CN108536879B - Multi-rotor unmanned aerial vehicle parameter identification method based on model reference self-adaption - Google Patents
Multi-rotor unmanned aerial vehicle parameter identification method based on model reference self-adaption Download PDFInfo
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Abstract
The invention relates to a multi-rotor unmanned aerial vehicle parameter identification method based on model reference self-adaptation. The method comprises the following steps: and establishing a corresponding relation of normalized PWM waves, rotating speed, force and moment in a curve fitting mode, and then obtaining a lift coefficient and a torque coefficient. Aiming at a nonlinear model of a multi-rotor unmanned aerial vehicle, a model reference self-adaptive parameter identification method is provided. Namely, by designing a slave system, the state is synchronized with the original nonlinear system, and meanwhile, the self-adaptive update rate is designed, so that the estimation of the parameters is converged to a true value. The invention can be applied to parameters existing in a nonlinear form, the asymptotic stability of which is demonstrated by the Lyapunov method and the principle of Lassel invariance. The simulation example can verify that the adaptive gain is reasonably selected, and even if the true value is mutated, the method can ensure that the estimated value is quickly converged to the latest true value.
Description
Technical Field
The invention belongs to the technical field of multi-rotor unmanned aerial vehicle model identification, and particularly relates to a multi-rotor unmanned aerial vehicle parameter identification method based on model reference self-adaptation.
Background
Because of having a series of advantages such as vertical take-off and landing, fixed point hover and super low-altitude flight, many rotor unmanned aerial vehicle is widely applied to military and civilian field, expands to civilian directions such as disaster monitoring, mapping, short distance delivery from military uses such as search and rescue, remote monitoring. In order to accomplish the above task, need carry out stable control to many rotor unmanned aerial vehicle. Undoubtedly, establishing a non-linear high fidelity kinetic model of a multi-rotor drone would greatly facilitate its precise control.
For the non-linear model of a multi-rotor drone, the parameters to be determined can be divided into the following two categories: (1) the aerodynamic coefficient of the propeller, namely the mapping relation from the rotating speed of the propeller to force/moment; (2) many rotor unmanned aerial vehicle body characteristics, including quality and inertia.
Since the rotational speed of the propeller is usually determined by the PWM wave input to the motor (control input), researchers often choose a curve fitting approach to establish the correspondence of the PWM wave to force and torque. However, different remote controllers often select different PWM intervals, and the value of the PWM wave is affected by voltage fluctuation, so that the corresponding relationship changes.
At present, a commonly used method for acquiring the rotational inertia is to perform three-line pendulum experiments or Solidworks software drawing estimation, and has the defects that the result is not accurate enough and can only be performed offline, and when the rotational inertia changes, identification needs to be performed again. The method of linearizing the kinetic equation near the equilibrium point to obtain an approximate model and then identifying by frequency sweep often requires a lot of experiments and it is difficult to obtain a model suitable for all-state flight. Parameter estimators based on Bayesian theory, such as Kalman filtering, extended Kalman filtering, colorless Kalman filtering, etc., often need to repeatedly adjust covariance matrix, and stability is difficult to guarantee.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a model reference self-adaptive multi-rotor unmanned aerial vehicle parameter identification method.
The technical scheme adopted by the invention is as follows: the multi-rotor unmanned aerial vehicle parameter identification method based on model reference self-adaptation comprises the following steps:
identifying lift coefficients and moment coefficients of the multi-rotor unmanned aerial vehicle;
the slave system of the multi-rotor unmanned aerial vehicle is constructed according to the original system of the multi-rotor unmanned aerial vehicle, and the identification of the rotary inertia is realized through the synchronization of the slave system and the original system.
Discern many rotor unmanned aerial vehicle lift coefficient and torque coefficient including following step:
1) the relationship of propeller speed to lift and torque is:
wherein i is the propeller number, T(i)And τ(i)Respectively single propeller with speed of rotation omegaiForces and moments generated;
2) and (3) carrying out normalization processing on the PWM wave, namely:
Pnrepresenting the value of the normalized PWM wave, PrRepresents the actual PWM value; pminAnd PmaxRespectively representing the minimum value and the maximum value of the actual PWM wave range;
3) obtaining P by curve fittingnTo a rotational speed omegaiThe corresponding relation of (1):
where k is the order of the fitted polynomial, akIs the coefficient of each order; n is the highest order of the fitted polynomial (P)n)kRepresents PnTo the k power of;
4) and (3) obtaining the corresponding relation between the PWM wave-rotating speed-force and moment according to the steps 1) -3), measuring the corresponding force and moment through a plurality of groups of given PWM wave values to obtain a plurality of groups of values of kappa and rho, and then averaging to obtain the lift coefficient kappa and the moment coefficient rho.
The identification of the moment of inertia through the synchronization of the slave system and the original system comprises the following steps:
2) G is prepared from1,g2,g3Andsubstituting the slave system of the multi-rotor unmanned aerial vehicle; and the stability theory of Lyapunov proves thatFinally, asymptotically converging to a, b and c, namely, obtaining a rotational inertia component Ix,Iy,IzThe value of (c).
The original system of the multi-rotor unmanned aerial vehicle is as follows:
(x1,x2,x3)T=(p,q,r)T,(a,b,c)T=(Ix,Iy,Iz)Ta, b and c are parameters to be identified, and a is more than 0, b is more than 0, and c is more than 0; (x)1,x2,x3) Representing system variables, τ1,τ2,τ3The moment input in the three directions of x, y and z is respectively; p, q, r are each rollerRoll, pitch, and yaw angular velocities; i isx,Iy,IzThe principal axis component of the moment of inertia.
The slave system of the multi-rotor unmanned aerial vehicle is as follows:
wherein the content of the first and second substances,andare respectively corresponding to the state quantities (x)1,x2,x3)TAnd parameter values (a, b, c)T(ii) estimate of (g)1,g2,g3)TIs a feedback function.
The invention provides a model reference self-adaptive multi-rotor unmanned aerial vehicle parameter identification method, which has the following main advantages:
(1) the method can directly and accurately identify the parameters in the nonlinear form;
(2) the algorithm has small calculated amount and can be used on line;
(3) the estimated parameters can quickly converge to the latest true value after the true value changes;
(4) the state quantity required by identification is easy to measure and obtain, and no additional mechanism design burden is required to be added.
Drawings
Figure 1 is a schematic diagram of a six-rotor drone architecture;
FIG. 2 is a diagram of the fitting effect of the relationship between the PWM wave and the propeller rotation speed;
FIG. 3 is a comparison graph of the parameter estimation effect of the method of the present invention and the UKF method.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention can be applied to parameters existing in a nonlinear form, the asymptotic stability of which is demonstrated by the Lyapunov method and the principle of Lassel invariance. The simulation example can verify that the adaptive gain is reasonably selected, and even if the true value is mutated, the method can ensure that the estimated value is quickly converged to the latest true value.
One, many rotor unmanned aerial vehicle system model
For parameter identification, a dynamic model of the system needs to be established. Taking a six-rotor unmanned aerial vehicle as an example, as shown in fig. 1, a dynamic model of the multi-rotor unmanned aerial vehicle is established by a newton-euler equation as follows:
wherein, the qualityMoment of inertia to be identifiedResultant external forceMoment of forceV=(u,v,w)TAnd ω ═ p, q, r)TRespectively linear and angular velocities in a body coordinate system,andlinear acceleration and angular acceleration, respectively.
From the propeller speed (ω)1,ω2,ω3,ω4,ω5,ω6) The mapping relation to the lifting force and the moment is as follows:
wherein, TmFor the total lift generated by the propeller, l is the distance from the center of the propeller to the center of gravity x in a body coordinate systembybAnd (3) plane projection, wherein kappa and rho are respectively a lift coefficient and a moment coefficient to be identified.
As can be seen from equations (1) and (2), to identify the moment of inertia, the lift coefficient κ and the moment coefficient ρ need to be obtained through experiments.
Identification of lift and moment coefficients
The relation of the rotating speed to the lifting force and the moment of a single propeller is as follows:
wherein i is the propeller number, T(i)And τ(i)Respectively the rotational speed of the paddle is omegaiThe forces and moments generated. Because the online measurement of the rotating speed of the propeller is difficult, and the rotating speed value is determined by the PWM wave input to the motor, the corresponding relation from PWM to the rotating speed can be established offline. Because different RC transmitters often correspond to different PWM ranges, the PWM can be normalized firstly, and then the corresponding relation is established. Namely:
wherein, PnRepresenting the value of the normalized PWM wave, PrRepresenting the actual PWM value. PminAnd PmaxRespectively representing the minimum and maximum values of the actual PWM wavelength range.
Then, a curve fitting method is used for obtaining PnTo a rotational speed omegaiThe corresponding relation of (1):
wherein k isOrder of the fitted polynomial, akFor each order coefficient, (P)n)kIs PnTo the k power of. And N is the highest order of the polynomial, and is usually 1-3, so that subsequent control quantity calculation is facilitated. The corresponding relation between PWM wave-rotating speed-force and moment can be established by the formulas (3) to (5), the corresponding force and moment data can be measured by giving multiple groups of PWM wave values, multiple groups of kappa and rho values can be obtained, and then the lift coefficient and the moment coefficient can be determined by averaging. As shown in fig. 2.
After the lift coefficient and the moment coefficient are determined, the moment of inertia can be identified by using the 2 nd equation of the equation (1), namely a rotational dynamics equation.
Adaptive identification of rotational inertia
1. Rotational dynamics equations and "Slave System" selection
The rotodynamic development format is as follows:
wherein p, q, r are roll, pitch and yaw angular velocities respectively,the derivatives of p, q, r with respect to time, respectively. Tau is1,τ2,τ3The moment input in the three directions of x, y and z, Ix,Iy,IzThe principal axis component of the moment of inertia. It is readily apparent that the moment of inertia parameter occurs in the form of a non-linear coupling.
Order (x)1,x2,x3)T=(p,q,r)TAnd (a, b, c)T=(Ix,Iy,Iz)TFormula (6) can be rewritten as:
wherein a, b and c are parameters to be identified, and satisfy the conditions of a > 0, b > 0 and c > 0 (physical characteristic determination).
The scheme of the invention firstly needs to construct the following slave system which is characterized in that the structure is similar to the original system:
wherein the content of the first and second substances,andare respectively corresponding to the state quantities (x)1,x2,x3)TAnd parameter values (a, b, c)TIs estimated by the estimation of (a) a,are respectively asDerivative with respect to time, (g)1,g2,g3)TIs the feedback function to be designed.
Next, the update rate of the feedback function and the parameter needs to be designed to achieve synchronization of the "slave system" state and the parameter with the original system, so as to achieve the goal of parameter identification.
2. Feedback function and parameter update rate design
wherein the content of the first and second substances,is composed ofUpdate rate of e1,e2,e3Error between estimated and true state values, gamma1,γ2,γ3And beta1,β2,β3Is a positive parameter that can be selected. By pairsBy integrating over time
Finally, it is necessary to prove that the designed scheme enables synchronization of states and identification of parameters.
3. Demonstration of stability
The stability of a nonlinear system is usually analyzed by the Lyapunov stability theory, whose idea is to prove its derivative with time by choosing a positive definite function V related to the error vectorNegative, the error may be shown to asymptotically stabilize to the origin. The specific steps are as follows:
the error is defined as follows:
e1,e2,e3andfor errors in state tracking and parameter estimation, respectively, the present goal is to design the feedback function (g)1,g2,g3)TAnd parameter estimationSuch that:
the Lyapunov function was chosen as follows:
wherein, γ1,γ2,γ3Is an optional positive parameter. The time derivative of equation (12) can be obtained:
wherein the content of the first and second substances,andthe derivatives of the state error and the parameter error, respectively, over time are defined as follows:
combining formulae (7) and (8) gives:
by bringing formula (15) into formula (13), it is possible to obtain:
substituting formula (9) into (a):
as known from the Lassel principle of invariance, the parameter estimation will converge asymptotically to a tight set when t → ∞In (1), e is equal to 0 andthe belt-in formulas (9) and (15) can give:
from equation (18) 1, one can obtain:
when signal [ x ]2x3(b-c)+τ1,-ax2x3]When the condition of continuous excitation is satisfied,namely haveSimilarly, the 2 nd expression of the expression (18) can be usedIn the simultaneous way, the user can know the content,namely, the parameter estimation error converges asymptotically to the zero point, and the completion is proved. Thus, the goal of parameter identification is achieved.
First, the experiment for identifying the lift and moment coefficient
A single propeller is used as a research object, a motor with the propeller is fixed on a horizontal base, and the lower end of a base is fixed with a six-dimensional force/torque sensor. When the propeller rotates, an upward lift force is generated, so that a difference value is generated between a numerical value obtained by measuring the six-dimensional force/moment and a static state, and the absolute values of the z-axis force and the moment difference value respectively correspond to the lift force and the torque generated by the propeller.
In the experiment, the electric speed regulator with the rotating speed closed-loop control is selected, in order to improve the safety, the propeller is firstly disassembled, and the rotating speed of the motor is measured through the digital tachometer so as to establish the corresponding relation between the value of the normalized PWM wave and the rotating speed. The range of PWM waves is 1075-2000 when the motor rotates, and a plurality of groups of PWM waves and rotating speed data are collected and are shown in a table 1:
TABLE 1 Propeller-free PWM-speed (RPM) measurement record
Calling a Matlab curve fitting function to obtain a function expression of fitting of 3 orders and 1 order as follows:
the effect of the curve fitting is shown in fig. 3. It can be seen that the electric tuning has excellent linearity, 1-order fitting can meet the requirement, and the calculation of the control quantity is convenient.
Next, collecting values of multiple sets of PWM waves and corresponding force and moment data, and calculating lift coefficient and moment coefficient from equations (3) and (20) as shown in table 2:
TABLE 2 Lift coefficient and Torque coefficient recordings
Number of times | 1 | 2 | 3 | 4 |
Coefficient of lift κ (10)-7) | 1.5677 | 1.5520 | 1.5956 | 1.5842 |
Moment coefficient rho (10)-9) | 2.8681 | 2.8932 | 2.8600 | 2.8384 |
The lift coefficient and the moment coefficient obtained by calculating the average value are respectively: k 1.5748e-7 and ρ 2.8649 e-9.
Second, self-adaptive identification simulation of rotational inertia
Because the corresponding relation of PWM-rotating speed-force and moment is established, the invention carries out simulation verification by knowing the moment information. The simulation runs in a Matlab environment under a windows 7 operating system, and the parameters of the to-be-identified rotational inertia are set as follows:
it can be seen that the simulation assumes that the parameter value has a sudden change at 20s to verify the adaptive performance of the proposed method. The simulation sampling time is 0.02s, and the initial estimation values of the state and the parameters are selected as follows:
to satisfy the continuous excitation condition, the control input selects sinusoids of different amplitudes and frequencies as follows:
τ1=0.5sin(0.5πt)
τ2=0.2cos(0.6πt) (23)
τ3=0.6sin(0.4πt)
the adaptive gain is set as follows:
meanwhile, the method is compared with a UKF parameter estimation method. The UKF method increases the state quantity as follows:
wherein epsilon1,ε2,ε3Is a gaussian noise component, i.e. the parameter is considered to be a signal driven by noise. Noise-driven matrix design as QT=3×10-12I3The comparison of the UKF parameter estimation and the proposed method effect is shown in FIG. 3.
As can be seen from FIG. 3, the UKF method and the method of the present invention can obtain accurate parameter estimation values in a short time. However, when the parameters change, the method provided by the invention can still quickly identify the latest true value, and the UKF method cannot perform accurate tracking.
Therefore, the superiority of the method provided by the invention is verified.
Claims (1)
1. The model reference self-adaptive-based multi-rotor unmanned aerial vehicle parameter identification method is characterized by comprising the following steps of:
identifying lift coefficients and moment coefficients of the multi-rotor unmanned aerial vehicle;
constructing a slave system of the multi-rotor unmanned aerial vehicle according to an original system of the multi-rotor unmanned aerial vehicle, and realizing the identification of the rotary inertia through the synchronization of the slave system and the original system;
discern many rotor unmanned aerial vehicle lift coefficient and torque coefficient including following step:
1) the relationship of propeller speed to lift and torque is:
wherein i is the propeller number, T(i)And τ(i)Respectively single propeller with speed of rotation omegaiForces and moments generated;
2) and (3) carrying out normalization processing on the PWM wave, namely:
Pnrepresenting the value of the normalized PWM wave, PrRepresents the actual PWM value; pminAnd PmaxRespectively representing the minimum value and the maximum value of the actual PWM wave range;
3) obtaining P by curve fittingnTo a rotational speed omegaiThe corresponding relation of (1):
where k is the order of the fitted polynomial, akIs the coefficient of each order; n is the highest order of the fitted polynomial (P)n)kRepresents PnTo the k power of;
4) obtaining a corresponding relation between PWM waves, rotating speed, force and moment according to the steps 1) to 3), measuring the corresponding force and moment through a plurality of groups of given PWM wave values to obtain a plurality of groups of values of lift coefficients and moment coefficients, and then averaging to obtain a lift coefficient kappa and a moment coefficient rho;
the identification of the moment of inertia through the synchronization of the slave system and the original system comprises the following steps:
(2) G is prepared from1,g2,g3Andsubstituting the slave system of the multi-rotor unmanned aerial vehicle; and the stability theory of Lyapunov proves thatAsymptotically converging to a, b, c, i.e. the rotational inertia component Ix,Iy,IzA value of (d);
the original system of the multi-rotor unmanned aerial vehicle is as follows:
(x1,x2,x3)T=(p,q,r)T,(a,b,c)T=(Ix,Iy,Iz)Tand a, b and c are to be identifiedIdentifying parameters, wherein a is more than 0, b is more than 0, and c is more than 0; (x)1,x2,x3) Representing system variables, τ1,τ2,τ3The moment input in the three directions of x, y and z is respectively; p, q, r are roll, pitch and yaw angular velocities, respectively; i isx,Iy,IzIs a rotational inertia component;
the slave system of the multi-rotor unmanned aerial vehicle is as follows:
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