Unit dual quaternion-based tiltrotor multi-rotor unmanned aerial vehicle tracking control method

Abstract

The present invention discloses a unit dual quaternion-based integrated multi-rotor unmanned aerial vehicle tracking control method, which is applied to the technical field of unmanned aerial vehicle control, and comprises the following steps: establishing an integrated dynamic model of the tiltrotor multi-rotor unmanned aerial vehicle; representing the model with a unit dual quaternion to obtain a unit dual quaternion-based integrated dynamic model of the tiltrotor multi-rotor unmanned aerial vehicle; establishing a unit dual quaternion-based integrated tiltrotor multi-rotor unmanned aerial vehicle tracking controller; and controlling an execution mechanism of the tiltrotor multi-rotor unmanned aerial vehicle. The present invention can couple the kinematic and dynamic analysis of translation and rotary motion; and can track the trace and attitude in real time while accounting for the characteristics of the tiltrotor multi-rotor unmanned aerial vehicle, eliminate tracking errors caused by time-varying disturbances, uncertainties, unmodeled forces and the like, thereby ensuring the constant stability of the tiltrotor multi-rotor unmanned aerial vehicle system.

Description

Tracking control method for tilt-rotor multi-rotor UAV based on dual quaternion Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) control, and in particular to an integrated tracking control method for a multi-rotor UAV based on unit dual quaternion. Background Art

[0002] Over the past few decades, unmanned aerial vehicles (UAVs) have rapidly developed and become increasingly widespread due to their superior adaptability, survivability, and relatively low cost. Among various types of UAVs, tiltrotor multirotor drones (UAVs) are a special type of rotary-wing drone. They have six controllable degrees of freedom (DoF), indicating that these drones are omnidirectional, meaning that the system's translational and rotational dynamics are decoupled, and they are fully actuated systems in any hovering orientation. These unique characteristics of tiltrotor multirotor UAVs allow for stable interaction with the environment, overturning the under-actuated limitations of traditional fixed-wing and fixed-rotor UAVs and providing a compelling solution for future aerial robotics applications.

[0003] The force omnidirectionality of tiltrotor multi-rotor drones gives them attitude omnidirectionality, enabling the system to achieve unrestricted aerial movement and robust tracking of six-degree-of-freedom trajectories. These advantages offer unique benefits for aerial photography, industrial inspection, interactive applications, and movement and operation in confined spaces.

[0004] In current research on the kinematic description of tiltrotor multirotor UAV controllers, the Euler angle method is preferred and widely used due to its intuitiveness. However, the Euler angle method used by most tiltrotor multirotor UAV controllers compromises the mathematical simplicity of the platform model. Furthermore, the use of Euler angles introduces discontinuities, making the analysis and control law design of tiltrotor multirotor UAVs cumbersome. A computationally simpler and more stable mathematical tool for modeling the position and attitude tracking of tiltrotor multirotor UAVs is the unit dual quaternion.

[0005] The unit-dual quaternion is a combination of a unit quaternion and a translation vector using Plück coordinates. Unlike the unit quaternion, which focuses only on attitude, the unit-dual quaternion represents not only changes in attitude but also the positional motion of a rigid body—using only eight numbers (two constraints). The unit-dual quaternion has been widely used in various fields over the past decade due to its compactness, unambiguity, lack of singularities, and computationally simple rigid body transformations. Among the many applications of the unit-dual quaternion, drones, robots, and similar platforms are typical examples.

[0006] In recent years, there has been extensive research on the position and attitude tracking of rigid bodies and the control of fixed-wing and quadrotor drones using dual quaternions. However, this research has primarily focused on the application of dual quaternions to underactuated systems such as fixed-wing and quadrotor drones. However, there has been relatively little research on the control of tilt-rotor multirotor drones using unit dual quaternions. Tilt-rotor multirotors are a type of drone that particularly requires unit dual quaternions due to their omnidirectional orientation.

[0007] Therefore, providing an integrated tracking control method for multi-rotor UAV based on unit dual quaternion is an urgent problem to be solved by those skilled in the art.

[0008] Summary of the Invention

[0009] In view of this, the present invention provides an integrated tracking control method for a multi-rotor UAV based on unit dual quaternion, so that the tilt-rotor multi-rotor UAV system is always stable.

[0010] In order to achieve the above object, the present invention adopts the following technical solutions:

[0011] The integrated tracking control method of a multi-rotor UAV based on unit dual quaternion includes the following steps:

[0012] S101. Establish an integrated dynamics model of a tilt-rotor multi-rotor UAV;

[0013] The integrated dynamics model of the tilt-rotor multi-rotor UAV obtained in S201 and S101 is expressed using a unit dual quaternion to obtain an integrated dynamics model of the tilt-rotor multi-rotor UAV based on the unit dual quaternion;

[0014] S301, establishing an integrated tracking controller for the tilt-rotor multi-rotor UAV based on the unit-dual quaternion according to the integrated dynamics model of the tilt-rotor multi-rotor UAV based on the unit-dual quaternion in S201;

[0015] S401, using the tilt-rotor multi-rotor UAV integrated tracking controller based on the unit dual quaternion in S301 to control the actuator of the tilt-rotor multi-rotor UAV.

[0016] Optional, S101 specifically states: The system dynamics of a tilt-rotor multi-rotor UAV is based on the Newton-Euler method, which describes the dynamics of the tilt-rotor multi-rotor UAV through translational and rotational dynamics. The integrated dynamics model of the tilt-rotor multi-rotor UAV is as follows:

[0017] Where m and J are the mass and inertia of the tiltrotor multi-rotor UAV, f and τ are the force and torque generated by the actuator, ω bis the angular velocity in the body coordinate system, is the acceleration in the body coordinate system, is the angular acceleration in the body coordinate system.

[0018] Optionally, the specific content of S201 is:

[0019] The integrated dynamic model of the tilt-rotor multi-rotor UAV expressed by unit dual quaternion is as follows:

[0020] in, a=-J -1 ω b ×Jω b (6)

[0021] represents dual quaternion multiplication, represents the actual position and attitude, ξ b is the torque in the body coordinate system, is the angular velocity in the body coordinate system, p b is the position in the body coordinate system, Yes b The derivative of .

[0022] Optionally, use Equation (7) to describe the rotation p and then the translation p of the tilt-rotor multi-rotor drone. b , see the following formula for details:

[0023] Among them, q represents the quaternion of rotation, Indicates actual position and attitude.

[0024] Optionally, S301 specifically includes the following steps:

[0025] S3011. Calculate tracking error based on error dynamics;

[0026] S3012. Based on the tracking error, establish a controller structure based on the feedback linearization principle;

[0027] S3013. Based on the controller structure in S3012, establish an integrated tracking controller for tilt-rotor multi-rotor UAV based on unit dual quaternion.

[0028] Optionally, the tracking error calculation formula in S3011 is as follows:

[0029] in, Indicates the actual position and posture, Indicates the desired configuration.

[0030] Optionally, the controller structure based on the feedback linearization principle in S3012 is:

[0031] Optionally, the integrated tracking controller for the tilt-rotor multi-rotor UAV based on the unit dual quaternion in S3013 is as follows:

[0032] in,

[0033] and are the proportional, integral and derivative gains respectively.

[0034] is an adjoint transformation and is calculated as follows:

[0035] Optionally, the required rotor speed ω of each rotor obtained in S401 is i and rotor direction α i The calculation formula is as follows:

[0036] in, yes The (·)th element in atan2(X,Y) represents the four-quadrant inverse tangent of the elements of X and Y, such that -π≤atan2(X,Y)≤π.

[0037] Optional,

[0038] Among them, f d is the desired force, τ d is the desired torque, is the pseudo-inverse matrix of the static allocation matrix, and n is the number of tilt rotors.

[0039] It can be seen from the above technical solution that compared with the existing technology, the present invention provides an integrated tracking control method for multi-rotor UAVs based on unit dual quaternions: it can couple the kinematic and dynamic analysis of translational and rotational motions; it can realize real-time tracking of trajectory and posture, taking into account the characteristics of tilt-rotor multi-rotor UAVs, eliminating tracking errors caused by time-varying disturbances, uncertainties, unmodeled forces, etc., so that the tilt-rotor multi-rotor UAV system is always stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0041] FIG1 is a flow chart of a tilt-rotor multi-rotor UAV tracking control method based on dual quaternions provided by the present invention;

[0042] Figure 2 shows the simulation results of the actual posture and actual position provided by an embodiment of the present invention, where 2.1 is the evolution of the four components of the actual posture q relative to time t (the solid line is the actual trajectory, and the dotted line is the expected trajectory), and 2.2 is the actual position p s The evolution of the four components of with respect to time t (the solid line is the actual trajectory, the dashed line is the expected trajectory);

[0043] FIG3 is an error simulation result provided by an embodiment of the present invention, wherein 3.1 is the evolution of the four components of the posture error q relative to time t, and 3.2 is the evolution of the posture error p s The evolution of the four components of with respect to time t;

[0044] FIG4 is a simulation trajectory diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] 1 , the present invention discloses an integrated tracking control method for a multi-rotor UAV based on a unit dual quaternion, comprising the following steps:

[0047] S101. Establish an integrated dynamics model of a tilt-rotor multi-rotor UAV;

[0048] The integrated dynamics model of the tilt-rotor multi-rotor UAV obtained in S201 and S101 is expressed using a unit dual quaternion to obtain an integrated dynamics model of the tilt-rotor multi-rotor UAV based on the unit dual quaternion;

[0049] S301, establishing an integrated tracking controller for the tilt-rotor multi-rotor UAV based on the unit-dual quaternion according to the integrated dynamics model of the tilt-rotor multi-rotor UAV based on the unit-dual quaternion in S201;

[0050] S401, using the tilt-rotor multi-rotor UAV integrated tracking controller based on the unit dual quaternion in S301 to control the actuator of the tilt-rotor multi-rotor UAV.

[0051] Furthermore, the specific content of S101 is: The system dynamics of the tilt-rotor multi-rotor UAV is based on the Newton-Euler method, and the dynamics of the tilt-rotor multi-rotor UAV is described by translational and rotational dynamics. The integrated dynamic model of the tilt-rotor multi-rotor UAV is as follows:

[0052] Where m and J are the mass and inertia of the tiltrotor multi-rotor drone, f and τ are the force and torque generated by the drive, ω b is the angular velocity in the body coordinate system, is the acceleration in the body coordinate system, is the angular acceleration in the body coordinate system.

[0053] Furthermore, the specific content of S201 is:

[0054] The integrated dynamic model of the tilt-rotor multi-rotor UAV expressed by unit dual quaternion is as follows:

[0055] in, a=-J -1 ω b ×Jω b (6)

[0056] represents dual quaternion multiplication, represents the actual position and attitude, ξ b is the torque in the body coordinate system, is the angular velocity in the body coordinate system, p b is the position in the body coordinate system. Yes b Further, use Equation (7) to describe the rotation p and then the translation p of the tilt-rotor multi-rotor drone. b , see the following formula for details:

[0057] Where q is the quaternion representing the rotation, Indicates actual position and attitude.

[0058] Furthermore, S301 specifically includes the following steps:

[0059] S3011. Calculate tracking error based on error dynamics;

[0060] S3012. Based on the tracking error, establish a controller structure based on the feedback linearization principle;

[0061] S3013. Based on the controller structure in S3012, establish an integrated tracking controller for tilt-rotor multi-rotor UAV based on unit dual quaternion.

[0062] Furthermore, the tracking error calculation formula in S3011 is as follows:

[0063] in, Indicates the actual position and posture, Indicates the desired configuration.

[0064] Furthermore, the controller structure based on the feedback linearization principle in S3012 is:

[0065] Furthermore, the integrated tracking controller of the tilt-rotor multi-rotor UAV based on the unit dual quaternion in S3013 is shown as follows:

[0066] in,

[0067] and are the proportional, integral and derivative gains respectively.

[0068] is an adjoint transformation and is calculated as follows:

[0069] Furthermore, the required rotor speed ω of each rotor obtained in S401 is i and rotor direction α i The calculation formula is as follows:

[0070] in, yes The (·)th element in atan2(X,Y) represents the four-quadrant inverse tangent of the elements of X and Y, such that -π≤atan2(X,Y)≤π.

[0071] Furthermore,

[0072] Among them, f d is the desired force, τ d is the desired torque, is the pseudo-inverse matrix of the static allocation matrix, and n is the number of tilt rotors.

[0073] Specifically, the force f and torque τ are related to the square of the rotor speed ω i , The relationship between

[0074] Where A is the static allocation matrix, as shown in the following formula, n is the number of tilt arms, α i is the rotor direction, vector The elements of correspond to the lateral and vertical components of each squared rotor speed, ω i , in their respective rotor unit frames.

[0075] where γ i is the angle between the body x-axis and arm i in the body xy-plane, β i is the angle between the body xy-plane and arm i. f is the rotor thrust coefficient, c d is the rotor drag coefficient (relative to c f ), s i is the direction of rotation of the rotor attached to arm i.

[0076] At the desired force f d and torque τ d After being derived from the controller formula, the actuator command - rotor speed (ω i ) and rotor direction (α i ) - needs to be determined using the aerodynamic model in the above formula. However, since the static distribution matrix A is not invertible, the system is underdetermined. In this case, one of the generalized inverse matrices, the Moore-Penrose pseudo-inverse matrix, can be used To calculate the rotor speed and direction. Moore-Penrose pseudo-inverse matrix The minimum norm solution of formula (14) can be obtained.

[0077] To verify the stability and superiority of the designed tracker, the designed PID feedback linearization tracker will be used to simulate the actual motion and rotation of a tilt-rotor hexacopter drone. A specific example will be used to demonstrate the working principle of the PID feedback linearization tracker. The specific implementation is as follows:

[0078] The relevant parameters of the tilt-rotor hexacopter UAV by Allenspach et al. can be used directly. The mass of the UAV is 4.27 kg, and the moment of inertia matrix J of the fuselage frame is as follows:

[0079] The parameters in the static allocation matrix A are set according to Table 1:

[0080] Table 1

[0081] The control gains of the PID feedback linearization tracker for the tilt-rotor hexacopter are as follows:

[0082] The desired motion trajectory and direction are designed as follows:

[0083] in, n=[1,2,3]

[0084] To better test the robustness of our proposed PID feedback linearized tracker to time-varying disturbances, uncertainties, and unmodeled forces, the following test was performed: under the above trajectory and attitude, a disturbance torque of 2 N·m and a disturbance force of 30 N were applied to the tilt-rotor hexacopter in the x-, y-, and z-directions from 150 to 153 seconds.

[0085] Using the scenario set up in the previous section, the results obtained from the PID feedback linearized tracker are shown in Figure 2. Figure 2.1 shows the evolution of the four components of the actual direction q with respect to time t, and Figure 2.2 shows the actual position p s The evolution of the three components of with respect to time t. As can be seen from Figure 2, the trajectory and attitude control of the tilt-rotor multi-rotor UAV is effective when using the PID feedback linearization tracker, and the changes in position and attitude are very smooth with almost no error and overshoot.

[0086] In order to better demonstrate the superiority of the proposed PID feedback linearization tracker, the attitude error and position error are shown in Figure 3. Figure 3.1 illustrates the attitude error q e The evolution of the four components of relative to time t, Figure 3.2 shows the position error The evolution of the three components of with respect to time t. As can be seen from Figure 3, the proposed PID feedback linearization tracker is very good at tracking control of position and attitude, that is, there is almost no error in position and attitude most of the time. Although the result of position control in Figure 3.2 is slightly inferior to that of attitude control, the position error of 8mm is also quite small relative to the entire motion trajectory. In addition, based on the response to 150 to 153 seconds of force and torque disturbances in the x-, y-, and z-directions, it can be proved that the designed PID feedback linearization tracker can achieve strong robustness of the tilt-rotor multi-rotor UAV against various interferences.

[0087] The motion trajectory in the aforementioned scenario is also plotted in Figure 4, demonstrating the tilt-rotor hexacopter's specific trajectory and attitude in greater detail. Figure 4 shows that the hexacopter's position trajectory and attitude angles are remarkably smooth, allowing it to roughly follow the desired trajectory and attitude without any singularities. Furthermore, the tilt-rotor hexacopter exhibits considerable robustness against interference.

[0088] The present invention also provides an integrated tracking control device for a multi-rotor UAV based on unit dual quaternion, comprising a processor and a memory storing program instructions. When the processor runs the program instructions, an integrated tracking control method for a multi-rotor UAV based on unit dual quaternion is executed.

[0089] The above description of the disclosed embodiments is presented in an incremental manner to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is to be construed in the widest possible manner consistent with the principles and novel features disclosed herein.

Claims

1. An integrated tracking control method for multi-rotor UAV based on unit dual quaternion, characterized in that: The following steps are involved: S101. Establish an integrated dynamics model of a tilt-rotor multi-rotor UAV; The integrated dynamics model of the tilt-rotor multi-rotor UAV obtained in S201 and S101 is expressed by a unit dual quaternion, thereby obtaining an integrated dynamics model of the tilt-rotor multi-rotor UAV based on the unit dual quaternion; S301, according to the tilt-rotor multi-rotor UAV integrated dynamics model based on the unit dual quaternion in S201, establishing a tilt-rotor multi-rotor UAV integrated tracking controller based on the unit dual quaternion; S401, using the tilt-rotor multi-rotor UAV integrated tracking controller based on the unit dual quaternion in S301 to control the actuator of the tilt-rotor multi-rotor UAV; The specific contents of S201 are: The integrated dynamics model of the tilt-rotor multi-rotor UAV expressed by unit dual quaternion is as follows: in, a=-J -1 oh b ×Jω b (6) ∈ is the dual unit, represents dual quaternion multiplication, ξ b is the rotation quantity of motion in the body coordinate system, is the linear velocity in the body coordinate system, p b is the position in the body coordinate system, Yes b The derivative of; m and J are the mass and inertia of the tilt-rotor multi-rotor UAV, f and τ are the force and torque generated by the actuator, ω b is the angular velocity in the body coordinate system, Indicates actual position and attitude.

2. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 1 is characterized in that: The specific content of S101 is: The system dynamics of the tilt-rotor multi-rotor UAV is based on the Newton-Euler method, and the dynamics of the tilt-rotor multi-rotor UAV is described by translational and rotational dynamics. The integrated dynamics model of the tilt-rotor multi-rotor UAV is as follows: Where m and J are the mass and inertia of the tiltrotor multi-rotor drone, f and τ are the force and torque generated by the actuator, ω b is the angular velocity in the body coordinate system, is the acceleration in the body coordinate system, is the angular acceleration in the body coordinate system.

3. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 1 is characterized in that: Formula (7) is used to describe the rotation p and then the translation p of the tilt-rotor multi-rotor UAV. b , see the following formula for details: Among them, q is the quaternion representing the rotation, Indicates actual position and attitude.

4. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 1 is characterized in that: S301 specifically includes the following steps: S3011. Calculate tracking error based on error dynamics; S3012. Based on the tracking error, a controller structure based on the feedback linearization principle is established; S3013. Based on the controller structure in S3012, establish an integrated tracking controller for a tilt-rotor multi-rotor UAV based on unit dual quaternion.

5. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 4 is characterized in that: The tracking error calculation formula in S3011 is as follows: in, Indicates the actual position and posture, Indicates the desired configuration.

6. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 4 is characterized in that: The controller structure based on the feedback linearization principle in S3012 is:

7. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 4 is characterized in that: The integrated tracking controller of the tilt-rotor multi-rotor UAV based on the unit dual quaternion in S3013 is as follows: in, and are proportional, integral and derivative gains respectively; is an adjoint transformation and is calculated as follows:

8. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 1 is characterized in that: The required rotor speed ω of each rotor obtained in S401 i and rotor direction α i The calculation formula is as follows: in, yes The (·)th element in , atan2(X,Y) represents the four-quadrant inverse tangent of the elements of X and Y, such that -π≤atan2(X,Y)≤π.

9. The integrated tracking control method for multi-rotor UAV based on unit dual quaternion according to claim 8 is characterized in that: Among them, f d is the desired force, τ d is the desired torque, is the pseudo-inverse matrix of the static allocation matrix, and n is the number of tilt rotors.

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