Summary of Project and Conclusions

At the beginning of this thesis, four research goals were listed:

1. Develop a Stewart platform through optimization techniques and by analyzing its kinematic properties.

2. Improve the speed and efficiency of existing optimization algorithms.

3. Research and choose the components that are most suited to the conditions and application of a pipeline spraying robot.

4. Build a 3-DOF Stewart platform prototype so that the trajectory path can be tested.

6.1.1 Summary of Parameter Optimization

An algorithm was proposed that uses a combination of the CRS algorithm to quickly find parameters that are in the neighbourhood of the optimum, and then use those parameters to speed up the convergence of the PSO algorithm by partially populating its swarm with those values. This proposed algorithm was first tested by optimizing a Delta robot so that it had the maximum workspace volume. The Delta robot was chosen because it is a parallel robot, but it has a simpler design than a 3-DOF Stewart platform. Five trials of the optimization were run using a PSO only algorithm and then another five trials were run using the proposed algorithm. The results of these trials were compared and it was found that the proposed algorithm converged to the optimum significantly faster overall than the PSO only algorithm.

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Once the effectiveness of the proposed algorithm had been verified by optimizing the parameters of the Delta robot, five trials of optimizing the Stewart platform were run using the PSO only algorithm, and five trials of optimizing the Stewart platform were run using the proposed algorithm. Since the focus of this project was to develop a Stewart platform capable of delivering a spray coating in a circular trajectory, a different objective function had to be devised rather than simply maximizing the workspace volume, because the 3-DOF Stewart platform has only one translational DOF. Therefore, an objective function was created that maximized the radius of the largest circular trajectory that the Stewart platform was capable of spraying for each base and top plate radius that were generated. When the results of the trials were compared, it again showed that the proposed algorithm decreased the total time it took for it to converge when compared to the PSO only algorithm. An especially important result was that the convergence speed of the PSO portion of the proposed algorithm was significantly faster than the convergence speed of the PSO only algorithm.

6.1.2 Summary of Robot Design

This chapter described the selection process for the individual components that comprise the robot. The first major component selected was the actuator. It was decided that an electric actuator would be the most suitable type of actuator for this application predominantly because of its accuracy, controllability, built-in position sensor, portability, robustness and sealability against environmental contamination. Specifically, the Thomson Electrak 1 SP12-09A-04 was chosen because it included aforementioned features, and its dimensions allowed it to be easily integrated into the robot design envelope. The Talon SR speed controller was chosen as the DC motor controller based on its performance graphs, and the MW126 power supply was selected because of its portability and its adequate power output.

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The second major component selected was the microprocessor, and this subsection is intended to be used as a guide for future projects that require the selection of a microprocessor based on a certain application. Three different microprocessor were tested at different parts of the design process. The Motorola 68HC12 was the first to be tested, but it suffered the drawbacks of having too few PWM output channels, a single ADC and it is programmable only in assembly language. The second microcontroller tested was the TMS320F28027 Piccolo microcontroller. This microcontroller was found to have difficulty with simultaneously sampling and converting the three positon signals from each of the potentiometers on the actuators.

Finally, the Delfino TMS320F28377D microcontroller was chosen. It featured four ADCs and it did not encounter the same problems with simultaneous signal sampling that were experienced with the Piccolo microcontroller. Therefore, this microcontroller was chosen as the one to be used in the robot prototype.

6.1.3 Summary of Trajectory Implementation

Two circular trajectories were implemented in the code that controls the Stewart platform prototype: one where there is an approximately 10° angle between the platform normal vector and the z-axis, and one where there is an approximately 20° between the platform normal vector and the z-axis. In order to determine how well the platform is able to follow these circular trajectories, several videos were recorded where a top down view of the colored lines taped onto the platform can be seen. From these videos, it has been qualitatively determined that the platform normal vector is able to follow the circular trajectories. However, an algorithm still needs to be developed that is able to extract the orientation of the platform at each of the seventeen desired orientations in the arrays. This algorithm will determine the actual orientation of the platform at each index in the array based on the apparent change in the length of the colored lines that can be seen in the videos of the platform running through the

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trajectories. Once the orientation at each index has been determined, the inverse kinematics can be used to calculate the each of the three platform joint centers. An error can then be calculated between the desired platform joint centers and the actual platform joint centers to quantitatively assess the accuracy of the Stewart platform prototype.