CN111240212A - Tilt rotor unmanned aerial vehicle control distribution method based on optimization prediction - Google Patents
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Abstract
The invention belongs to the field of unmanned aerial vehicle control distribution, and relates to a tilt rotor unmanned aerial vehicle control distribution method based on optimization prediction. The optimal predictive control allocation method introduces a null space concept on the basis of the traditional pseudo-inverse method, and expands the reachable control set of the pseudo-inverse solution through the compensation term of the null space vector, so that the reachable set of the torque of the traditional pseudo-inverse method is expanded, and the control allocation efficiency is improved. Aiming at the phenomena of control redundancy and complex disturbance existing in the transitional mode of the tilt rotor unmanned aerial vehicle, the optimal predictive control distribution method can realize complete distribution of torque in a reachable set, realize control decoupling, ensure stable attitude in the transitional process and improve the control effect.
Description
Technical Field
The invention belongs to the field of unmanned aerial vehicle control distribution, and relates to a tilt rotor unmanned aerial vehicle control distribution method based on optimization prediction.
Background
Rotor unmanned aerial vehicle verts combines the advantage of traditional helicopter and fixed wing aircraft, can realize VTOL, and high-speed cruise is applicable to different actual scenes, satisfies different task demands. But the tiltrotor design places even greater demands on control distribution. Taking the transition stage as an example, regarding the attitude control of the tilt rotor unmanned aerial vehicle, the rotor and the control surface can both play a control role, and the phenomenon of control redundancy exists, and the forward-leaning rotor has component force in the forward direction and the vertical direction, so that the control coupling phenomenon exists in the roll control and the yaw control of the rotor. In addition, due to the fact that a complex internal and external disturbance phenomenon exists in the transition stage, the posture fluctuation is large in the transition process, the safety of the unmanned aerial vehicle is threatened, the control redundancy and control coupling problems need to be solved by applying a control distribution technology, meanwhile, the maneuvering capacity of the tilt rotor unmanned aerial vehicle can be improved by completely distributing the expected torque, and the stability and the safety in the transition process are guaranteed.
Control allocation techniques are divided into two categories in principle: linear allocation algorithms and non-linear allocation algorithms. The nonlinear algorithm is more suitable for the problems of high dimensionality and strong nonlinearity, but is difficult to be practically applied due to the limitation of airborne capacity. The linear distribution algorithm is simple to implement and is widely applied in engineering practice, but the method cannot realize complete distribution in a reachable set of torque.
Disclosure of Invention
Aiming at the problem that the linear distribution algorithm cannot realize complete distribution in the reachable set of the torque, the invention provides the tilt rotor unmanned aerial vehicle control distribution method based on the optimization prediction.
The invention provides a tilt rotor unmanned aerial vehicle control distribution method based on optimization prediction, which comprises the following steps:
s1: calculating a control efficiency matrix B of the tilt rotor unmanned aerial vehicle in the current mode;
s2: inputting unitized vector of expected triaxial momentIs the desired triaxial moment vector, where L, M, N represents roll, pitch and yaw moments, respectively;
s3: computing pseudo-inverse solutionsAnd solving the pseudo-inverse vectorThe unit pseudo inverse solution is obtained by the unit processing
S4: based on the unit pseudo-inverse solution calculated in step S3Judging a first saturated actuator;
s5, calculating a pseudo-inverse solution coefficient and a zero space coefficient;
s6: determining a next saturated actuator and updating the optimized prediction solution coefficient;
s7: judging whether all the actuators are traversed, if the optimal prediction solution coefficients of all the actuators in the saturation process are determined, performing the step S8, otherwise, continuously executing the step S6 until all the actuators are saturated;
s8: the look-up table determines an optimal predicted solution at any desired torque.
Further, the step S1 specifically includes the following steps:
and calculating a control efficiency matrix in the transition process of the tilt rotor unmanned aerial vehicle. Confirm a certain state point in the rotor unmanned aerial vehicle that verts transition corridor, obtain safe and reliable's airspeed V and nacelle angle of verting delta, carry out balancing and linearization to rotor unmanned aerial vehicle that verts six degrees of freedom nonlinear dynamical models under current state, obtain the perturbation equation of state:
wherein x is a system state variable; y is the system output; u is the system control input; superscript · denotes first derivative; A. b isuAnd C both represent constant matrices;
extracting coefficient matrix BuThe moment coefficient in obtains control efficiency matrix B under the current mode of the tilt rotor unmanned aerial vehicle:
wherein, CL,CM,CNRespectively representing a rolling moment coefficient, a pitching moment coefficient and a yawing moment coefficient; { Delta ]gAnd | g |, 1,2, … m } represents the actuators, and m is the number of actuators.
Further, the step S3 specifically includes the following steps:
solving a control distribution problemBy solving the inverse B of the control efficiency matrix B-1To obtain a pseudo-inverse solutionTo pseudo inverse solutionPerforming unitization to obtain unit pseudo inverse solution
Further, the step S4 specifically includes the following steps:
unit pseudo-inverse solution calculated based on step S4Finding a pseudo-inverse solution system that saturates only one actuatorNumber a0So thatSatisfies formula (2):
in the formula,representing the maximum moment along the desired moment direction that the pseudo-inverse can output within the achievable control set Ω;representing a pseudo-inverse solution portion of the optimized predictive solution;representing a null-space solution portion of the optimized prediction solution; omega is the set of reachable controls,wherein,representing actuator position vector, uiIndicating the position of the actuator i, m is the number of actuators,representing an m-dimensional vector space, ulwriRepresents the lower limit, u, of the position of the actuator iupriRepresents the upper limit of the position of the actuator i; δ (Ω) represents the boundary of the reachable control set; pSminA set of pseudo-inverse solutions is represented,phi is the achievable set of torques, representing an n-dimensional vector space of the image,representing a torque vector within the achievable set phi of torques; calculating pseudo-inverse solution coefficients a that saturate only one actuator0And obtaining a first saturated actuator.
Further, the step S5 specifically includes the following steps:
the pseudo-inverse solution coefficient a obtained in step S4 when only one actuator is saturated0Corresponding zero space coefficientLet the pseudo-inverse solution coefficient at the next actuator saturation be a1Solving the corresponding zero space coefficient
wherein, superscript T represents a transpose matrix;representing a lagrange operator;an orthonormal basis representing a null space;representing the pseudo-inverse solution coefficient as a0Pseudo-inverse solution of time correspondence Representing the pseudo-inverse solution coefficient as a1Pseudo-inverse solution of time correspondenceThe subscript sat represents the element in the vector corresponding to the saturation actuator;
further, the step S6 specifically includes the following steps:
assuming that the actuator gradually reaches full saturation from the unsaturated state as the expected torque amplitude gradually increases, the saturation order and the pseudo-inverse solution coefficient corresponding to the saturation set need to be determined for this purpose, and the pseudo-inverse solution coefficient a of the next actuator at saturation in step S5 is solved1;
Defining:
wherein,indicating an input desired torque ofPseudo-inverse solution of time;indicating an input desired torque ofPseudo-inverse solution of time; Δ a represents the pseudo-inverse coefficient increment;
solving the pseudo-inverse solution of equation (4)Respectively corresponding null-space solutionsThe optimal control quantity is obtained as follows:
Wherein,to representThe value corresponding to the medium unsaturated actuator i;to representThe value corresponding to the medium unsaturated actuator i; s1Representing a set of unsaturated actuators;
wherein sgn represents a sign function;
obtaining an actuator saturation evaluation parameter delta a from equations (6) and (7)0(i):
Evaluating the parameter deltaa for minimal actuator saturation0(imin) Corresponding index iminAdding a set S of currently saturated actuators2Calculating the pseudo-inverse solution coefficient a when the next actuator is saturated1:
a1=a0+Δa+δa0(imin) (9)
Calculating a pseudo inverse solution coefficient a by the formula (4)1Corresponding zero space coefficientObtaining the current saturation set S2Optimized predictive solution of
Further, the step S8 specifically includes the following steps:
is provided withRepresents the optimized prediction solution coefficient when the iteration number is s, s is 0,1, and k is 1, and the two-norm of the corresponding vector isWill be provided withThe set is written in matrix form:
wherein k represents the iteration number when the actuators are all saturated;
for an arbitrary moment vectorAnd isObtaining an optimized predictive solution by equations (11) and (12)The following three cases are specifically discussed:
1) the situation is as follows: at this time, the pseudo-inverse method is used to satisfy the position clipping requirement, so that:
2) the situation is as follows: because the desired torque exceeds the torque reachable set Φ, the optimal prediction solution is located at the boundary δ (Ω) of the reachable control set, i.e., the optimal prediction solution coefficientsThus:
3) the situation is as follows: firstly, determining s by means of piecewise linearization:
setting the equation:
where G is the optimal prediction solution coefficient determined by the indices i and i +1, and C is written as:
wherein the up and down vectors of C are the regression intercept and the slope gain vector, respectively, thereforeComprises the following steps:
the invention has the beneficial effects that:
the invention can realize the optimization of the boundary of the reachable set of the torque, thereby improving the distribution efficiency of the traditional pseudo-inverse method, compared with the mode of optimizing in the whole reachable set of the control by setting a target optimization function in the common optimization method, the invention improves the calculation speed by optimizing along the direction of the expected torque vector, lightens the calculation burden and has the capability of on-line optimization.
Drawings
Fig. 1 is a flowchart of an optimal prediction based tilt rotor unmanned aerial vehicle control distribution method of the present invention;
FIG. 2 is a schematic diagram of an optimization prediction algorithm;
FIG. 3 is a schematic view of the actuator according to an embodiment of the present invention showing a saturation tendency;
FIG. 4 is a comparison graph of the output torque of the optimized prediction algorithm of the present invention and the conventional pseudo-inverse method.
Detailed Description
The invention is further described below with reference to the accompanying drawings and examples, it being understood that the examples described below are intended to facilitate the understanding of the invention, and are not intended to limit it in any way.
As shown in fig. 1, the tilt rotor unmanned aerial vehicle control distribution method based on optimization prediction of the invention comprises the following steps:
s1: calculating a control efficiency matrix B under a transition mode of the tilt rotor unmanned aerial vehicle;
selecting a nacelle angle delta of 60 degrees and a speed V of 16m/s under the transition mode of the tilt rotor unmanned aerial vehicle, balancing and linearizing a six-degree-of-freedom nonlinear dynamics model of the tilt rotor unmanned aerial vehicle under the current state, and obtaining a coefficient matrix B by a small disturbance equationuThe extraction control performance matrix B is:
the actuator position amplitude limit is:
umax=[2.5 2.5 10 10 15 15 25 25 15 15]T
umin=[-2.5 -2.5 -10 -10 -15 -15 -25 -25 -15 -15]T
wherein u ismaxIs at the position of an actuatorLimit uminIs the lower limit of the actuator position.
Normalizing the position amplitude limit of the actuator:w represents a coefficient matrix to obtainAnd
wherein,representing a normalized control effectiveness matrix;representing a normalized upper actuator position limit;representing a normalized actuator position lower limit;
S3: computing pseudo-inverse solutionsAnd solve the pseudo-inverseThe unit pseudo inverse solution is obtained by the unit processing
S4: actuator for judging first saturation
Setting:
wherein u islimAn upper or lower actuator position limit (by)Symbol judgment of) 0.1080 is the largest element in r, and the corresponding actuator 1 is the actuator most easily saturated in position, that is, as the amplitude of the input expected torque vector increases, the actuator 1 reaches saturation first;
s5: calculating the pseudo-inverse solution coefficient aiAnd zero space coefficient bi
As shown in fig. 3, the optimal prediction solution calculated by the optimal prediction method includes two parts: the method comprises a pseudo-inverse solution and a null-space solution, wherein the pseudo-inverse solution realizes the expected torque output, and the null-space solution limits the part of the pseudo-inverse solution exceeding the reachable control set without changing the torque output, so that the reachable torque set is expanded.
The actuator j that first reaches saturation is obtained in step S4 { j ∈ 1: m | r (j) | | r | | |∞} (j is the index corresponding to the actuator, m is the number of the actuators, | r | | calculation∞The largest value of r), the pseudo-inverse solution coefficient at which the pseudo-inverse solution reaches the boundary is calculatedCoefficient of null space
S6: determining a next saturated actuator and optimizing the updating of the prediction solution coefficient;
calculating the corresponding pseudo-inverse solution coefficient a when the next actuator is saturated1;
Defining:
wherein,indicating an input desired torque ofThe pseudo-inverse solution of the time is,indicating an input desired torque ofPseudo-inverse solution of time. Is provided withThe corresponding is obtained from formula (4)The optimal control quantity is as follows:
definition of units per a0The rate of the optimal control solution under change is changed to:
wherein,to representThe value corresponding to the medium unsaturated actuator i;to representThe value corresponding to the medium unsaturated actuator i; s1Representing a set of unsaturated actuators;
the trend of the variation of the respective unsaturated actuator (towards a maximum or minimum value) as the gain varies is described:
wherein sgn represents a sign function;represents the upper limit of the position of the actuator i;represents the lower limit of the position of the actuator i;
obtaining delta a from the two formulas (6) and (7)0i:
Will be the smallest delta a0(i) Corresponding index imin(imin2) adding a saturated actuator set S2Calculating the corresponding pseudo-inverse solution coefficient a1:
a1=a0+Δa+δa0(i)=1.5782
The zero space coefficient is obtained by the calculation of the formula (4)Obtaining the current saturation set S2Optimized predictive solution of
S7: judging whether to traverse all the actuators
Judging whether all the actuators are traversed or not, if the optimal prediction solution coefficients of all the actuators in the saturation process are determined, performing the step S8, otherwise, continuously executing the step S6 until all the actuators are saturated, and obtaining the saturation sequence of the actuators as shown in FIG. 3;
s8: lookup table method for determining control gain under any expected torque
Is provided withRepresents the optimized prediction solution coefficient when the iteration number is s, and the two norms of the corresponding vector areWill be provided withThe set is written in matrix form:
wherein k represents the iteration number when the actuators are all saturated;
for an arbitrary moment vectorAnd isObtaining an optimized predictive solution by equations (11) and (12)The following three cases are specifically discussed:
1) the situation is as follows: at this time, the pseudo-inverse method can meet the position amplitude limiting requirement, so that:
2) the situation is as follows: since the desired torque exceeds the torque reachable set Φ, the optimal prediction method solution lies at the boundary δ (Ω) of the reachable control set, i.e. the optimal prediction solution coefficientsThus:
3) the situation is as follows: firstly, determining s by means of piecewise linearization:
setting the equation:
where G is the optimal prediction solution coefficient determined by the indices i and i +1, and C is written as:
wherein, the upper and lower line vectors of C are regression intercept and slope gain vector respectively,comprises the following steps:
the incoming data yields:
torque achievable output torque pair ratio in the set is shown in fig. 4;
output torque of an optimized prediction algorithm:
output torque by pseudo-inverse method:
it will be apparent to those skilled in the art that various modifications and improvements can be made to the embodiments of the present invention without departing from the inventive concept thereof, and these modifications and improvements are intended to be within the scope of the invention.
Claims (7)
1. A tilt rotor unmanned aerial vehicle control distribution method based on optimization prediction is characterized by comprising the following steps:
s1: calculating a control efficiency matrix B of the tilt rotor unmanned aerial vehicle in the current mode;
s2: inputting unitized vector of expected triaxial moment Is the desired triaxial moment vector, where L, M, N represents roll, pitch and yaw moments, respectively;
s3: computing pseudo-inverse solutionsAnd solving the pseudo-inverse vectorThe unit pseudo inverse solution is obtained by the unit processing
S4: based on the unit pseudo-inverse solution calculated in step S3Judging a first saturated actuator;
s5, calculating a pseudo-inverse solution coefficient and a zero space coefficient;
s6: determining a next saturated actuator and updating the optimized prediction solution coefficient;
s7: judging whether all the actuators are traversed, if the optimal prediction solution coefficients of all the actuators in the saturation process are determined, performing the step S8, otherwise, continuously executing the step S6 until all the actuators are saturated;
s8: the look-up table determines an optimal predicted solution at any desired torque.
2. The method according to claim 1, wherein step S1 is implemented as follows:
calculate the control efficiency matrix in the rotor unmanned aerial vehicle that verts transition process, confirm a certain state point in the rotor unmanned aerial vehicle that verts transition corridor, obtain safe and reliable's flying speed V and nacelle angle of verting delta, carry out balancing and linearization to the rotor unmanned aerial vehicle that verts six degrees of freedom nonlinear dynamical model under current state, obtain the perturbation equation of state:
wherein x is a system state variable; y is the system output; u is the system control input; superscript · denotes first derivative; A. b isuAnd C both represent constant matrices;
extracting coefficient matrix BuThe moment coefficient in obtains control efficiency matrix B under the current mode of the tilt rotor unmanned aerial vehicle:
wherein, CL,CM,CNRespectively representing a rolling moment coefficient, a pitching moment coefficient and a yawing moment coefficient; { Delta ]gAnd | g |, 1,2, … m } represents the actuators, and m is the number of actuators.
3. The method according to claim 1, wherein step S3 is implemented as follows:
4. The method according to claim 1, wherein step S4 is implemented as follows:
unit pseudo-inverse solution calculated based on step S4Finding the pseudo-inverse solution coefficient a that saturates only one actuator0So thatSatisfies formula (2):
in the formula,representing the maximum moment along the desired moment direction that the pseudo-inverse can output within the achievable control set Ω;representing a pseudo-inverse solution portion of the optimized predictive solution;representing a null-space solution portion of the optimized prediction solution; omega is the set of reachable controls,wherein,representing actuator position vector, uiIndicating the position of the actuator i, m is the number of actuators,representing an m-dimensional vector space, ulwriRepresents the lower limit, u, of the position of the actuator iupriRepresents the upper limit of the position of the actuator i; δ (Ω) represents the boundary of the reachable control set; pSminA set of pseudo-inverse solutions is represented,phi is the achievable set of torques, representing an n-dimensional vector space of the image,representing a torque vector within the achievable set phi of torques; calculating pseudo-inverse solution coefficients a that saturate only one actuator0And obtaining a first saturated actuator.
5. The method according to claim 1, wherein step S5 is implemented as follows:
the pseudo-inverse solution coefficient a obtained in step S4 when only one actuator is saturated0Corresponding zero space coefficientLet the pseudo-inverse solution coefficient at the next actuator saturation be a1Solving the corresponding zero space coefficient
wherein, superscript T represents a transpose matrix;representing a lagrange operator;an orthonormal basis representing a null space;representing the pseudo-inverse solution coefficient as a0Pseudo-inverse solution of time correspondence Representing the pseudo-inverse solution coefficient as a1Pseudo-inverse solution of time correspondenceThe subscript sat represents the element in the vector corresponding to the saturation actuator;
6. the method according to claim 5, wherein step S6 is implemented as follows:
assuming that the actuator gradually reaches full saturation from the unsaturated state as the expected torque amplitude gradually increases, the saturation order and the pseudo-inverse solution coefficient corresponding to the saturation set need to be determined for this purpose, and the pseudo-inverse solution coefficient a of the next actuator at saturation in step S5 is solved1;
Defining:
wherein,indicating an input desired torque ofPseudo-inverse solution of time;indicating an input desired torque ofPseudo-inverse solution of time; Δ a represents the pseudo-inverse coefficient increment;
solving the pseudo-inverse solution of equation (4)Respectively corresponding null-space solutionsThe optimal control quantity is obtained as follows:
Wherein,to representThe value corresponding to the medium unsaturated actuator i;to representThe value corresponding to the medium unsaturated actuator i; s1Representing a set of unsaturated actuators;
trend of variation of each unsaturated actuator with variation of gainComprises the following steps:
wherein sgn represents a sign function;
obtaining an actuator saturation evaluation parameter delta a from equations (6) and (7)0(i):
Evaluating the parameter deltaa for minimal actuator saturation0(imin) Corresponding index iminAdding a set S of currently saturated actuators2Calculating the pseudo-inverse solution coefficient a when the next actuator is saturated1:
a1=a0+Δa+δa0(imin) (9)
Calculating a pseudo inverse solution coefficient a by the formula (4)1Corresponding zero space coefficientObtaining the current saturation set S2Optimized predictive solution of
7. The method according to claim 1, wherein step S8 is implemented as follows:
is provided withRepresents the optimized prediction solution coefficient when the iteration number is s, s is 0,1, and k is 1, and the two-norm of the corresponding vector isWill be provided withThe set is written in matrix form:
wherein k represents the iteration number when the actuators are all saturated;
for an arbitrary moment vectorAnd isObtaining an optimized predictive solution by equations (11) and (12)The following three cases are specifically discussed:
1) the situation is as follows: at this time, the pseudo-inverse method is used to satisfy the position clipping requirement, so that:
2) the situation is as follows: because the desired torque exceeds the torque reachable set Φ, the optimal prediction solution is located at the boundary δ (Ω) of the reachable control set, i.e., the optimal prediction solution coefficientsThus:
3) the situation is as follows: firstly, determining s by means of piecewise linearization:
setting the equation:
where G is the optimal prediction solution coefficient determined by the indices i and i +1, and C is written as:
wherein the up and down vectors of C are the regression intercept and the slope gain vector, respectively, thereforeComprises the following steps:
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CN112068582A (en) * | 2020-09-24 | 2020-12-11 | 北京航空航天大学 | Method for identifying transition mode model of tilt rotor unmanned aerial vehicle |
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