# Research on Kinematics Analysis and Trajectory Planning of Novel EOD Manipulator
## 5 Simulation and Experiment  
### Simulation of Manipulator Trajectory Planning  
The purpose of trajectory planning is to generate reference input of the motion control system by analyzing the desired motion path. The aim is to complete the path in the shortest time under certain constraints on factors such as the speed and acceleration of joints [20]. At present, trajectory planning is mainly divided into two aspects: one is multiple continuous points along the specified path, and the other is the starting and ending point of the specified path. In this paper, the working condition of the manipulator is to move between two points, so the second idea is chosen. Let the starting point of the manipulator be point A, as shown in Figure 6a, and the ending point of the manipulator be point B, as shown in Figure 6b. On the premise of determining the pose matrix of the two points A and B, the path point is converted into the angles \(q_{a}\) and \(q_{b}\) of each joint at two points through inverse kinematics analysis. Subsequently, the constraint conditions of each joint during the motion of the manipulator are considered comprehensively, so as to obtain the changing trajectory of the manipulator.  
We use MATLAB Robotic Toolbox to simulate the trajectory of the manipulator. By calling the jtraj( ) command, the 5 th order polynomial interpolation trajectory in joint space can be obtained. By bringing each joint angle \(q_{0}=[0,0,pi/2,pi/2,-pi/2,0]\) and \(q_{1}=[-0.117*pi,0.3*pi,-0.728*pi,pi/2,-0.202*pi,pi/2]\) of the above starting and ending point into \([\text{q}\text{q}\text{q}\text{q}\text{q}\text{q}\text{d}]=\text{t}\text{r} \text{a}\text{j}(q_{0},q_{1},\text{step})\), the variation curves of each joint q, velocity qd and acceleration qdd of the manipulator are obtained, as shown in Figure 7a-c.  
Figure 7a shows the change in angular displacement of each joint. Each joint angle smoothly changes from the initial angle to the terminal angle, and the virtual joint angle does not change. According to the inverse kinematics solution of the two points, it can be seen that the motion of each joint is correct. Figure 7b,c prove that the angular velocity and angular acceleration curves of each joint of the manipulator obtained by simulation are successive and smooth, which proves that each joint of the manipulator operates steadily during the movement, and there is no obvious catastrophe point. It meets the working requirements of the manipulator. The terminal trajectory of the manipulator is shown in Figure 8.  
Figure 8 shows that the proposed algorithm can be used to move the EOD manipulator from the initial position to the target position through each expected point, which guarantees the functionality of the EOD manipulator and proves the reliability of the algorithm.  
Figure 6: MATLAB simulation diagram: (**a**) Initial position and orientation; (**b**) Terminal position and orientation.  
Figure 8: End displacement curve of the manipulator.  
Figure 7: (**a**) Angular displacement curve of each joint; (**b**) Angular velocity curves of each joint; (**c**) Angular acceleration curves of each joint.