a study of evolvable hardware adaptive oscillators for augmentation of flapping-wing micro air vehicle altitude control

A Study of Evolvable Hardware Adaptive Oscillators for Augmentation of Flapping-Wing Micro Air Vehicle Altitude Control A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Engineering By Bharath Venugopal Chengappa B E., Visvesvaraya Technological University, Belgaum, India, 2005 2010 Wright State University WRIGHT STATE UNIVERSITY SCHOOL OF GRADUATE STUDIES June 29, 2010 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Bharath Venugopal Chengappa ENTITLED A Study of Evolvable Hardware Adaptive Oscillators for Augmentation of Flapping-Wing Micro Air Vehicle Altitude Control BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Computer Engineering John C Gallagher, Ph.D Thesis Director Mateen M Rizki, Ph.D Department Chair Committee on Final Examination John C Gallagher, Ph.D Michael Raymer, Ph.D Mateen M Rizki, Ph.D John A Bantle, Ph.D Vice President for Research and Graduate Studies and Interim Dean of Graduate Studies Abstract Venugopal Chengappa, Bharath M.S.C.E, Department of Computer Science and Engineering, Wright State University, 2010 A Study of Evolvable Hardware Adaptive Oscillators for Augmentation of Flapping-Wing Micro Air Vehicle Altitude Control The control of insect-sized flapping-wing micro air vehicles is fraught with difficulties Even when adequate control laws are known, limits on computational precision and floating-point processing can render it difficult to field implementations that provide sufficiently accurate and precise vehicle body placement and pose Augmentation of an existing altitude controller with an Evolvable Adaptive Hardware (EAH) oscillator has been proposed as a means for an on-board altitude controller to correct control precision and accuracy difficulties during normal flight This thesis examines a range of setting of the internal learning algorithms for the EAH oscillator and provides empirical evidence about which setting are most optimal for the control of a flapping-wing micro air vehicle (FW-MAV) based on the Harvard MicroFly Implications for future multi-degree of freedom control are also considered iii Contents Introduction 1.1 Motivation and Introduction 1.2 Altitude Control: A detailed View 1.3 Flapping-Wing Micro Air Vehicle 1.4 Objectives and Organization of this Thesis Background and Literature Review 2.1 Evolutionary Computation 2.1.1 Genetic Algorithms 10 2.1.2 Terms Frequently Used 14 2.2 The Mini Population Algorithm 18 2.3 Evolvable Hardware 21 2.4 The Flapping-Wing Micro Air Vehicle (FW-MAV) 21 2.4.1 Altitude Control using the ACTC 23 2.4.2 Split-Cycle Control 25 Methodology and Model 29 3.1 Introduction 29 3.2 Model Overview 30 3.3 Non-EAH Based Controller Architecture 35 3.4 EAH Based Controller Architecture 40 3.5 Modified Minipopulationary Algorithm 43 Simulation Setup and Performance Analysis 47 4.1 Simulation Setup 47 4.2 Assessment Parameters for Altitude Tracking 51 4.3 Performance Assessment of the Modified Minipop Algorithm 52 iv 4.3.1 Analysis for the Mutation Rate Sweep 52 4.3.2 Analysis for the Population Size Sweep 56 4.3.3 Analysis for the Combined Sweep 60 Conclusions 70 5.1 Results and Summary 70 5.2 Future Work 72 Bibliography 74 v List of Figures The Degrees of Freedom in a 3-D Space First insect scale flying robot able to take off.[1] Hummingbird Hovering in mid air General Scheme for a GA as a flowchart 11 Pesudo-code for a GA 11 Selection and Recombination in a Genetic Algorithm.[2] 13 Pesudo-code for a Standard Minipop Algorithm.[3] 19 The FW-MAV Orthographic View[4] 22 The Block Diagram of the Altitude Command Tracking Controller[4] 24 10 Sample Generated outputs from EAH-Oscillator 28 11 The Basis Functions stored in the Wave Table ROM 29 12 General Assembly of the FW-MAV [5] 31 13 The Wing Design used for Force Calculations 32 14 Split-Cycle Cosine Module for the Non EAH Controller.[4] 36 15 Split-Cycle Cosine Module for the Micro-controller.[4] 40 16 Split-Cycle Cosine Module for the EAH Based Controller.[4] 41 17 A Better Look at the Shuffle LUT and Wave Table ROM 43 18 Pseudocode for the Modified Minipop Algorithm 44 19 Test Pattern Design 50 20 Data Analysis for Mutation Rate Sweep 55 21 Data Analysis for Population Size Sweep 58 22 T-Test Results for Population Size Sweep 59 23 Surface Plot for Combined Sweep of Population Size and Mutation Rate 60 24 Surface Plot of Standard Deviation for Combined Sweep of Population Size and Mutation Rate vi 61 25 Surface Plot of Fitness Value for Combined Sweep of Population Size and Mutation Rate 62 26 Surface Plot Standard Deviation for Fitness Value 63 27 Surface Plot for Flaps per Evaluation Parameter at 40 64 28 Surface Plot of Standard Deviation for Flaps per Evaluation Parameter at 40 64 29 Surface Plot of Fitness Value for Flaps per Evaluation Parameter at 40 65 30 Surface Plot Standard Deviation for Fitness Value Flaps per Evaluation Parameter at 40 65 31 Surface Plot for Flaps per Evaluation Parameter at 60 67 32 Surface Plot of Standard Deviation for Flaps per Evaluation Parameter at 60 67 33 Surface Plot of Fitness Value for Flaps per Evaluation Parameter at 60 69 34 Surface Plot Standard Deviation for Fitness Value Flaps per Evaluation Parameter at 60 35 69 Summary of the Learning Parameter Sweeps 71 vii List of Tables Minipop Parameters 20 FW-MAV Model Parameters 30 FW-MAV Model Constant parameters 31 Input parameters for the Non-EAH Oscillator module 36 Output parameters for the Non-EAH Oscillator module 37 Initial settings for Mutation Rate Sweep 48 Initial settings for Population Size Sweep 48 Initial settings for Population Size and Mutation Rate Sweep 49 Combination list for the Population Size and Mutation Rate Sweep 49 10 Parameter settings for Flaps per Evaluation Sweep 50 11 Learning Times for Varying Mutation Rate 53 12 Fitness Values for Varying Mutation Rate 53 13 T-Test Results for Varying Mutation Rate 54 14 Learning Times for Varying Population Size 56 15 Fitness Values for Varying Population Size 57 16 ANOVA Results Flaps per Evaluation - 50 63 17 ANOVA Results Flaps per Evaluation - 40 66 18 ANOVA Results Flaps per Evaluation - 60 69 viii ACKNOWLEDGMENTS I would like to acknowledge my gratitude to my advisor Dr John Gallagher, for the unconditional support, guidance, extended patience, and encouragement throughout my graduate career I would also like to thank Dr Mateen Rizki and Dr Michael Raymer for their patience, feedback and suggestions about my work I would like to thank all my friends for their support and friendship Lastly I would like to thank my father, mother and brother for helping me be strong throughout my studies Dedicated to Dr John Gallagher, papa and mummy 66 iii From the plot it can be observed that the rest of the cases have a similarity to the previous setting of 50 flaps per evaluation It has the same linear rise in learning times as the population size is increased and the effect of of mutation rate can be noticed only for 64 bits iv From the standard deviation plot we can conclude that the maximum deviation is seen at high mutation rates, which shows the presence of simulation runs that have not learned in 4000000 evaluations v In Figures 29 and 30 it is clearly visible that the fitness criterion was not met at high mutation rate of 64 bits The Anova test was conducted on the data collected for the above parameter settings The P-value for the Anova test was found to be zero, which rejects the null hypotheses that the means of all the groups are equal The F-value was found to be a high value which tells us that there exists a large difference between the groups under consideration The Anova test results are tabulated below, Table 17: ANOVA Results Flaps per Evaluation - 40 Source of Variation df F P-Value F crit Between Groups Within Groups Total 79 4338.746527 399920 399999 1.27533684 The effect of decreasing the number of flaps for each population member on the learning time of the algorithm was analyzed in the above section The effect of increasing the number of flaps per evaluation to 60 is analyzed below by plotting the analyzed data from the simulations run at these settings Figures 31,32,33 and 34 show the surface plots for the learning 67 time, standard deviation , fitness value and its standard deviation Figure 31: Surface Plot for Flaps per Evaluation Parameter at 60 Figure 32: Surface Plot of Standard Deviation for Flaps per Evaluation Parameter at 60 The effects of increasing the flaps per evaluation parameter observed from the above surface plots are explained in the following points i The learning times range between [500 - 8000] seconds, which when compared to the above to conditions is a significant change in the range ii From the surface plot it can be observed that the high learning times are caused in the low mutation rate settings and low population sizes 68 as this is the area where the learning times have shot up to 8000 seconds iii The surface plot for the standard deviation with in the groups supports the above observation that the increase in flaps per evaluation has a direct and significant effect on the learning of the algorithm in the low mutation rates This effect is more towards the low population sizes, in other words when the search space is limited the algorithm cannot learn to meet the required fitness value iv The raw data was analyzed to look for particular cases where the algorithm had timed out due to exceeding the maximum evaluations and most of the simulations that had timed out lie in the region as observed in the surface plot v The rest of the area in the plot has the same observations seen in the flaps set at 50 case, where the increase in population size has a small but linear increase in learning times, effect of mutation rate is also similar in the higher settings vi The fitness values plotted in Figure 33 and its standard deviations in the groups in Figure 34 confirm the observations made earlier and clearly show that in the low mutation rate and small population sizes the algorithm did not satisfy the required fitness value Figure 34 supports Figure 33 by showing large deviations in the groups in the same area The Anova test was conducted on the data obtained for flaps per evaluation set at 60 and are tabulated above The P-value returned by the 69 Figure 33: Surface Plot of Fitness Value for Flaps per Evaluation Parameter at 60 Figure 34: Surface Plot Standard Deviation for Fitness Value Flaps per Evaluation Parameter at 60 Table 18: ANOVA Results Flaps per Evaluation - 60 Source of Variation df F P-Value F crit Between Groups Within Groups Total 79 3828.363685 399920 399999 1.27533684 Anova test is zero which rejects the null hypotheses that the means of all the groups considered are equal 70 Conclusions A overview of the results observed and the conclusions drawn from these observations are discussed in this chapter 5.1 Results and Summary The results and analysis from the previous chapter help us to better understand the performance of the Modified Minipop algorithm designed specifically for this EAH-Oscillator in the controller for the FW-MAV The summary of the three main learning parameter sweeps can be seen in Figure 35 The observations from the results shown in the previous chapter can be summarized as follows, i Population Size, Mutation Rate and Flaps per Evaluation parameters have a significant effect on the learning time of the Modified Minipop Algorithm used here in the design of the EAH enabled controller for a Flapping-Wing Micro Air Vehicle ii Population Size has a direct effect on the learning time as more number of population members means more computation time required The balance of accuracy and time, population size has a significant effect, hence will remain a parameter to tune as progress is made in the controller design iii Mutation Rate is a parameter which directly affect the learning of the algorithm A very high mutation rate will open the search space for learning and hence the cosine generated by learning might end up producing more force than the required amount hence more time 71 Figure 35: Summary of the Learning Parameter Sweeps is needed to correct this error When low mutation rates are used the search space for the driving cosine is very limited and hence the time required for the controller to learn will increase From the above results it is observed that 75 percent is a good mutation rate to achieve a good learning time 72 iv Flaps per evaluation also have a very significant effect on the learning of the algorithm This is the only parameter that caused the algorithm to time out and not achieve the required fitness value from the above test results it can be observed that it is centered around 50 flaps, if decreased the algorithm times out at high mutation rates and high population sizes and if increased the algorithm times out at low population sizes and low mutation rates This reflects the relation that more flaps tested on few population members and the search space is limited to minimum keeps the algorithm from finding the right solution and when flaps are reduced from 50 it shows that the vehicle has insufficient flaps when tested with more number of population members and maximum search space The data obtained for all the above test cases are significant assuming the mathematical model, ideal natural conditions for a single degree of freedom FW-MAV and this particular version of the Modified Minipop Algorithm These concluded settings will not be significant in any way for the final EAH enabled controller, but the performance of the algorithm when subjected to variable learning parameters is significant 5.2 Future Work The work of this thesis has demonstrated that the FW-MAV MINIPOP algorithm can construct custom oscillators capable of correcting wing drag fault induced hover deficits The algorithm as presented seems somewhat tolerant to different settings of learning algorithm parameters Except for ”extreme settings”, the evolutionary search is well-behaved and produces workable solutions in minutes of flight time This is acceptable for the 73 application at hand However, it has become clear from ongoing work that has occurred in parallel to this thesis that learning oscillators for the control of multiple degrees of freedom is significantly more difficult and extends learning times onto the scale of hours of flight time This information, combined with the parameter sweep information given in this thesis, strongly suggests that we turn our attention to issues of representation and meaningful recombination as a means to make maximally effective use of the information drawn from each expensive candidate evaluation This thesis demonstrates that solutions are robustly obtainable What remains is to make FW-MAV MINIPOP modifications that obtain those solutions as quickly as possible 74 References [1] R.J Wood 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Evolvable Hardware Adaptive Oscillators for Augmentation of Flapping-Wing Micro Air Vehicle Altitude Control The control of insect-sized flapping-wing micro air vehicles is fraught... precise vehicle body placement and pose Augmentation of an existing altitude controller with an Evolvable Adaptive Hardware (EAH) oscillator has been proposed as a means for an on-board altitude controller... Evolvable Hardware Adaptive Oscillators for Augmentation of Flapping-Wing Micro Air Vehicle Altitude Control BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science