In this set of experiments three controllers were compared with each other. They were a PID controller, a type-1 fuzzy logic controller and the novel dual surface type-2 fuzzy logic controller. The purpose of the experiment was to establish a baseline set of results and to discover if there were any differences between the controllers when they were used to control a micro robot.
7.5. Method for Comparing the Controllers 169 The experiments were carried out on the robot soccer pitch. For each robot controller five strategy files were created. The strategy files only differed in the speed demand setting that was used. The speed demand settings were 10, 20, 40, 80 and 120. Four robots were used in the experiment. This was a precaution, due to reliability problems that had been experienced previously with the robots. It was expected that at least one set of results would be obtained for each set of speed demands and controllers across the set of robots in any of the test runs of the experiment.
The blue bodied robot team was used in the experiment. The robot soccer engine was configured in a left to right playing mode for the purposes of the experiments. The robots were positioned against the bottom length edge of the robot soccer pitch, at approximately 40, 80, 130 and 170 cm from the left goal facing forward with the pitch in front of the viewer. To reduce experimental error the robots were positioned against a maker at these points on the pitch. The actual position of the robots was recorded by the RSE for each test run, so the variation could be investigated if required. The repeatability of the start position was not considered to be important to the results since the travel time was being measured. Selection of the type of controller to use in a robot, was by a transmitted parameter.
Under control of the Robot Soccer Engine (RSE), the robots were command to move forward from their start positions, across the width of robot soccer pitch, at the speed demand setting of the strategy command file. The start command was sent serially to all the robots in the same command cycle within the Robot Soccer Engine. This allowed the response of each of the robots to be compared in case of internal problems within the robots causing systematic errors. The expectation was that the robots would move in a straight line across the width of the pitch, travelling parallel to each other. No other commands were sent and no mid course corrections were allowed. This was to ensure that the experiments were not biased by external commands.
In this set of experiments the dual surface fuzzy logic controller was set to operate as an Average dual surface controller. This is the classic type-2 crisp output, and was used to provide a baseline set of results for the dual surface type-2 controller in a configuration that was well understood.
by the three term trapezoidal triangular membership function shapes with ACT PROD and threshold 0.9 given in Tables E.2 and E.3 respectively. The surface used in the type- 1 fuzzy logic controller was the corresponding three term type-1 trapezoidal triangular function shapes, given in Table E.5. The PID parameters used in the PID controller tests were pP = 80, pI = 16, pD = 16. These are the parameters that were established in Chapter 4 - Development of a Baseline PID controller.
In total thirty test runs were made. These consisted of five speed demand strategies for each of the three controller types. The test runs were made with and with out a ramp function being applied. The purpose of the ramp function was to smooth the controller output especially at the higher speed demand settings. This was necessary due to the robots careering off line when high speed demands were directly applied. The number of runs in each test run was nominally 10. If an obvious failure occurred during a run then that run was repeated. For the tests of the type-1 and type-2 fuzzy logic controllers, robot number 4 always used the PID controller with the above parameters of pP = 80, pI = 16, pD = 16. The purpose of having a micro robot with a PID controller was to provide a test run comparison for each run within the test speed setting.
Robot Responses during Runs
Generally the robots travelled across the width of the robot soccer pitch in a straight line without colliding with an other robot, or hitting the sides before the minimum acceptable run distance was achieved. However during the runs individual robots failed to start, or at low speeds stalled. At high speeds the robots became unstable and went round in circles or crashed into the sides of the arena. During the runs robots would collide with each other. There was no supervisory positioning commands given by the RSE, once a robot started it continued along the trajectory. Periodically the wheels became loose and disengage from the motor drive resulting in the robot driving differentially and travel in a circle. After each run the robots were checked for wheel problems and if found the runs were repeated. Genuine control failures often exhibited the characteristics of loose wheels so care had to be taken on this issue.
7.5. Method for Comparing the Controllers 171
7.5.1
Results for Comparing the Controllers
The necessary distance travelled to be included in the results was to pass the 127 cm point on the robot soccer pitch. However if the robot passed the 150 cm point then this point was used in the calculation of the average speed of the robot. Between 127 and 150 cm the stop distance was used. A Pythagorean adjustment was made to give a straight line speed for the robots from their start position. The justification for this was that sometimes the robot would slew at the start and then travel in a straight line past the 127 cm criteria. In some of the runs robot number 3 just failed to respond at all to any of the commands. This also happened with robot number 4 but not as frequently. This is designated by ** in the averages tables. The initial expectation of the robots was that they would not usually travel in straight lines along their intended trajectories and that some correction would be needed to be programmed into the strategy to ensure that deviations were corrected or compensated for. However there were runs where the robots travelled along the intended trajectories, or carried on in a straight trajectory after an initial slew.
An investigation as to why the failures were occurring was carried out. The robots were all reloaded with the control image and set up using a hyper terminal file. This was to prevent errors from being introduced. Each robot was given fully charged batteries and then moved under hyper terminal control to check that it was receiving signals via the bluetooth communications system. They were then put under RSE control and the tests were executed. However the problem still remained. Each robot was then driven singu- larly and moved as command. The only explanation was that there was a problem with bluetooth communicating with all the robots. However it was intermittent. When running the robots in the football configuration, bluetooth commands are sent continually to all the robots. So if a single command was missed, the effect would have been negligible. However in the experiment the start command is only sent once to each robot. If it was not sent then the robot would not move. To my knowledge there were never instances of a robot not obeying a received command, in all the time that I used them.
The tests carried out for the comparison of the three controllers, PID, type-1 and average dual surface type-2 fuzzy logic controllers are given in Table E.8. The results obtained for the comparison of the three controllers are given in Table E.9. The means and standard deviations for the three controllers are given in Table E.10 and for the speed
demands in Table E.11.
Within the results it is expected that for the same speed demand from each controller the actual speed obtained would be the same. The speeds achieved for the ramped option would be expected to be lower than that of the no ramp option, especially at the higher speed demand value. The results show that the PID controller delivers a higher actual speed for the same speed demand when compared against the two fuzzy logic controllers. This is not considered to be a problem since the fuzzy logic controllers were using the same internal scaling parameters that the PID controller was set up to use. In the three controller version of the micro robot used in these experiments, it was decided not to change the parameters from the PID settings. This was done so that the baseline results can be used across all the experiments if required. Obviously if the same actual speed was required from the fuzzy controllers as that delivered by the PID controller then a calibration exercise would be required. A t-test was carried out on the mean speeds of the controllers to test the null hypothesis that there was no difference between the means against the alternative hypothesis that there is a difference between them. This showed that there was no significant difference between the means of the fuzzy logic controllers but there was a significant difference between the PID controller and the two fuzzy logic controllers. This was partly expected due to the scaling issue previously discussed. The differences between the means of the two fuzzy logic controllers is very close. Again this is expected since the type-2 controller was generated from the type-1 controller by blurring the membership functions. The only anomaly is in tests 21 and 27 for the no ramp option of the type-2 controller. At speed demands of 80 and 120 there is virtually no difference between the mean values of the actual speed. However the standard deviations reported show a much larger spread of data at these values. At the start of the runs the controllers would be operating at the edges of the controller surface which was limited between -120 and 120 for both the error and change error input variables. An explanation of this anomaly is that the 120 speed demand has saturated the controller and so it delivers the best performance which is at the 80 speed demand. In the corresponding ramp tests 22 and 28, a small difference in the actual speeds is seen, where the change in speed demand is only small in the ramp when compared to the 120 speed demand step change. Having completed the three controller comparison experiment and established that there were no
7.6. Introduction to Dual Surface Type-2 Controller 173