CN114879739A - Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space - Google Patents

Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space Download PDF

Info

Publication number
CN114879739A
CN114879739A CN202210605426.4A CN202210605426A CN114879739A CN 114879739 A CN114879739 A CN 114879739A CN 202210605426 A CN202210605426 A CN 202210605426A CN 114879739 A CN114879739 A CN 114879739A
Authority
CN
China
Prior art keywords
rotor
alpha
unmanned aerial
representing
aerial vehicle
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202210605426.4A
Other languages
Chinese (zh)
Inventor
管若乔
郝宁
贺风华
邢锐
田春耕
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology
Original Assignee
Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN202210605426.4A priority Critical patent/CN114879739A/en
Publication of CN114879739A publication Critical patent/CN114879739A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

A control distribution method and a control distribution system for a tiltable quad-rotor unmanned aerial vehicle based on a null space belong to the technical field of unmanned aerial vehicle control and are used for solving the problem that an accurate actuator control instruction cannot be obtained in the prior art. The method comprises the steps of carrying out model transformation on a kinetic model of the tiltable quad-rotor unmanned aerial vehicle to obtain a control efficiency matrix containing time-varying parameters, and transferring the time-varying parameters in the control efficiency matrix to a virtual thrust vector by using variable transformation; obtaining an explicit expression of the virtual thrust vector by using the properties of the matrix pseudo-inverse and the null space; when the number of the expected overlimit instructions in the virtual thrust vector is not more than 2, obtaining an accurate solution of the control instruction of the actuator by adopting a nonlinear redistribution method; and when the number of the expected instructions exceeding the limit is more than 2, carrying out quadratic programming based on the precise solution of the control instruction at the previous moment so as to obtain the instruction variation and the optimal solution of the instruction at the current moment. The method is suitable for control distribution calculation in the whole flight period of the tiltable four-rotor unmanned aerial vehicle.

Description

Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space
Technical Field
The invention relates to the technical field of unmanned aerial vehicle control, in particular to a control distribution method and system for a tiltable quad-rotor unmanned aerial vehicle based on a null space.
Background
The inability of standard quadrotors to achieve decoupled control of position and attitude limits their performance in challenging tasks, such as flying at a particular attitude, changing attitude at hover, and other interactive tasks. To overcome this drawback, in recent years, an overdriven quad-rotor drone with tiltable rotors has received extensive attention from researchers. The redundant actuator of the unmanned aerial vehicle can provide omnidirectional thrust, so that the maneuverability and the fault tolerance of the system are improved. However, redundant configurations also result in numerous solutions to the control allocation of the system. Control distribution can reasonably distribute forces and torques on the actuators according to the desired pose commands. Therefore, it is a challenging problem to determine an optimal solution to the control distribution problem to fully utilize the maneuverability of an aircraft.
In recent years, there have been some research efforts in the control distribution strategy of the overdrive system. The main methods are divided into two categories, namely direct allocation methods and numerical optimization methods. The direct distribution method utilizes the pseudo-inverse of the control efficiency matrix to determine the unique mapping of the virtual control quantity, and then utilizes a variable substitution method to realize the linearization of the nonlinear mapping. The advantage of this method is that the calculation is fast and an accurate solution of the actual control quantity is usually available. However, when the aircraft tracks a high maneuver trajectory, the solution to the direct assignment method may exceed the velocity and position limits of the actuators, thereby causing the actuators to prematurely enter a saturation state. Furthermore, when the actuators change near the singularity, the jump may cause the attitude of the aircraft to be unstable, although the extreme constraints may be satisfied. At this time, a numerical optimization method is required to process a plurality of different types of constraint conditions, however, errors are introduced in the approximation process of the objective function in the conventional optimization method, so that the calculation result inevitably deviates from an accurate solution.
Disclosure of Invention
In view of the above problems, the invention provides a null space-based control distribution method and a null space-based control distribution system for a tiltable quad-rotor unmanned aerial vehicle, which are used for solving the problem that the existing control distribution method for the tiltable quad-rotor unmanned aerial vehicle cannot obtain an accurate actuator control instruction.
According to an aspect of the invention, there is provided a null-space based control distribution method for a tiltable quad-rotor unmanned aerial vehicle, the method comprising the steps of:
step one, establishing a dynamic model of the tiltable quad-rotor unmanned aerial vehicle according to a Newton-Euler equation; the kinetic model is represented as:
Figure BDA0003671112720000011
wherein m represents the mass of the unmanned aerial vehicle; j represents the inertia matrix of the unmanned aerial vehicle;
Figure BDA0003671112720000021
representing the mass center linear acceleration of the unmanned aerial vehicle under a body coordinate system;
Figure BDA0003671112720000022
representing the angular acceleration of the unmanned aerial vehicle under a body coordinate system; g represents the gravitational acceleration; vector e 3 ＝[0；0；1](ii) a Omega represents the angular velocity of the unmanned aerial vehicle under the body coordinate system; f drag And M drag Respectively representing the air resistance and the moment applied to the mass center of the aircraft;
Figure BDA0003671112720000023
representing a rotation matrix from the body coordinate system to the world coordinate system, I 3 Representing a 3 rd order identity matrix; u shape F (α i ,n i ) And U M (α i ,n i ) Respectively representing combined external thrust and moment, alpha, received by the centre of mass of the aircraft i Indicating the tilting angle of No. i rotor around the tilting axis, n i The rotating speed of the No. i rotor is represented, i is 1,2,3 and 4;
step two, for a given unmanned aerial vehicle expected flight track, obtaining expected control input U according to the dynamic model d (α i ,n i ) Comprises the following steps:
Figure BDA0003671112720000024
inputting desired control into U d (α i ,n i ) The decomposition is as follows: control efficiency matrix gamma (alpha) with time-varying parameters i ) Left-handed rotor thrust vector T (n) i ) Namely:
U d (α i ,n i )＝Γ(α i )T(n i )
step three, controlling the efficiency matrix gamma (alpha) i ) Time-varying parameter α in i Transfer to rotor thrust vector T (n) i ) To obtain a virtual thrust vector N (alpha) i ,n i ) And establishing a virtual thrust vector N (alpha) i ,n i ) And the equation relation with the free vector in the null space, wherein the equation relation is as follows:
Figure BDA0003671112720000025
wherein matrix B represents a control efficiency matrix without time-varying parameters,
Figure BDA0003671112720000026
a right pseudo-inverse matrix representing matrix B; v represents a set of orthogonal bases of the null space of matrix B; k represents an adjustment factor and has a value of 0 at the initial moment of flight;
step four, aligning the virtual thrust vector N (alpha) i ,n i ) Solving the equality relation with the free vector in the null space to obtain the tilting angles alpha of the four rotors around the respective tilting shafts i And the rotational speed n of the rotor i To solve for the desired control input U of the drone d (α i ,n i )。
Further, the air resistance experienced at the center of mass of the aircraft in step one is expressed as:
Figure BDA0003671112720000027
wherein, c F The air resistance coefficient is more than or equal to 0; rho air Represents the air density; s uav Representing the frontal area of the aircraft;
Figure BDA0003671112720000028
representing the mass center linear velocity of the aircraft under a body coordinate system;
air resistance moment M suffered by aircraft centroid drag Expressed as:
Figure BDA0003671112720000029
wherein, c M The air resistance moment coefficient is more than or equal to 0;
closed external thrust U applied to aircraft mass center F (α i ,n i ) Expressed as:
Figure BDA0003671112720000031
wherein k is f The thrust coefficient of the rotor wing is more than or equal to 0;
Figure BDA0003671112720000032
a column vector representing the thrust of the propeller in the coordinate system of the body,
Figure BDA0003671112720000033
λ i the X axis of the body coordinate system rotates to the included angle of the No. i rotor wing along the clockwise direction, and:
Figure BDA0003671112720000034
the resultant external moment experienced at the aircraft's center of mass is expressed as:
Figure BDA0003671112720000035
wherein k is m The rotor wing reaction torque coefficient is more than or equal to 0;
Figure BDA0003671112720000036
representing the coordinates of the geometrical center of the propeller in a coordinate system of the body,
Figure BDA0003671112720000037
where l represents the distance from the origin of the body coordinate system to the origin of the rotor coordinate system.
Further, the tilting angles alpha of the four rotors around the respective tilting shafts obtained in the fourth step i And the rotational speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is one or two, a set of exact solutions of the equation relationship is found by adopting a nonlinear redistribution method:
Figure BDA0003671112720000038
wherein N is the virtual thrust vector N (alpha) i ,n i )。
Further, the specific steps of finding a set of exact solutions of the equation relationship using a non-linear redistribution method include: will virtual thrust vector N (alpha) i ,n i ) The partitioning is as follows:
Figure BDA0003671112720000039
wherein N is d1 Corresponding to overrun part of thrust, N d2 Corresponding to the remaining portion; meanwhile, the orthogonal basis matrix V is also partitioned, and the partitioning rule and the virtual thrust vector N (alpha) are matched i ,n i ) The block division rules of (1) correspond to each other; then the virtual thrust vector N (alpha) i ,n i ) Equality relation with free vector in null space
Figure BDA00036711127200000310
The following steps are changed:
Figure BDA00036711127200000311
wherein, V 1 、V 2 Respectively represent corresponding to N d1 、N d2 The orthogonal basis block matrix of (a); the calculation formula for obtaining the adjustment factor K is: k is V 1 -(N d1 -N 1 ) And substituting the adjustment factor K into the matrix equation again to obtain a redistributed virtual thrust vector:
Figure BDA0003671112720000041
and finally obtaining an accurate solution of the control instruction of the actuator through nonlinear transformation:
Figure BDA0003671112720000042
further, the tilting angles alpha of the four rotors around the respective tilting shafts obtained in the fourth step i And the rotational speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is more than two, a quadratic programming method is adopted to find a group of optimal solutions close to an accurate solution of the equation relationship:
Figure BDA0003671112720000043
in the formula, alpha i0 ,n i0 Respectively representing the tilting angle of each rotor wing around the respective tilting shaft and the rotating speed of the rotor wing at the previous moment; delta alpha i 、△(n i 2 ) Respectively represent eachThe rate of change of the tilt angle of each rotor about its respective tilt axis and the rate of change of the rotor speed.
Further, the specific step of finding a group of optimal solutions close to the exact solution of the equation relationship by using a quadratic programming method in the fourth step includes:
and (3) constructing an equality constraint required by a quadratic programming method:
Figure BDA0003671112720000044
wherein X [. DELTA.. alpha. ] i ,△(n i 2 )]A rate of change vector representing a control instruction; d is a high-order nonlinear term;
constructing an objective function required by a quadratic programming method:
g(X,D,K)＝X T PX+D T QD+K T RK
in the formula, P, Q and R are parameter diagonal matrixes with scales of 8 dimensions, 8 dimensions and 2 dimensions respectively;
constructing the extreme value constraint required by a quadratic programming method:
Figure BDA0003671112720000045
in the formula, Delta alpha max Limit value, n, representing rate of change of tilt angle max A limit value representing a rotational speed;
inputting the equality constraint, the objective function and the extreme value constraint into a quadratic programming solver to obtain the delta alpha at the current moment i ,△n i To obtain an optimal solution alpha i And n i 。
According to another aspect of the present invention, there is provided a null-space based control distribution system for a tiltable quad-rotor drone, the system comprising:
a model building module configured to build a kinetic model of the tiltable quad-rotor unmanned aerial vehicle according to a newton-euler equation; the kinetic model is represented as:
Figure BDA0003671112720000051
wherein m represents the mass of the unmanned aerial vehicle; j represents the inertia matrix of the unmanned aerial vehicle;
Figure BDA0003671112720000052
representing the mass center linear acceleration of the unmanned aerial vehicle under a body coordinate system;
Figure BDA0003671112720000053
representing the angular acceleration of the unmanned aerial vehicle under a body coordinate system; g represents the gravitational acceleration; vector e 3 ＝[0；0；1](ii) a Omega represents the angular velocity of the unmanned aerial vehicle under the body coordinate system; f drag And M drag Respectively representing the air resistance and the moment applied to the mass center of the aircraft;
Figure BDA0003671112720000054
representing a rotation matrix from the body coordinate system to the world coordinate system, I 3 Representing a 3 rd order identity matrix; u shape F (α i ,n i ) And U M (α i ,n i ) Respectively representing combined external thrust and moment, alpha, received by the centre of mass of the aircraft i Indicating the tilting angle of No. i rotor around the tilting axis, n i The rotating speed of the No. i rotor is represented, i is 1,2,3 and 4; wherein, the first and the second end of the pipe are connected with each other,
the air resistance experienced at the aircraft center of mass is expressed as:
Figure BDA0003671112720000055
wherein, c F The air resistance coefficient is more than or equal to 0; ρ is a unit of a gradient air Represents the air density; s uav Representing the frontal area of the aircraft;
Figure BDA0003671112720000056
representing the mass center linear velocity of the aircraft under a body coordinate system;
received at the centre of mass of the aircraftAir resistance moment M drag Expressed as:
Figure BDA0003671112720000057
wherein, c M The air resistance moment coefficient is more than or equal to 0;
closed external thrust U applied to aircraft mass center F (α i ,n i ) Expressed as:
Figure BDA0003671112720000058
wherein k is f The thrust coefficient of the rotor wing is more than or equal to 0;
Figure BDA0003671112720000059
a column vector representing the thrust of the propeller in the coordinate system of the body,
Figure BDA00036711127200000510
λ i the X axis of the body coordinate system rotates to the included angle of the No. i rotor wing along the clockwise direction, and:
Figure BDA00036711127200000511
the resultant external moment experienced at the aircraft's center of mass is expressed as:
Figure BDA0003671112720000061
wherein k is m The rotor wing reaction torque coefficient is more than or equal to 0;
Figure BDA0003671112720000062
representing the coordinates of the geometrical center of the propeller in a coordinate system of the body,
Figure BDA0003671112720000063
wherein l represents the distance from the origin of the body coordinate system to the origin of the rotor wing coordinate system;
a desired control input transformation module configured to obtain, for a given desired flight trajectory of the drone, a desired control input U from the dynamical model d (α i ,n i ) Comprises the following steps:
Figure BDA0003671112720000064
inputting desired control into U d (α i ,n i ) The decomposition is as follows: control efficiency matrix gamma (alpha) with time-varying parameters i ) Left-handed rotor thrust vector T (n) i ) Namely:
U d (α i ,n i )＝Γ(α i )T(n i )；
the efficiency matrix Γ (α) will be controlled i ) Time-varying parameter α in i Transfer to rotor thrust vector T (n) i ) To obtain a virtual thrust vector N (alpha) i ,n i ) And establishing a virtual thrust vector N (alpha) i ,n i ) And the equation relation with the free vector in the null space, wherein the equation relation is as follows:
Figure BDA0003671112720000065
wherein matrix B represents a control efficiency matrix without time-varying parameters,
Figure BDA0003671112720000066
a right pseudo-inverse matrix representing matrix B; v represents a set of orthogonal bases of the null space of matrix B; k represents an adjustment factor and has a value of 0 at the initial moment of flight;
a desired control input resolving module configured to resolve a virtual thrust vector N (α) i ,n i ) Solving the equality relation with the free vector in the null space to obtainTilting angle alpha of four rotors around respective tilting shaft i And the rotational speed n of the rotor i To solve for the desired control input U of the drone d (α i ,n i )。
Further, the tilt angles α of the four rotors about the respective tilt axes obtained in the desired control input resolving module i And the rotational speed n of the rotor i In eight elements in total, if the number of the elements exceeding the physical limit of the unmanned aerial vehicle actuator is one or two, a group of accurate solutions of the equation relation is found by adopting a nonlinear redistribution method; the method specifically comprises the following steps: will virtualize the thrust vector N (alpha) i ,n i ) The partitioning is as follows:
Figure BDA0003671112720000067
wherein N is d1 Corresponding to overrun part of thrust, N d2 Corresponding to the remaining portion; meanwhile, the orthogonal basis matrix V is also partitioned, and the partitioning rule and the virtual thrust vector N (alpha) are matched i ,n i ) The block division rules of (1) correspond to each other; then the virtual thrust vector N (alpha) i ,n i ) Equality relation with free vector in null space
Figure BDA0003671112720000068
The following steps are changed:
Figure BDA0003671112720000069
wherein, V 1 、V 2 Respectively represent corresponding to N d1 、N d2 The orthogonal basis block matrix of (a); the calculation formula of the adjustment factor K is obtained as follows: k is V 1 - (N d1 -N 1 ) And substituting the adjustment factor K into the matrix equation again to obtain a redistributed virtual thrust vector:
Figure BDA0003671112720000071
and finally obtaining an accurate solution of the control instruction of the actuator through nonlinear transformation:
Figure BDA0003671112720000072
further, the tilt angles α of the four rotors about the respective tilt axes obtained in the desired control input resolving module i And the speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is more than two, a quadratic programming method is adopted to find a group of optimal solutions close to an accurate solution of the equation relationship:
Figure BDA0003671112720000073
in the formula, alpha i0 ,n i0 Respectively representing the tilting angle of each rotor wing around the respective tilting shaft and the rotating speed of the rotor wing at the previous moment; delta alpha i 、△(n i 2 ) Respectively representing the tilt angle change rate and the rotor rotation speed change rate of each rotor around the respective tilt shaft.
Further, the specific step of finding a set of optimal solutions close to an accurate solution of the equation relationship by using a quadratic programming method in the desired control input solution module includes:
and (3) constructing an equality constraint required by a quadratic programming method:
Figure BDA0003671112720000074
wherein X [. DELTA.. alpha. ] i ,△(n i 2 )]A rate of change vector representing a control instruction; d is a high-order nonlinear term;
constructing an objective function required by a quadratic programming method:
g(X,D,K)＝X T PX+D T QD+K T RK
in the formula, P, Q and R are parameter diagonal matrixes with scales of 8 dimensions, 8 dimensions and 2 dimensions respectively;
constructing the extreme value constraint required by a quadratic programming method:
Figure BDA0003671112720000075
in the formula, Delta alpha max Limit value, n, representing rate of change of tilt angle max A limit value representing the rotational speed;
inputting the equality constraint, the objective function and the extreme value constraint into a quadratic programming solver to obtain the delta alpha at the current moment i ,△n i To obtain an optimal solution alpha i And n i 。
The beneficial technical effects of the invention are as follows:
the method comprises the steps of carrying out model transformation on a kinetic model of the tiltable quad-rotor unmanned aerial vehicle to obtain a control efficiency matrix containing time-varying parameters, and transferring the time-varying parameters in the control efficiency matrix to a virtual thrust vector by using variable transformation; obtaining an explicit expression of the virtual thrust vector by using the properties of the matrix pseudo-inverse and the null space; when the number of the expected overlimit instructions in the virtual thrust vector is not more than 2, obtaining an accurate solution of the control instruction of the actuator by adopting a nonlinear redistribution method with good real-time performance; and when the number of the expected instructions in the virtual thrust vector exceeds 2, carrying out quadratic programming based on the precise solution of the control instruction at the previous moment so as to obtain the variable quantity of the instruction and the optimal solution of the instruction at the current moment. The method has good real-time performance, and the obtained solution is an accurate solution or an optimal solution; the method is suitable for any stage of tiltable four-rotor flight, and the resolving effective rate is more than 99%; the method is also suitable for the unmanned aerial vehicle to track high maneuverability and singular tracks.
Drawings
Fig. 1 is a schematic structural diagram of a tiltable quad-rotor unmanned aerial vehicle according to an embodiment of the invention;
fig. 2 is a schematic diagram of the coordinate system establishment of a tiltable quad-rotor unmanned aerial vehicle according to the embodiment of the invention;
FIG. 3 is a diagram of a real tracking trajectory of a DA method of a comparison method in an embodiment of the present invention;
FIG. 4 is a schematic representation of rotor speed for a comparative method DA in accordance with an embodiment of the present invention;
FIG. 5 is a schematic diagram of the tilt angle of a comparative process DA in an example of the invention;
FIG. 6 is a diagram of a true tracking trajectory for a method of an embodiment of the present invention;
FIG. 7 is a schematic representation of rotor speed for a method in accordance with an embodiment of the present invention;
FIG. 8 is a schematic illustration of the tilt angle of the method of an embodiment of the present invention;
fig. 9 is a schematic structural diagram of a control distribution system of a tiltable quad-rotor unmanned aerial vehicle based on a null space according to an embodiment of the invention.
Detailed Description
In order that those skilled in the art will better understand the disclosure, exemplary embodiments or examples of the disclosure are described below with reference to the accompanying drawings. It is obvious that the described embodiments or examples are only some, but not all embodiments or examples of the invention. All other embodiments or examples obtained by a person of ordinary skill in the art based on the embodiments or examples of the present invention without any creative effort shall fall within the protection scope of the present invention.
Firstly, deducing a kinematic model and a kinetic model of the tiltable quad-rotor unmanned aerial vehicle by utilizing coordinate transformation and kinetic analysis; converting the model to obtain a control efficiency matrix containing time-varying parameters, and transferring the time-varying parameters in the control efficiency matrix to the virtual thrust vector by using variable substitution; obtaining an explicit expression of the virtual thrust vector by using the properties of the matrix pseudo-inverse and the null space; when the number of the expected overrun instructions in the virtual thrust vector is not more than 2, partitioning the matrixes corresponding to the overrun parts and the non-overrun parts to obtain a calculation formula of an adjustment factor, substituting the adjustment factor into a partitioned matrix equation again to obtain a redistributed virtual thrust vector, and finally obtaining an accurate solution of the control instruction of the actuator through nonlinear transformation; and when the number of the expected instructions in the virtual thrust vector exceeds 2, performing quadratic programming based on the precise solution of the control instruction at the previous moment, and further obtaining the variable quantity of the instruction and the optimal solution of the instruction at the current moment.
The embodiment of the invention provides a control distribution method of a tiltable four-rotor unmanned aerial vehicle based on a null space, which comprises the following steps:
step one, establishing a world coordinate system
Figure BDA0003671112720000091
Body coordinate system
Figure BDA0003671112720000092
And rotor coordinate system
Figure BDA0003671112720000093
The origin of the rotor coordinate system is fixed to the mass center of the motor I; the tilting angle of the No. i rotor wing around the tilting shaft is alpha i The tilting directions of the rotors with adjacent serial numbers are the same; the initial positions of the 4 rotors are vertical to the rotating plane and upward, the No. 1 propeller and the No. 3 propeller rotate along the anticlockwise direction, and the No. 2 propeller and the No. 4 propeller rotate along the clockwise direction;
according to the embodiment of the invention, as shown in fig. 1, the tiltable quad-rotor unmanned aerial vehicle comprises a body 1, a flight controller 2, a GPS positioning module 3, four brushless motors 4-1, 4-2, 4-3, 4-4 and four tilting steering engines 5-1, 5-2, 5-3, 5-4, wherein the tilting steering engines are arranged on arms of the quad-rotor unmanned aerial vehicle, and after receiving a motor rotation speed instruction and a steering engine deflection instruction, rotors of the brushless motors rotate at a specified speed, and the tilting steering engines generate deflection angles of different angles, so as to drive the brushless motors to rotate around the arms integrally. As shown in FIG. 2, a ground coordinate system is established
Figure BDA0003671112720000094
Body coordinate system
Figure BDA0003671112720000095
And rotor coordinate system
Figure BDA0003671112720000096
The origin of the rotor coordinate system is fixed at the mass center of the motor I,
Figure BDA0003671112720000097
the shaft passes through the axis of the arm where the motor I is positioned and the positive direction faces outwards,
Figure BDA0003671112720000098
the positive direction of the axis is vertically upward,
Figure BDA0003671112720000099
the axis conforms to the right-hand screw rule.
Step two, establishing a kinetic model of the tiltable quad-rotor unmanned aerial vehicle according to a Newton-Euler equation as follows:
Figure BDA00036711127200000910
wherein m represents the mass of the unmanned aerial vehicle; j ═ diag (J) xx ,J yy ,J zz ) Representing the inertia matrix (J) of the unmanned aerial vehicle xx ,J yy ,J zz Respectively representing the moments of inertia of the body when rotating about the principal axes xx, yy, zz),
Figure BDA00036711127200000911
represents the linear acceleration (a) of the mass center of the unmanned aerial vehicle under the coordinate system of the body x ；a y ；a z Respectively representing the linear acceleration of the center of mass of the aircraft in the directions of the x axis, the y axis and the z axis of the aircraft system);
Figure BDA00036711127200000912
representing the angular acceleration (a) of the UAV in the coordinate system of the aircraft body roll ；a pitch ；a yaw Respectively representing the angular acceleration of the aircraft for rolling, pitching and yawing under the aircraft system); g represents the gravitational acceleration; vector e 3 ＝[0；0；1]；Ω＝[p；q；r]Representing the angular speed (p, q, r respectively representing the angular speed of the unmanned aerial vehicle for rolling, pitching and yawing under the aircraft system) under the body coordinate system; f drag And M drag Respectively representing the air resistance and the moment applied to the mass center of the aircraft;
Figure BDA0003671112720000101
representing a rotation matrix from the body coordinate system to the world coordinate system,
Figure BDA0003671112720000102
I 3 representing a 3 rd order identity matrix; u shape F (α i ,n i ) And U M (α i ,n i ) Respectively representing combined external thrust and moment, alpha, received by the centre of mass of the aircraft i Indicating the tilting angle of No. i rotor around the tilting axis, n i The number of rotations of the i-th rotor is represented, and i is 1,2,3, and 4.
Step three, further unfolding the air resistance F borne by the body in the dynamic model drag Air resistance moment M drag Closing external thrust U F Combined external thrust U M ；
According to the embodiment of the invention, the air resistance F is applied to the machine body drag Air resistance moment M drag And air density ρ air Windward area S of aircraft uav Linear speed of flight
Figure BDA0003671112720000103
Angular acceleration of flight
Figure BDA0003671112720000104
Figure BDA0003671112720000105
Figure BDA0003671112720000106
Wherein, c F ,c M More than or equal to 0 respectively represents the air resistance and the resistance moment coefficient.
External thrust U exerted on machine body F The total thrust produced by the 4 propellers, i.e.
Figure BDA0003671112720000107
Wherein k is f Not less than 0 is the thrust coefficient of the rotor, n i Is the speed of the i rotor, λ i Is x B Rotate to the included angle of the i-shaped rotor wing along the clockwise direction, and
Figure BDA0003671112720000108
the column vector representing the propeller thrust in the body coordinate system (s (-), c (-), t (-), respectively, represents sin (-), cos (-), tan (-)):
Figure BDA0003671112720000109
wherein R is X (·),R Y (·),R Z (. is) an axial rotation matrix under the right hand system:
Figure BDA00036711127200001010
external thrust U borne by machine body M Consisting of a total thrust torque and its reaction torque produced by 4 propellers, i.e.
Figure BDA00036711127200001011
Wherein k is m More than or equal to 0 is the rotor wing reaction torque coefficient,
Figure BDA00036711127200001012
coordinates representing the geometric center of the propeller in the coordinate system of the body:
Figure BDA0003671112720000111
wherein l is O B To
Figure BDA0003671112720000112
Of the distance of (c).
Decomposing the expected control input into a form of a control efficiency matrix with time-varying parameters multiplied by a thrust vector at the left side;
according to the embodiment of the invention, under the condition of giving the expected flight path, the expected control input U can be obtained according to the dynamic model d (α i ,n i ). Introducing a control efficiency matrix gamma (alpha) i ,n i ) For inputting control into U d (α i ,n i ) Mapping to rotor thrust vector T (n) i )：
Figure BDA0003671112720000113
Wherein, gamma (alpha) i ) Corresponds to the spatial degree of freedom x, y, z, roll, pitch, yaw, and the column corresponds to the propeller number i being 1,2,3, 4.
According to the external thrust U applied to the body F Combined external thrust U M Obtaining an explicit expression of a control efficiency matrix:
Figure BDA0003671112720000114
transferring time-varying parameters in the control efficiency matrix to a thrust vector, wherein the thrust vector is changed into a virtual thrust vector, and further establishing an equality relation between the virtual thrust vector and a free vector in a null space;
according to the embodiment of the invention, remapping is realized by using a variable substitution method, and the thrust T (n) of the rotor wing is converted into the thrust T (n) i )∈R 4×1 Conversion to virtual thrust N (alpha) i ,n i )∈R 8×1 And a control efficiency matrix Γ (α) in the form of a variable i ) The control efficiency matrix B e R that becomes scalar form 6×8 。
U d (α i ,n i )＝BN(α i ,n i )
Figure BDA0003671112720000121
Since B has a right pseudo-inverse
Figure BDA0003671112720000122
Thus is provided with
Figure BDA0003671112720000123
And because of
Figure BDA0003671112720000124
The property of zero space is used to expand the above equation:
Figure BDA0003671112720000125
wherein I ∈ R 8×8 ,V∈R 8×2 Is a set of orthogonal bases of null space of B, K ═ K 1 k 2 ] T Is a set of adjustment factors and at the initial time of flight K ═ 00]. VK is a set of vectors that lie in the null space of B and which, after being mapped by B, are zero vectors, i.e., B (VK) ═ 0. Furthermore, the equation relationship between the virtual thrust vector and the free vector in the null space is:
Figure BDA0003671112720000126
step six, control command alpha received by the actuator i ,n i And (i is 1,2,3 and 4) is the tilting angle of 4 steering engines and the rotating speed of 4 motors respectively. In general, the command cannot exceed the physical limits of the actuators, which would otherwise easily cause actuator failure and destabilize the drone. However, since tiltrotor quad-rotor drones have 2 additional degrees of freedom, there are 2 orthogonal bases in the null space of their scalar control distribution matrix. Furthermore, when the number of the elements M exceeding the limit in the virtual thrust vector does not exceed 2, nonlinear reallocation with good real-time performance can be adoptedThe method finds a set of exact solutions;
according to an embodiment of the invention, a desired virtual thrust is defined and the system is partitioned into
Figure BDA0003671112720000127
Wherein N is d1 Corresponding to the overrun portion of the desired thrust, N d2 Corresponding to the remaining portion; meanwhile, the orthogonal basis matrix V is also partitioned, and the partitioning rule corresponds to the partitioning rule of the virtual thrust matrix; then the original system is composed of
Figure BDA0003671112720000128
The following steps are changed:
Figure BDA0003671112720000129
wherein the content of the first and second substances,
Figure BDA00036711127200001210
represents the actual virtual thrust and
Figure BDA00036711127200001211
V＝[V 1 V 2 ] T ，V 1 、V 2 respectively represent corresponding to N d1 、N d2 The block matrix of (2). Due to the special form of the virtual thrust vector, the overrun elements within it always appear in pairs, for example at n 1 >n max When is, N (α) i ,n i ) 1 st element of (1)
Figure BDA00036711127200001212
And a second element
Figure BDA00036711127200001213
All exceed the limit, at which point V 1 ∈R 2×2 ，V 2 ∈R 6×2 And V is 1 Having an inverse matrix V 1 - ，V 2 Has a left pseudo inverse
Figure BDA00036711127200001215
The formula K ═ V calculated from the above formula 1 - (N d1 -N 1 ) Further, the actual virtual thrust may be redistributed using the following equation:
Figure BDA0003671112720000131
from the above transformation, when N is d1 When the constraint is exceeded, the adjustment factor K always enables the overrun part to satisfy the constraint again, and the result of reallocation is still an accurate solution. After obtaining the values of all elements in N, the motor rotation speed alpha required at the current moment can be calculated by using the following formula i And steering engine tilting angle n i 。
Figure BDA0003671112720000132
Wherein N is the virtual thrust vector N (alpha) i ,n i )。
And seventhly, when the number of the elements (M) exceeding the limit in the virtual thrust vector exceeds 2, because the number of the orthogonal bases is not enough to redistribute the instructions into the constraint space, finding a group of optimal solutions close to the accurate solution by adopting a quadratic programming method with better real-time performance in the optimization method.
According to the embodiment of the invention, the specific process of finding a group of optimal solutions close to an accurate solution by adopting a quadratic programming method with better real-time property in the optimization method comprises the following steps:
and seventhly, constructing equation constraints required by a quadratic programming method. Because the initial action of the unmanned aerial vehicle is generally a steady takeoff instruction, the control instruction of the actuator cannot be exceeded, and therefore the control instruction in the initial stage is generally obtained by calculation in the fifth step and the sixth step. After the quadratic programming method is triggered, defining the actuator control command at the previous moment as alpha i0 ,n i0 (has been calculated at the last time). Further, a Jacobian matrix is utilized
Figure BDA0003671112720000133
For non-linear equation
Figure BDA0003671112720000134
The linear expansion is performed to obtain the equality constraint of the quadratic programming problem as shown in the following formula:
Figure BDA0003671112720000135
wherein X [. DELTA.. alpha. ] i ,△(n i 2 )]Representing the rate of change vector of the control instruction, D is a high order nonlinear term.
And seventhly, constructing an objective function required by the quadratic programming method. In the invention, the planning objects of the objective function are an actuator instruction state, a high-order nonlinear term and a zero-space parameter vector:
g(X,D,K)＝X T PX+D T QD+K T RK
wherein, P, Q and R are parameter diagonal matrixes with the scales of 8 dimensions, 8 dimensions and 2 dimensions respectively.
And seventhly, constructing extreme value constraint required by the quadratic programming method. According to a constraint space pi { [ Delta ] alpha of an actuator instruction i ≤△α max ,n i ∈[0,n max ]Determine actuator command state X [ delta ] α [ ] i ,△(n i 2 )]Of where Δ α max Limit value, n, representing the rate of change of the steering engine tilt angle max Limit value representing the motor speed:
Figure BDA0003671112720000141
seventhly, inputting the equality constraint, the objective function and the extreme value constraint into a quadratic programming solver to obtain the value delta alpha of the current X moment i ,△n i Finally, obtaining the motor rotating speed alpha required by the current moment through the following formula i And steering engine tilting angle n i ：
Figure BDA0003671112720000142
The pseudo code of the control allocation algorithm based on the null space is shown as follows.
Figure BDA0003671112720000143
The technical effect of the invention is further verified through experiments.
The processor of the flight controller is an ARM series STM32H7 type single chip microcomputer, the processing frequency reaches 500Hz, and the requirement of control distribution resolving is met. The process of the present invention is compared with the direct partitioning (DA) process. Under the condition of no external disturbance, track tracking and attitude transformation experiments are carried out, and the effect of the method is verified. The preset parameters are shown in table 1.
TABLE 1 simulation example-related parameters
Figure BDA0003671112720000144
Figure BDA0003671112720000151
The expected trajectory tracked is as follows:
x d ＝0,0<t≤30
y d ＝0,0<t≤30
Figure BDA0003671112720000152
Figure BDA0003671112720000158
Figure BDA0003671112720000153
ψ d ＝0,0<t≤30
the real tracking track of the DA method is shown in fig. 3, and the rotor rotation speed and the tilt angle are shown in fig. 4 and fig. 5, respectively; the real tracking track of the method is shown in figure 6, and the rotating speed and the tilting angle of the rotor are shown in figures 7 and 8. As can be seen from the figure, the DA method diverges when tracking the expected track, but the method of the invention enables the unmanned aerial vehicle to smoothly complete track tracking and the tracking error is within 2% of the error band.
Another embodiment of the present invention provides a null-space-based control distribution system for a tiltable quad-rotor unmanned aerial vehicle, as shown in fig. 9, the system including:
a model building module 10 configured to build a kinetic model of the tiltable quad-rotor unmanned aerial vehicle according to newton-euler equations; the kinetic model is represented as:
Figure BDA0003671112720000154
wherein m represents the mass of the unmanned aerial vehicle; j represents the inertia matrix of the unmanned aerial vehicle;
Figure BDA0003671112720000155
representing the mass center linear acceleration of the unmanned aerial vehicle under a body coordinate system;
Figure BDA0003671112720000156
representing the angular acceleration of the unmanned aerial vehicle under a body coordinate system; g represents the gravitational acceleration; vector e 3 ＝[0；0；1](ii) a Omega represents the angular velocity of the unmanned aerial vehicle under the body coordinate system; f drag And M drag Respectively representing the air resistance and the moment applied to the mass center of the aircraft;
Figure BDA0003671112720000157
representing a rotation matrix from the body coordinate system to the world coordinate system, I 3 Representing a 3 rd order identity matrix; u shape F (α i ,n i ) And U M (α i ,n i ) Respectively representing combined external thrust and moment, alpha, received by the centre of mass of the aircraft i Indicating the tilting angle of No. i rotor around the tilting axis, n i The rotating speed of the No. i rotor is represented, i is 1,2,3 and 4; wherein the content of the first and second substances,
the air resistance experienced at the aircraft center of mass is expressed as:
Figure BDA0003671112720000161
wherein, c F The air resistance coefficient is more than or equal to 0; rho air Represents the air density; s uav Representing the frontal area of the aircraft;
Figure BDA0003671112720000162
representing the mass center linear velocity of the aircraft under a body coordinate system;
air resistance moment M suffered by aircraft centroid drag Expressed as:
Figure BDA0003671112720000163
wherein, c M The air resistance moment coefficient is more than or equal to 0;
closed external thrust U applied to aircraft mass center F (α i ,n i ) Expressed as:
Figure BDA0003671112720000164
wherein k is f The thrust coefficient of the rotor wing is more than or equal to 0;
Figure BDA0003671112720000165
a column vector representing the thrust of the propeller in the coordinate system of the body,
Figure BDA0003671112720000166
λ i the X axis of the body coordinate system rotates to the included angle of the No. i rotor wing along the clockwise direction, and:
Figure BDA0003671112720000167
the resultant external moment experienced at the aircraft's center of mass is expressed as:
Figure BDA0003671112720000168
wherein k is m The rotor wing reaction torque coefficient is more than or equal to 0;
Figure BDA0003671112720000169
representing the coordinates of the geometrical center of the propeller in a coordinate system of the body,
Figure BDA00036711127200001610
wherein l represents the distance from the origin of the body coordinate system to the origin of the rotor wing coordinate system;
a desired control input transformation module 20 configured to obtain, for a given desired flight trajectory of the drone, a desired control input U from said dynamical model d (α i ,n i ) Comprises the following steps:
Figure BDA00036711127200001611
inputting desired control into U d (α i ,n i ) The decomposition is as follows: control efficiency matrix gamma (alpha) with time-varying parameters i ) Left-handed rotor thrust vector T (n) i ) Namely:
U d (α i ,n i )＝Γ(α i )T(n i )；
the efficiency matrix Γ (α) will be controlled i ) Time-varying parameter α in i Transfer to rotor thrust vector T: (n i ) To obtain a virtual thrust vector N (alpha) i ,n i ) And establishing a virtual thrust vector N (alpha) i ,n i ) And the equation relation with the free vector in the null space, wherein the equation relation is as follows:
Figure BDA0003671112720000171
wherein matrix B represents a control efficiency matrix without time-varying parameters,
Figure BDA0003671112720000172
a right pseudo-inverse representing matrix B; v represents a set of orthogonal bases of the null space of matrix B; k represents an adjustment factor and has a value of 0 at the initial moment of flight;
the desired control input solver module 30, which is configured to couple to a virtual thrust vector N (α) i ,n i ) Solving the equality relation with the free vector in the null space to obtain the tilting angles alpha of the four rotors around the respective tilting shafts i And the rotational speed n of the rotor i To solve for the desired control input U of the drone d (α i ,n i )。
In the present embodiment, optionally, the tilt angles α of the four rotors about the respective tilt axes obtained in the desired control input resolving module i And the rotational speed n of the rotor i In eight elements in total, if the number of the elements exceeding the physical limit of the unmanned aerial vehicle actuator is one or two, a group of accurate solutions of the equation relation is found by adopting a nonlinear redistribution method; the method specifically comprises the following steps: will virtualize the thrust vector N (alpha) i ,n i ) The partitioning is as follows:
Figure BDA0003671112720000173
wherein N is d1 Corresponding to overrun part of thrust, N d2 Corresponding to the remaining portion; meanwhile, the orthogonal basis matrix V is also partitioned, and the partitioning rule and the virtual thrust vector N (alpha) are matched i ,n i ) The block division rules of (1) correspond to each other; then the virtual thrust vector N (alpha) i ,n i ) Equation relation with free vector in null spaceIs a system
Figure BDA0003671112720000174
The following steps are changed:
Figure BDA0003671112720000175
wherein, V 1 、V 2 Respectively represent corresponding to N d1 、N d2 The orthogonal basis block matrix of (a); the calculation formula for obtaining the adjustment factor K is: k is V 1 - (N d1 -N 1 ) And substituting the adjustment factor K into the matrix equation again to obtain a redistributed virtual thrust vector:
Figure BDA0003671112720000176
and finally obtaining an accurate solution of the control instruction of the actuator through nonlinear transformation:
Figure BDA0003671112720000177
in the present embodiment, optionally, the tilt angles α of the four rotors about the respective tilt axes obtained in the desired control input resolving module i And the rotational speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is more than two, a quadratic programming method is adopted to find a group of optimal solutions close to an accurate solution of the equation relationship:
Figure BDA0003671112720000178
in the formula, alpha i0 ,n i0 Respectively representing the tilting angle of each rotor wing around the respective tilting shaft and the rotating speed of the rotor wing at the previous moment; delta alpha i 、△(n i 2 ) Respectively representing the rate of change of the tilt angle of each rotor about its respective tilt axis and the rate of change of the rotor speed.
In this embodiment, optionally, the specific step of finding a group of optimal solutions close to the exact solution of the equation relationship by using a quadratic programming method in the expected control input solution module includes:
and (3) constructing an equality constraint required by a quadratic programming method:
Figure BDA0003671112720000181
wherein X [. DELTA.. alpha. ] i ,△(n i 2 )]A rate of change vector representing a control instruction; d is a high-order nonlinear term;
constructing an objective function required by a quadratic programming method:
g(X,D,K)＝X T PX+D T QD+K T RK
in the formula, P, Q and R are parameter diagonal matrixes with scales of 8 dimensions, 8 dimensions and 2 dimensions respectively;
constructing the extreme value constraint required by a quadratic programming method:
Figure BDA0003671112720000182
in the formula, Delta alpha max Limit value, n, representing rate of change of tilt angle max A limit value representing a rotational speed;
inputting the equality constraint, the objective function and the extreme value constraint into a quadratic programming solver to obtain the delta alpha at the current moment i ,△n i To obtain an optimal solution alpha i And n i 。
In this embodiment, functions of the control and distribution system for a tiltable quadrirotor drone based on a null space can be described by the control and distribution method for a tiltable quadrirotor drone based on a null space, so that detailed description is omitted in this embodiment, and reference may be made to the above method embodiments, and further description is omitted here.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.

Claims (10)

1. A control distribution method for a tiltable four-rotor unmanned aerial vehicle based on null space is characterized by comprising the following steps:
step one, establishing a dynamic model of the tiltable quad-rotor unmanned aerial vehicle according to a Newton-Euler equation; the kinetic model is represented as:
Figure FDA0003671112710000011
wherein m represents the mass of the unmanned aerial vehicle; j represents the inertia matrix of the unmanned aerial vehicle;
Figure FDA0003671112710000012
representing the mass center linear acceleration of the unmanned aerial vehicle under a body coordinate system;
Figure FDA0003671112710000013
representing the angular acceleration of the unmanned aerial vehicle under a body coordinate system; g represents the gravitational acceleration; vector e 3 ＝[0；0；1](ii) a Omega represents the angular velocity of the unmanned aerial vehicle under the body coordinate system; f drag And M drag Respectively representing the air resistance and the moment applied to the mass center of the aircraft;
Figure FDA0003671112710000014
representing a rotation matrix from the body coordinate system to the world coordinate system, I 3 Representing a 3 rd order identity matrix; u shape F (α i ,n i ) And U M (α i ,n i ) Respectively representing combined external thrust and moment, alpha, received by the centre of mass of the aircraft i Indicating the tilting angle of No. i rotor around the tilting axis, n i Indicating the speed of rotation of No. i rotor，i＝1、2、3、4；
Step two, for a given unmanned aerial vehicle expected flight path, obtaining expected control input U according to the dynamic model d (α i ,n i ) Comprises the following steps:
Figure FDA0003671112710000015
inputting desired control into U d (α i ,n i ) The decomposition is as follows: control efficiency matrix gamma (alpha) with time-varying parameters i ) Left-handed rotor thrust vector T (n) i ) Namely:
U d (α i ,n i )＝Γ(α i )T(n i )
step three, controlling the efficiency matrix gamma (alpha) i ) Time-varying parameter α in i Transfer to rotor thrust vector T (n) i ) To obtain a virtual thrust vector N (alpha) i ,n i ) And establishing a virtual thrust vector N (alpha) i ,n i ) And the equation relation with the free vector in the null space, wherein the equation relation is as follows:
Figure FDA0003671112710000016
wherein matrix B represents a control efficiency matrix without time-varying parameters,
Figure FDA0003671112710000017
a right pseudo-inverse matrix representing matrix B; v represents a set of orthogonal bases of the null space of matrix B; k represents an adjustment factor and has a value of 0 at the initial moment of flight;
step four, aligning the virtual thrust vector N (alpha) i ,n i ) Solving the equality relation with the free vector in the null space to obtain the tilting angles alpha of the four rotors around the respective tilting shafts i And the rotational speed n of the rotor i To solve for the desired control input U of the drone d (α i ,n i )。
2. The null-space based control distribution method for tiltable quad-rotor Unmanned Aerial Vehicles (UAVs) according to claim 1, wherein the air resistance at the center of mass of the aircraft in the first step is expressed as:
Figure FDA0003671112710000018
wherein, c F The air resistance coefficient is more than or equal to 0; rho air Represents the air density; s uav Representing the frontal area of the aircraft;
Figure FDA00036711127100000210
representing the mass center linear velocity of the aircraft under a body coordinate system;
air resistance moment M suffered by aircraft centroid drag Expressed as:
Figure FDA0003671112710000021
wherein, c M The air resistance moment coefficient is more than or equal to 0;
closed external thrust U applied to aircraft mass center F (α i ,n i ) Expressed as:
Figure FDA0003671112710000022
wherein k is f The thrust coefficient of the rotor wing is more than or equal to 0;
Figure FDA0003671112710000023
a column vector representing the thrust of the propeller in the coordinate system of the body,
Figure FDA0003671112710000024
λ i the X axis of the body coordinate system rotates to the included angle of the No. i rotor wing along the clockwise direction, and:
Figure FDA0003671112710000025
the resultant external moment experienced at the aircraft's center of mass is expressed as:
Figure FDA0003671112710000026
wherein k is m The rotor wing reaction torque coefficient is more than or equal to 0;
Figure FDA0003671112710000027
representing the coordinates of the geometrical center of the propeller in a coordinate system of the body,
Figure FDA0003671112710000028
where l represents the distance from the origin of the body coordinate system to the origin of the rotor coordinate system.
3. The null-space-based control distribution method for tiltable quad-rotor Unmanned Aerial Vehicles (UAVs) according to claim 2, wherein the tilting angles α of the four rotors around the respective tilting axes obtained in step four are i And the rotational speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is one or two, a set of exact solutions of the equation relationship is found by adopting a nonlinear redistribution method:
Figure FDA0003671112710000029
wherein N is the virtual thrust vector N (alpha) i ,n i )。
4. The null-space based control and distribution method for tiltable quad-rotor Unmanned Aerial Vehicles (UAVs) according to claim 3, wherein the specific step of finding a set of exact solutions of the equation relationship by using a nonlinear redistribution method comprises: will virtual thrust vector N (alpha) i ,n i ) The partitioning is as follows:
Figure FDA0003671112710000031
wherein, N d1 Corresponding to overrun part of thrust, N d2 Corresponding to the remaining portion; meanwhile, the orthogonal basis matrix V is also partitioned, and the partitioning rule and the virtual thrust vector N (alpha) are matched i ,n i ) The block rules of (2) correspond; then the virtual thrust vector N (alpha) i ,n i ) Equality relation with free vector in null space
Figure FDA0003671112710000032
The following steps are changed:
Figure FDA0003671112710000033
wherein, V 1 、V 2 Respectively represent corresponding to N d1 、N d2 The orthogonal basis blocking matrix of (a); the calculation formula for obtaining the adjustment factor K is:
Figure FDA0003671112710000038
substituting the adjustment factor K into the matrix equation again to obtain a redistributed virtual thrust vector:
Figure FDA0003671112710000034
and finally obtaining an accurate solution of the control instruction of the actuator through nonlinear transformation:
Figure FDA0003671112710000035
5. the null-space-based control distribution method for tiltable quad-rotor Unmanned Aerial Vehicles (UAVs) according to claim 2, wherein the tilting angles α of the four rotors around the respective tilting axes obtained in step four are i And the rotational speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is more than two, a quadratic programming method is adopted to find a group of optimal solutions close to an accurate solution of the equation relationship:
Figure FDA0003671112710000036
in the formula, alpha i0 ,n i0 Respectively representing the tilting angle of each rotor wing around the respective tilting shaft and the rotating speed of the rotor wing at the previous moment; delta alpha i 、△(n i 2 ) Respectively representing the tilt angle change rate and the rotor rotation speed change rate of each rotor around the respective tilt shaft.
6. The null-space-based control distribution method for tiltable quad-rotor Unmanned Aerial Vehicles (UAVs) according to claim 5, wherein the specific step of finding a set of optimal solutions close to an accurate solution of the equation relationship by quadratic programming in step four comprises:
and (3) constructing an equality constraint required by a quadratic programming method:
Figure FDA0003671112710000037
wherein X [. DELTA.. alpha. ] i ,△(n i 2 )]A rate of change vector representing a control instruction; d is a high-order nonlinear term;
constructing an objective function required by a quadratic programming method:
g(X,D,K)＝X T PX+D T QD+K T RK
in the formula, P, Q and R are parameter diagonal matrixes with scales of 8 dimensions, 8 dimensions and 2 dimensions respectively;
constructing the extreme value constraint required by a quadratic programming method:
Figure FDA0003671112710000041
in the formula, Delta alpha max Limit value, n, representing rate of change of tilt angle max A limit value representing a rotational speed;
inputting the equality constraint, the objective function and the extreme value constraint into a quadratic programming solver to obtain the delta alpha at the current moment i ,△n i To obtain an optimal solution alpha i And n i 。
7. A tiltable quad-rotor unmanned aerial vehicle control distribution system based on null space, comprising:
a model building module configured to build a kinetic model of the tiltable quad-rotor unmanned aerial vehicle according to a newton-euler equation; the kinetic model is represented as:
Figure FDA0003671112710000042
wherein m represents the mass of the unmanned aerial vehicle; j represents the inertia matrix of the unmanned aerial vehicle;
Figure FDA0003671112710000043
representing the mass center linear acceleration of the unmanned aerial vehicle under a body coordinate system;
Figure FDA0003671112710000044
representing the angular acceleration of the unmanned aerial vehicle under a body coordinate system; g represents the gravitational acceleration; vector e 3 ＝[0；0；1](ii) a Omega represents the angular velocity of the unmanned aerial vehicle under the body coordinate system; f drag And M drag Respectively representing the air resistance and the moment applied to the mass center of the aircraft;
Figure FDA0003671112710000045
representing a rotation matrix from the body coordinate system to the world coordinate system, I 3 Representing a 3 rd order identity matrix; u shape F (α i ,n i ) And U M (α i ,n i ) Respectively representing combined external thrust and moment, alpha, received by the centre of mass of the aircraft i Indicating the tilting angle of No. i rotor around the tilting axis, n i The rotating speed of the No. i rotor is represented, i is 1,2,3 and 4; wherein the content of the first and second substances,
the air resistance experienced at the aircraft center of mass is expressed as:
Figure FDA0003671112710000046
wherein, c F The air resistance coefficient is more than or equal to 0; rho air Represents the air density; s uav Representing the frontal area of the aircraft;
Figure FDA0003671112710000048
representing the mass center linear velocity of the aircraft under a body coordinate system;
air resistance moment M suffered by aircraft centroid drag Expressed as:
Figure FDA0003671112710000047
wherein, c M The air resistance moment coefficient is more than or equal to 0;
closed external thrust U applied to aircraft mass center F (α i ,n i ) Expressed as:
Figure FDA0003671112710000051
wherein k is f The thrust coefficient of the rotor wing is more than or equal to 0;
Figure FDA0003671112710000052
a column vector representing the thrust of the propeller in the coordinate system of the body,
Figure FDA0003671112710000053
λ i the X axis of the body coordinate system rotates to the included angle of the No. i rotor wing along the clockwise direction, and:
Figure FDA0003671112710000054
the resultant external moment experienced at the aircraft's center of mass is expressed as:
Figure FDA0003671112710000055
wherein k is m The rotor wing reaction torque coefficient is more than or equal to 0;
Figure FDA0003671112710000056
representing the coordinates of the geometrical center of the propeller in a coordinate system of the body,
Figure FDA0003671112710000057
wherein l represents the distance from the origin of the body coordinate system to the origin of the rotor wing coordinate system;
a desired control input transformation module configured to obtain, for a given desired flight trajectory of the drone, a desired control input U from the dynamical model d (α i ,n i ) Comprises the following steps:
Figure FDA0003671112710000058
inputting desired control into U d (α i ,n i ) The decomposition is as follows: control efficiency matrix gamma (alpha) with time-varying parameters i ) Left-handed rotor thrust vector T (n) i ) Namely:
U d (α i ,n i )＝Γ(α i )T(n i )；
the efficiency matrix Γ (α) will be controlled i ) Time-varying parameter α in i Transfer to rotor thrust vector T (n) i ) To obtain a virtual thrust vector N (alpha) i ,n i ) And establishing a virtual thrust vector N (alpha) i ,n i ) And the equation relation with the free vector in the null space, wherein the equation relation is as follows:
Figure FDA0003671112710000059
wherein matrix B represents a control efficiency matrix without time-varying parameters,
Figure FDA00036711127100000510
a right pseudo-inverse matrix representing matrix B; v represents a set of orthogonal bases of the null space of matrix B; k represents an adjustment factor and has a value of 0 at the initial moment of flight;
a desired control input resolving module configured to resolve a virtual thrust vector N (α) i ,n i ) Solving the equality relation with the free vector in the null space to obtain the tilting angles alpha of the four rotors around the respective tilting shafts i And the rotational speed n of the rotor i To solve for the desired control input U of the drone d (α i ,n i )。
8. The null-space-based control and distribution system for tiltable quad-rotor Unmanned Aerial Vehicles (UAVs) according to claim 7, wherein the desired control input calculating module obtains tilt angles (a) of the four rotors around respective tilt axes i And the rotational speed n of the rotor i Namely, in eight elements in total, if the number of the elements exceeding the physical limit of the unmanned aerial vehicle actuator is one or two, a nonlinear reallocation method is adopted to find out one of the equality relationsGroup exact solution; the method specifically comprises the following steps: will virtualize the thrust vector N (alpha) i ,n i ) The partitioning is as follows:
Figure FDA0003671112710000061
wherein N is d1 Corresponding to overrun part of thrust, N d2 Corresponding to the remaining portion; meanwhile, the orthogonal basis matrix V is also partitioned, and the partitioning rule and the virtual thrust vector N (alpha) are matched i ,n i ) The block division rules of (1) correspond to each other; then the virtual thrust vector N (alpha) i ,n i ) Equality relation with free vector in null space
Figure FDA0003671112710000062
The following steps are changed:
Figure FDA0003671112710000063
wherein, V 1 、V 2 Respectively represent corresponding to N d1 、N d2 The orthogonal basis block matrix of (a); the calculation formula for obtaining the adjustment factor K is:
Figure FDA0003671112710000067
substituting the adjustment factor K into the matrix equation again to obtain a redistributed virtual thrust vector:
Figure FDA0003671112710000064
and finally obtaining an accurate solution of the control instruction of the actuator through nonlinear transformation:
Figure FDA0003671112710000065
9. the null-space based tiltable quad-rotor unmanned aerial vehicle control distribution system of claim 7,characterized in that the desired control input is obtained in the calculation module as the tilt angles alpha of the four rotors about the respective tilt axes i And the rotational speed n of the rotor i In other words, if the number of elements exceeding the physical limit of the unmanned aerial vehicle actuator is more than two, a quadratic programming method is adopted to find a group of optimal solutions close to an accurate solution of the equation relationship:
Figure FDA0003671112710000066
in the formula, alpha i0 ,n i0 Respectively representing the tilting angle of each rotor wing around the respective tilting shaft and the rotating speed of the rotor wing at the previous moment; delta alpha i 、△(n i 2 ) Respectively representing the rate of change of the tilt angle of each rotor about its respective tilt axis and the rate of change of the rotor speed.
10. The null-space based control and distribution system for tiltable quad-rotor unmanned aerial vehicles according to claim 9, wherein the specific steps of finding a set of optimal solutions of the equality relationship close to an exact solution using quadratic programming in the desired control input solution module comprises:
and (3) constructing an equality constraint required by a quadratic programming method:
Figure FDA0003671112710000071
wherein X [. DELTA.. alpha. ] i ,△(n i 2 )]A rate of change vector representing a control instruction; d is a high-order nonlinear term;
constructing an objective function required by a quadratic programming method:
g(X,D,K)＝X T PX+D T QD+K T RK
in the formula, P, Q and R are parameter diagonal matrixes with scales of 8 dimensions, 8 dimensions and 2 dimensions respectively;
constructing the extreme value constraint required by a quadratic programming method:
Figure FDA0003671112710000072
in the formula, Delta alpha max Limit value, n, representing rate of change of tilt angle max A limit value representing a rotational speed;
inputting the equality constraint, the objective function and the extreme value constraint into a quadratic programming solver to obtain the delta alpha at the current moment i ,△n i To obtain an optimal solution alpha i And n i 。
CN202210605426.4A 2022-05-31 2022-05-31 Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space Pending CN114879739A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210605426.4A CN114879739A (en) 2022-05-31 2022-05-31 Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210605426.4A CN114879739A (en) 2022-05-31 2022-05-31 Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space

Publications (1)

Publication Number Publication Date
CN114879739A true CN114879739A (en) 2022-08-09

Family

ID=82679919

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210605426.4A Pending CN114879739A (en) 2022-05-31 2022-05-31 Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space

Country Status (1)

Country Link
CN (1) CN114879739A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117608198A (en) * 2023-12-22 2024-02-27 广东智能无人系统研究院(南沙) Method, system and device for distributing weighted pseudo-inverse thrust of propeller
WO2024087271A1 (en) * 2022-10-26 2024-05-02 广东汇天航空航天科技有限公司 Multi-rotor aircraft, control method therefor, device, and computer-readable storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2024087271A1 (en) * 2022-10-26 2024-05-02 广东汇天航空航天科技有限公司 Multi-rotor aircraft, control method therefor, device, and computer-readable storage medium
CN117608198A (en) * 2023-12-22 2024-02-27 广东智能无人系统研究院(南沙) Method, system and device for distributing weighted pseudo-inverse thrust of propeller

Similar Documents

Publication Publication Date Title
CN108958289B (en) Cluster unmanned aerial vehicle collision avoidance method based on relative velocity obstacle
CN114879739A (en) Control distribution method and system for tiltable quad-rotor unmanned aerial vehicle based on null space
CN109062042B (en) Limited time track tracking control method of rotor craft
CN112394739B (en) Active-deformation active-disturbance-rejection flight control method for four-rotor aircraft
CN108313271B (en) Eight-rotor aircraft capable of realizing decoupling control of gesture and position
Bodie et al. Towards efficient full pose omnidirectionality with overactuated mavs
CN112346470A (en) Four-rotor attitude control method based on improved active disturbance rejection control
CN108614573B (en) Automatic fault-tolerant attitude control method for six-rotor unmanned aerial vehicle
Matouk et al. Quadrotor position and attitude control via backstepping approach
Lifeng et al. Trajectory tracking of quadrotor aerial robot using improved dynamic inversion method
CN109885074B (en) Finite time convergence attitude control method for quad-rotor unmanned aerial vehicle
Mazeh et al. Fault-tolerant control of an hexarotor unmanned aerial vehicle applying outdoor tests and experiments
CN112558621A (en) Decoupling control-based flying mechanical arm system
CN112034871A (en) Omnidirectional control method of tiltable multi-rotor aircraft
CN114911265A (en) Four-rotor unmanned aerial vehicle formation cooperative maneuvering control method
CN115016268A (en) Fault-tolerant control method for tiltable four-rotor unmanned aerial vehicle based on sliding mode theory
CN113961010A (en) Four-rotor plant protection unmanned aerial vehicle tracking control method based on anti-saturation finite time self-adaptive neural network fault-tolerant technology
CN111897219A (en) Optimal robust control method for transitional flight mode of tilting quad-rotor unmanned aerial vehicle based on online approximator
Cao et al. Decoupled translational and rotational flight control designs of canted-rotor hexacopters
Orsag et al. Hybrid fly-by-wire quadrotor controller
Wang et al. Architecture design and flight control of a novel octopus shaped multirotor vehicle
Li et al. BioTetra: a bioinspired multi-rotor aerial vehicle
CN113296533B (en) Generalized actuator control allocation and reconfiguration method, device and related components thereof
Zawiski et al. Dynamics and optimal control of quadrotor platform
Flores et al. Fully actuated Hexa-rotor UAV: Design, construction, and control. Simulation and experimental validation

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination