , *θ*<sup>6</sup> of the manipulator between the proposed and existing

tional trajectory generation method.

*Optimal Trajectory Generation of Parallel Manipulator DOI: http://dx.doi.org/10.5772/intechopen.96462*

segments.

**67**

**Figure 5.**

#### **5. Discussion and conclusions**

An optimal trajectory generation methodology is proposed which generates errorless continuous path motion with fast converging the Gray Wolf Optimization (GWO) method. The proposed OTG method using GWO algorithm is compared

*Optimal Trajectory Generation of Parallel Manipulator DOI: http://dx.doi.org/10.5772/intechopen.96462*

**Figure 5.** *Comparison plot for time segment vs. acceleration for projected and existing method.*

with the GA (Genetic Algorithm) based trajectory generation method and a traditional trajectory generation method.

The mean, maximum and minimum acceleration value is also less for the proposed OTG with GWO method when compared to the existing methods. The least acceleration value is attained for the joint angle. Finally, the Joint jerk value is also calculated for all the joint angles using proposed and exiting methods with 15 segments.

The comparison of joint velocity, joint acceleration and joint jerks for all active joints angles *θ*1, *θ*2, … , *θ*<sup>6</sup> of the manipulator between the proposed and existing

three measurements named as acceleration, jerk and velocity in which all these are going to be compare with different time segments. It is clearly shows that the proposed method achieves minimum effective value as compared to the exiting

*Comparison plot for time segment vs. velocity for proposed and existing method.*

An optimal trajectory generation methodology is proposed which generates errorless continuous path motion with fast converging the Gray Wolf Optimization (GWO) method. The proposed OTG method using GWO algorithm is compared

techniques.

**66**

**Figure 4.**

**5. Discussion and conclusions**

*Collaborative and Humanoid Robots*

iii. The jerk maximum average value of the proposed GWO based OTG is observed that 2.41 times and 2.04 times lesser than GA based OTG and

iv. Proposed OTG GWO generates minimum 118.4% and maximum 236.1% better velocity, minimum 156.4% and maximum 592% better acceleration,

The efficiency of projected methodology has been analyzed with the actual research works. The experimental result shows that a good optimization of developed OTG method in terms of shared speed, joint speed ripples, and joint lurching move measures. This proves that the proposed OTG algorithm works effectively to follow the optimal trajectory with less tracking error and smooth continuous path

and minimum 108.7% and maximum 310.7% better jerk.

non-optimize method.

*Optimal Trajectory Generation of Parallel Manipulator DOI: http://dx.doi.org/10.5772/intechopen.96462*

motion.

**Author details**

Chandan Choubey<sup>1</sup>

Kurukshetra, India

**69**

of Institutions, Greater Noida, India

provided the original work is properly cited.

\* and Jyoti Ohri2

1 Department of Electronics and Communication Engineering, Dronacharya Group

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 Department of Electrical Engineering, National Institute of Technology,

\*Address all correspondence to: er.choubey.chandan@gmail.com

**Figure 6.** *Comparison plot for time segment vs. jerk for proposed and existing method.*

methods. The below simulated results shows smooth motion with optimal velocity at each joints of the robotic arm (manipulator).

Comparison results can be summarized as follows:


The efficiency of projected methodology has been analyzed with the actual research works. The experimental result shows that a good optimization of developed OTG method in terms of shared speed, joint speed ripples, and joint lurching move measures. This proves that the proposed OTG algorithm works effectively to follow the optimal trajectory with less tracking error and smooth continuous path motion.
