Thrust estimation by fuzzy modeling of coaxial propulsion unit for multirotor UAVs

Transcription

1 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2016) Kongresshaus Baden-Baden, Germany, Sep , 2016 Thrust estimation by fuzzy modeling of coaxial propulsion unit for multirotor UAVs Przemysław Ga sior, Adam Bondyra, Stanisław Gardecki, Wojciech Giernacki and Andrzej Kasiński Abstract In this paper, a simple and easily applicable model of the coaxial propulsion unit for multirotor UAVs is presented. Measurements performed on the experimental test bench provided information about the generated thrust in relation to PWM control signals and supply voltage. Modelling techniques based on Takagi-Sugeno fuzzy interface and surface fitting are proposed. Implementation of the first order inertial element with the varying time constant allows to consider the propulsion unit s dynamics. A fuzzy model was chosen for implementation taking into consideration a computational complexity benchmark. Fusion of four independent models provides information about a total thrust generated by the physical platform during real flight scenarios. Promising results of experimental studies open the way for possible applications of the presented method, such as expanding estimation algorithms of attitude and vertical velocity or improvement of the mathematical model. I. INTRODUCTION Propulsion units in micro multirotor aerial vehicles typically consists of the ESC (Electronic Speed Controller), BLDC (Brushless Direct Current) electric motor and propeller. Majority of such vehicles are equipped with a various number of independent propulsion units located at the end of each arm. Recently, a different hardware approach was adopted - two identical drives working in coaxial configuration, one atop the another, rotating in different directions [1], [2], [3], [4]. This approach allows to increase produced thrust while keeping similar external dimensions of the vehicle. However, in many cases, it is achieved at the expense of a flight time. Despite this disadvantage, this concept is better suited for some research purposes during indoor flights, where ability to lift additional equipment in a limited space is a crucial parameter. The same idea was introduced for helicopters, for which one of the most important features is balancing the torque effect for both rotating propellers [5], [6]. In contrast to the single propulsion unit, coaxials have much more complicated mathematical model. It is caused by additional aerodynamic effects to consider [7], [8], [9]. Information about the generated thrust can be used in various estimation algorithms to enhance their output, i.e. attitude, altitude or vertical velocity estimates [10], [11] and also to detect drive failures [12]. The use of appropriate models is significant from the perspective of UAV s control and reliability. Models need to be complex and accurate enough for used control technique Polish Aerial Robotics Team, Institute of Control and Information Engineering, Faculty of Electrical Engineering, Poznan University of Technology, Poland przemyslaw.gasior@cie.put.poznan.pl, {adam.bondyra, stanislaw.gardecki, wojciech. giernacki, andrzej.kasinski}@ put.poznan.pl as long as the implementation possibilities on the on-board processing unit exist [13]. However, it should be remembered that even in the simplest control strategies (i.e. still commonly used PID controller) inclusion of drag effects (such as blade flapping, induced drag, translational drag, profile drag) in the model allow to apply more robust UAV control. On the other hand, the high computational complexity prevents the system from being applied on real robot. Hence, authors propose the simplified method of thrust estimation based on experimental data from the test stand. The first idea is to combine the control signal vectors with measured thrust generated by the propulsion unit [14]. However, in this concept, the effect of supply voltage s influence on the output is omitted. During the operation on battery voltage drops along with battery s discharge level, which affects the performance of propulsion unit. We propose series of experiments which helped to create a proper model of propulsion unit. However, there are many different approaches, e.g. using rotational velocities of the rotors, which excludes the supply voltage and control signal from considerations. The paper is organized as follows - in Section II a description of the flying platform and the test stand that has been used for the data acquisition is provided. Conducted experiments are characterized in details in Section III, which presents the brief characteristic of associated works and encountered problems as well. Section IV contains a description of proposed estimation methods, along with formulation of the final concept. Section V is devoted to the experimental verification performed on the test stand and on the physical platform. Conclusions and plans of further research are described in the section VI. II. DATA ACQUISITION The features of the flying platform used in experiments, applied propulsion s configuration, system of symbols describing coaxial configuration and the test bench used for data acquisition are provided in the following subsections. A. The physical platform Falcon V5 platform was designed in Institute of Control and Information Engineering at Poznan University of Technology by PART* research group. The robot is built in X8 configuration. It consists of four coaxial propulsion drives presented in Fig. 1. Propulsion units can be divided into two types, i.e. CW-CCW and CCW-CW, with rotors rotating clockwise (CW) or counter-clockwise (CCW). 418

2 Fig. 1. The Falcon V5 platform CAD model with propulsion units configuration, CW-1,4,5,8 and CCW-2,3,6,7 generated thrust and power consumption (supply voltage and current) as a function of the PWM control signal parameters. III. EXPERIMENTS The choice of type and scale of performed tests was based on the previous results presented in [15]. The standardized rate of duty cycle for PWM signals driving ESCs was chosen as input for each motor. The process of experiment planning and gathered results are presented in following subsections. A. The planning of experiment The concept of control in coaxial propulsion is more complex than in the case of single motor unit. During the flight the stabilisation of attitude in yaw axis causes the difference in control signals between pairs in every coaxial unit. Therefore, in standard conditions these two values differ most of the time. This case is presented in Fig. 3, where the distribution of mutual control signal during the test flight is presented. B. The test bench In order to collect data for following analysis, experiments were performed on the test bench described in [15], with modified version of controller and software. Thanks to recent changes, the measurement circuit is more compact and reliable. All components of the mentioned device are showed in Fig. 2. Fig. 3. Mutual control signals distribution in coaxial propulsion unit during test flight (red) and thrust measurement points (blue) Fig. 2. The test stand with modified control module (propulsion unit consisting of MN3110 BLDC motors with 10 propellers) Every propulsion unit consists of two MN3110 BLDC motors produced by RC Tiger Motors with 10 carbon fiber propellers. The same components were used in Falcon V5 platform described in [1]. As can be seen, a steel arm does not correspond to the one used in real robot. This may cause a small discrepancies compared to the real vehicle and will be considered and analysed in ongoing research. This custom test bench allows to acquire measurements of Based on this example and other similar cases analyzed from flight data, authors determined that the maximum difference between these two signals is up to 20%. For example, if the upper motor (PWM1) has the control rate of 45%, then the second one can take values from 25% to 65%. These limits allowed to create the overall plan for the experiment. Measurement points, also presented in Fig. 3, were concentrated around the most common preset levels. This approach led to design more accurate approximation. Working points during the flight are changing depending on maneuvers, load and weather conditions, therefore values around diagonal from 0% to 100% were covered. One of the critical parameters for the propulsion unit s performance is supply voltage. On Falcon V5 platform, the 4-cell Lithium- Polymer battery was used. To cover as many flight scenarios as possible, every measurement point was considered with supply voltage ranging from the maximum battery charge (up to 16.8V), to the battery bottom voltage limit (almost 419

3 14 V ). This approach allowed us to create the dependence between the model s output thrust and supply voltage values. B. Performed tests Authors divided measurement points presented in previous subsection into nine different sequences. For every sequence one fully charged battery was used and the test was performed repeatedly until the lower voltage limit was reached. Surprisingly, tests showed that each configuration (CW-CCW and CCW-CW) had different performance, therefore separate experiments for both cases were performed. The total number of 256 test cycles were completed. Manual processing of this amount of data was almost impossible, therefore authors created an algorithm to gather all measurements in a single structure. During all of following analysis, the MATLAB R2014a software was used. Two of processed sequences are demonstrated in Fig. 4. This example represents the case when control signal for the first drive is maintained at the steady level and the second one has a variable preset signal. Results are represented as a thrust in function of supply voltage. The most important conclusion from this figure is that there is a difference if the pusher (lower) propeller or the tractor (upper) propeller is rotating with higher speed. If the pusher rotates faster than the tractor, the total thrust is lower than in the opposite case. Respectively, if the tractor is rotating faster than the pusher, the thrust is higher. This effect is caused by the work conditions of the pusher, which operates in the propwash of tractor. The conclusion is that presented data can be easily approximated by linear functions with good accuracy, which allowed to propose the simple model. C. Encountered problems Authors encountered two major problems during experiments. First one was the noise present in thrust data, in most cases caused by mechanical vibrations of the test stand. At the specific rotational speeds of propellers, the test bench entered into oscillations which increased the noise. Those effects were solved by averaging steady state thrust values, because oscillations occurred around a true value. Second issue was caused by lack of the rotational speed feedback. Test sequences consisted of few rising steps of the control signal followed by some downward steps. Therefore, controlling the propulsion unit only with PWM duty cycle resulted in difference in thrust at the same level of control signals. This effect, caused by control method in off-theshelf ESCs, results in the ambiguity of thrust characteristics. Examples of this effect are showed in Fig. 5. The linear Fig. 5. Example of ambiguity in performed measurements during sequences in CCW-CW configuration where PWM1 (tractor) and PWM2 (pusher) control signals are equal regression based on this data is placed between two visible trends which leads to errors in the final thrust estimate. IV. THRUST ESTIMATION Fig. 4. Data of two sequences in CCW-CW configuration where PWM1 is the tractor s control signal and PWM2 - pusher s Datasets described in previous section were used to design the model of a coaxial propulsion unit. After combining of all linear regressions, each measurement point had its own linear function describing thrust according to the supply voltage. Every linear regressions has two parameters a (linear scaling) and b (offset), which can be represented as two sets of 3D points in function of both control signals. Due to spacings between measurement points, they had to be interpolated to cover all values in range of (0 100%). For this task authors selected two methods: Open Curve Fitting Tool from MATLAB; Fuzzy modeling using Takagi-Sugeno interface. Both methods and motivation for choosing them are described in following sections. 420

4 A. Surface approximation One of the simplest ways to interpolate a 3D surface is to use the Curve Fitting Tool provided by MATLAB software. This tool allows to import data and select the specific fitting method. Based on the fitting accuracy and shape of the surface, authors selected two methods - Linear and Biharmonic (v4) interpolators. Other approaches, like polynomials, did not brought satisfactory results. Two different surfaces were generated for a and b parameters of linear functions, one is presented in Fig. 6. implemented as AND operator method. The weighted average was used in the defuzzification phase and in calculations of final output values. C. Final model Thrust estimation is the first step in modeling of propulsion unit. All of measurements were gathered from steady state levels, therefore there is a need to implement dynamics of such drive. Based on the graphical analysis of dynamical parts of characteristics, authors concluded that this behaviour can be approximated by the first order inertia element, similar to [14]. The determination of time constant gave different results for various PWM ranges. Therefore, authors proposed to estimate time constant in relation to PWM signal values, which can be approximated by the exponential function (with minimum time constant of 0.01s and maximum of 0.4s). The structure of the fuzzy thrust estimation algorithm with dynamic effects (taking into consideration all of the mentioned elements) is showed in Fig. 7. Implementation Fig. 6. Surface of a parameter interpolated with Biharmonic (v4) method Unfortunately, these approaches do not have explicit analytical representation, therefore their implementation would be very complicated. In addition, the computational complexity could overload the microcontroller in the UAV s control unit with too many operations. Therefore, the implementable approximation method of generated surfaces had to be found. B. Fuzzy model Second approach to estimate the generated thrust was to apply the fuzzy logic. For linear functions in the supply voltage domain (gathered from measurements), a Takagi- Sugeno fuzzy interface, which is widely used in modeling [16], fits perfectly. Firstly, the structure of the model had to be developed. Authors assumed that the fuzzy model will have three inputs and single output. Two of those inputs (PWM1 and PWM2 signals) will be used to generate rules based on membership functions, and the third one (supply voltage) serves only to calculate thrust based on the output functions. Both input membership functions were designed as evenly distributed triangles, every 5% of control signal with base width of 10%, ranging from 0% to 100%. This approach allows to reduce the number of activated rules and computational complexity. As can be noted, not all of the rules will be covered by measurement points, therefore missing values of a and b were gathered from interpolated surfaces described in previous subsection. In every cycle, there is a maximum of four activated rules (pairs of PWM signals), where the product is Fig. 7. Block diagram of fuzzy model for a single coaxial propulsion unit of such adaptable dynamical model required discretization of the first order inertial element and moving to the state space model. Assumed transfer function G(s) = 1 1+sT has been discretized by Tustin method and moved to the state space representation. This approach allows to create easily implementable routine calculating inertia on platform s main processing unit. D. Implementation The most important design requirement is that the proposed algorithm has to be implementable in the embedded control system on real platform. A computational unit used for test purposes is an ARM microcontroller with Cortex- M4F core, also used in the main avionic s processing unit. Because of many other executed flight tasks and limited memory, the implementation had to be very compact and with minimum number of operations. The not explicit representation of surface models forced authors to compare processing time instead of a number of operations. Test were performed on MATLAB software during the calculation of single experimental sequence with 4660 samples. The results of mentioned test were in favor of the fuzzy model, which achieved mean sequence execution time of 0.04s, compared to 3.8s and 14.0s for Linear and Biharmonic (v4) surface interpolators respectively. This implies that the fuzzy 421

5 model is simplest, most lightweight and better suited for implementation in the embedded system. V. EXPERIMENTAL VERIFICATION A. Verification on the test stand The next step was to verify the proposed model. For this task, control signals from the single flight were gathered for each propulsion unit and recreated on the test bench. The same sequences were started multiple times on the same battery to simulate voltage drop during the flight. Results showed, that the thrust estimated with presented model is close to measurements. One of the examples for second propulsion unit (motors 3 and 4) is showed in Fig. 9. Characteristics for both surface approaches and the fuzzy model are almost identical. Thrust from the test bench was filtered by Savitsky-Golay filter, used in [4], which allowed to maintain desired dynamics with rejection of the noise. Based on the filtered thrust, RMSE (Root Mean Square Error) was calculated for every estimation approach. The results are shown in Table 1. TABLE I ROOT MEAN SQUARE ERROR RESULTS FOR MODELING APPROACHES Surface - Bih Surface - Lin Fuzzy model RMSE [gf] Max error [gf] In every case, the estimated thrust is very similar. In overall, RMSE values did not exceeded 10 gf in all cases. B. Verification on the physical platform The second stage of verification was performed on the physical platform - Falcon V5. Authors had to determine the reference for estimated thrust. The structure presented Fig. 8. Block diagram of the verification algorithm in Fig. 8 was proposed. This approach converts gathered thrust into force and then into acceleration, based on precise measurements of the vehicle s mass. This acceleration can be compared with the accelerometer s output from AHRS (Attitude and Heading Reference System). Both the force and acceleration are transformed to the inertial reference frame thanks to the attitude information in form of quaternions. The final results are showed in Fig. 10, where the vertical acceleration from the on-board AHRS module with estimated acceleration from presented model are compared. The test flight was performed in Poznan University of Technology s sports hall and different types of movements were tested (ascending, descending, yaw rotating and flying on very low altitude). The platform started from the the ground and performed mentioned maneuvers. The presented algorithm worked with 20Hz frequency and was based on PWM control signals and voltage measurements only. One of the most noticeable things is a static error, which is present during the whole sequence. This is a result of the divergence between the estimated thrust and the real thrust. Source of this phenomenon comes probably from aerodynamic effects, which apparently are slightly different between the test stand and the real platform. At the beginning of the sequence, the estimated acceleration has a large negative value, which is caused by a small thrust generated by propulsion units at low PWMs values compared to the gravitational force. At the very end of the flight, the ground effect [2], [17] can be noticed, when the estimated acceleration decreased, but the platform s acceleration oscillated around 0 m s 2. Despite of mentioned effects, characteristics are very similar and the further research can be conducted to enhance estimated results. VI. CONCLUSIONS AND FURTHER RESEARCH In the presented paper, authors performed series of experiments on the test stand concerning coaxial propulsion units. Measurement points were assigned based on the analysis of real flight data and gathered values were used to develop the thrust estimation method. Three different approaches were proposed: two surfaces (Biharmonic (v4) and Linear) interpolated on measurement points and one based on Takagi-Sugeno fuzzy interface. The study on the propulsion unit s dynamics was also performed and first order inertial element with the varying time constant was proposed as an appropriate model. All of three methods were verified on the test bench during the recreated control signal sequence based on the real flight. Gathered results showed that estimated values of thrust were satisfactory and very similar for each approach. Unfortunately, errors caused by the ambiguity of thrust measurements during modeling caused errors in final results. Taking into consideration computational requirements, the fuzzy model was chosen as the best one for implementation in the platform s controller. Authors proposed the verification method for designed model of coaxial propulsion unit, based on the acceleration reference from the AHRS module. After the experiment, results showed, that presented model provide accurate estimates with the slight static error, which was caused by the difference of hardware design between the test bench and real platform. This effect can probably be eliminated by scaling thrust estimates during the flight. Further research will be performed to verify this assumption. 422

6 Fig. 9. Results of the verification of different models on test stand Fig. 10. Results of the fuzzy model verification during the test flight Information about thrust, force or vertical acceleration can be used in many other estimation algorithms executed during the flight, e.g. altitude and vertical velocity estimates [11]. In addition, the platform s mathematical model can be enhanced with new data. Authors plan to perform extended experiments, where more measurement points will be considered. Additionally, replacing PWM signal data with propeller s rotational speed will eliminate problems with the thrust ambiguity. Moreover, an aerodynamic drag should be considered in the acceleration estimation algorithm for further improvements. REFERENCES [1] A. Bondyra, S. Gardecki, P. Ga sior, A. Kasiński: Falcon: A compact multirotor flying platform with high load capability, Advances in Intelligent Systems and Computing, Vol. 351, 35-44, 2015 [2] I. Sharf et al.: Ground effect experiments and model validation with Draganflyer X8 rotorcraft, Unmanned Aircraft Systems (ICUAS), 2014 International Conference on, Orlando, FL, 2014 [3] G. B. Kim et al.: Design and Development of a Class of Rotorcraftbased UAV, International Journal of Advanced Robotic Systems, 10:131, 2013 [4] R. Czyba, G. Szafrański, M. Janik, K. Pampuch and M. Hecel: Development of Co-Axial Y6-Rotor UAV Design, Mathematical Modeling, Rapid Prototyping and Experimental Validation, Unmanned Aircraft Systems (ICUAS), 2015 International Conference on, Denver, CO, 2015 [5] J. Gordon Leishman: Principles of Helicopter Aerodynamics, Cambridge University Press, 2002 [6] J. Seddon, S. Newman: Basic Helicopter Aerodynamics, Second Edition, Blackwell Science, 2002 [7] C. P. Coleman: A Survey of Theoretical and Experimental Coaxial Rotor Aerodynamic Research, NASA Technical Paper No. 3675, 1997 [8] W. Giernacki, J. Gośliński: Coaxial quadrotor - from most important physical aspects to useful mathematical model for control purposes, International Journal of Applied Mathematics and Computer Science, (in review) [9] J. Gośliński, A. Kasiński, W. Giernacki, S. Gardecki, P. Owczarek: A Study on Coaxial Quadrotor model identification and parameters estimation: The Improved Square Root Unscented Kalman Filter, Robotics and Autonomous Systems, (in review) [10] P. Ga sior, S. Gardecki, J. Gośliński, W. Giernacki: Estimation of Altitude and Vertical Velocity for Multirotor Aerial Vehicle Using Kalman Filter, Advances in Intelligent Systems and Computing, Vol. 267, , 2014 [11] P. Ga sior, A. Bondyra, S. Gardecki, W. Giernacki: Robust estimation algorithm of altitude and vertical velocity for multirotor UAVs, In Methods and Models in Automation and Robotics (MMAR), 21st International Conference on, 2016 [12] M. Saied, H. Shraim, C. Francis, I. Fantoni, B. Lussier: Actuator fault diagnosis in an octorotor UAV using sliding modes technique: Theory and experimentation, Control Conference (ECC), 2015 European, , 2015 [13] A. Bondyra, S. Gardecki, P. Ga sior: Distributed control system for multirotor aerial platforms, Measurement Automation Monitoring, Vol. 61, , 2015 [14] W. Giernacki, D. Horla, T. Sadalla, J. P. Coelho: Robust CDM and Pole Placement PID Based Thrust Controllers for Multirotor Motor- Rotor Simplified Model, In 2016 International Siberian Conference on Control and Communications (SIBCON), 2016 [15] A. Bondyra, S. Gardecki, P. Ga sior, W. Giernacki: Performance of coaxial propulsion in design of multi-rotor UAVs, Advances in Intelligent Systems and Computing, Vol. 440, , 2016 [16] R. Babuška: Fuzzy Modeling for Control, Springer Science+Business Media, LLC, 1998 [17] H. Nakanishi, S. Kanata, T. Sawaragi: Measurement model of barometer in ground effect of unmanned helicopter and its application to estimate terrain clearance, Safety, Security, and Rescue Robotics (SSRR), 2011 IEEE International Symposium on, ,