Air transportation load trajectory tracking method and system based on lifting rope length optimization

Abstract

The invention discloses an air transportation load trajectory tracking method and system based on lifting rope length optimization. The method comprises the steps of obtaining state information of a multi-rotor unmanned aerial vehicle air transportation system; according to the state information of the system, the system tracking controller and the lifting rope length generator, a control signal of the transportation system is determined; wherein the system tracking controller is determined through a backstepping method based on a dynamic model of the multi-rotor unmanned aerial vehicle air transportation system with the adjustable lifting rope length; the lifting rope length generator is determined according to the change relation between the movement of the multi-rotor unmanned aerial vehicle body and the length of the lifting rope; and controlling the multi-rotor unmanned aerial vehicle air transportation system according to the control signal of the transportation system. And the dynamic adjustment of the length of the lifting rope is completed while the precise tracking of a load track is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic control of nonlinear underactuated electromechanical systems, and in particular to a load trajectory tracking method and system for aerial transportation based on optimization of the length of a sling. BACKGROUND

[0002] With the continuous progress of electronic technology and control algorithms, unmanned aerial vehicles have become a key equipment in many industries such as agriculture, logistics, and rescue. Among them, the use of multi-rotor unmanned aerial vehicles for sling suspension load transportation can not only significantly improve the efficiency of material delivery, but also complete engineering construction and emergency rescue tasks in environments where ground vehicles are difficult to reach, such as post-disaster ruins and remote mountain areas. Therefore, in recent years, sling suspension aerial transportation systems, especially multi-rotor unmanned aerial vehicles with adjustable sling lengths, have become a research hotspot.

[0003] In related technologies, when using a multi-rotor unmanned aerial vehicle with adjustable sling length for sling suspension load transportation, the expected trajectory of the multi-rotor and the expected trajectory of the sling need to be set in advance. Then, the multi-rotor motion tracking and sling motion tracking are performed according to the expected trajectories of the multi-rotor and the sling, respectively.

[0004] However, the position of the load is determined by the motion of the multi-rotor and the length of the sling. When tracking and controlling the multi-rotor and the sling separately, the accuracy of the load position cannot be guaranteed. SUMMARY

[0005] To achieve precise load trajectory tracking and multi-rotor-sling motion coordination control for a multi-rotor unmanned aerial vehicle with adjustable sling length, the present application proposes a load trajectory tracking method and system for aerial transportation based on optimization of the length of the sling. This method achieves precise load trajectory tracking while dynamically adjusting the length of the sling.

[0006] To achieve the above-mentioned purpose, the present application adopts the following technical solutions: In a first aspect, a load trajectory tracking method for aerial transportation based on optimization of the length of the sling is proposed, which includes: Obtaining the state information of the multi-rotor unmanned aerial vehicle aerial transportation system; Determining the control signal of the transportation system according to the state information of the system, a system tracking controller, and a sling length generator. The system tracking controller is determined based on the dynamics model of the multi-rotor unmanned aerial vehicle aerial transportation system with adjustable sling length through the backstepping method. The sling length generator is determined according to the relationship between the motion of the multi-rotor unmanned aerial vehicle body and the change of the sling length; Controlling the multi-rotor unmanned aerial vehicle aerial transportation system according to the control signal of the transportation system.

[0007] Further, the acquired state information includes unmanned aerial vehicle attitude information, hoisting rope length information, hoisting rope direction information, and load position information. The system tracking controller includes a load position tracking controller, a hoisting rope length tracking controller, a hoisting rope direction tracking controller, and a multi-rotor attitude tracking controller.

[0008] Further, the control signals of the transportation system include thrust and moment generated by the multi-rotor, and hoisting rope axial force generated by the hoisting rope length adjustment mechanism for lifting and lowering the load.

[0009] Further, the control signals of the transportation system are determined by aiming at minimizing the error between the system state and the desired state.

[0010] Further, the load position tracking controller is:

[0011] wherein, is a load position control virtual force, is an arbitrary element-wise operation on a vector, is a load position error, is a load velocity error, and is a positive definite gain matrix, is a desired acceleration of the load, is a load mass, is a gravitational acceleration, is a unit vector.

[0012] The hoisting rope length tracking controller is:

[0013] wherein, is a hoisting rope length controller, is a hoisting rope length adjustment error, is a hoisting rope length change velocity error, is a positive gain matrix, is a multi-rotor mass, is a hoisting rope length, is a hoisting rope direction vector, is a desired acceleration of the hoisting rope length, is a force required for lifting / lowering the load, is an upper bound of the hoisting rope length error tolerance.

[0014] The hoisting rope direction tracking controller is:

[0015] wherein, For rope direction tracking controller, For the quality of drones, This refers to the length of the hoisting rope. It is the direction vector of the suspension rope. To account for the error in the direction of the hoisting rope, This refers to the angular velocity error in the direction of the suspension rope. Defined as a two-dimensional spherical manifold The following configuration error, Positive control gain, It is the angular velocity in the direction of the suspension rope. For the desired angular velocity of the suspension rope, This is a positive constant used to specify the upper limit of the allowable deviation of the suspension rope direction.

[0016] The multi-rotor attitude tracking controller is:

[0017] in, For the attitude tracking error of the UAV, For the attitude error of the UAV, For the angular velocity error of the UAV, For the angular velocity of the drone, Here is the rotational inertia matrix of the UAV. It is a positive control gain. For the desired attitude of a multi-rotor drone, For the desired angular velocity, .

[0018] Furthermore, the rope length generator is as follows:

[0019] in, For the cost function, a generalized state vector is introduced. To describe nonlinear optimization problems, i.e. Among them and It is the position and speed of the multi-rotor drone. It is the generalized expected trajectory of the suspension rope length, including and its first to fourth derivatives; It is the generalized expected trajectory vector of the load. and for The lower and upper bounds of the constraints and for The lower and upper bounds.

[0020] Secondly, this invention proposes an aerial transport load trajectory tracking system based on rope length optimization, comprising: A state information acquisition unit is configured to acquire state information of the multi-rotor unmanned aerial vehicle air transportation system. A system control signal determination unit is configured to determine a control signal of the transportation system according to the state information of the system, a system tracking controller and a tether length generator. A system control unit is configured to control the multi-rotor unmanned aerial vehicle air transportation system according to the control signal of the transportation system.

[0021] In a third aspect, a computer device is provided, and the device comprises: A processor adapted to execute a computer program; A computer readable storage medium having a computer program stored therein, wherein the computer program is adapted to be loaded and executed by the processor to implement the air transportation load trajectory tracking method based on tether length optimization according to the first aspect.

[0022] In a fourth aspect, a computer readable storage medium is provided, and the computer readable storage medium stores a computer program, wherein the computer program is adapted to be loaded and executed by a processor to implement the air transportation load trajectory tracking method based on tether length optimization according to the first aspect.

[0023] In a fifth aspect, a computer program product is provided, and the computer program product comprises a computer program, wherein the computer program is executed by a processor to implement the air transportation load trajectory tracking method based on tether length optimization according to the first aspect.

[0024] Compared with the prior art, the present application has the following beneficial effects: The aerial transportation load trajectory tracking method and system based on the length optimization of a sling rope provided by the application take a multi-rotor unmanned aerial vehicle aerial transportation system with adjustable sling rope length as a core carrier, combine a system tracking controller and a sling rope length generator to construct a complete control system, so as to solve the dynamic coupling and state constraint problems in practical applications. Due to the complex nonlinear dynamic coupling among the multi-rotor, the sling rope and the load in the actual transportation scene, and the lack of flexibility caused by the manual predefinition of the sling rope trajectory in the traditional scheme, the application specifically designs a nonlinear control scheme: the system tracking controller does not need to linearize the system dynamics model, and can ensure the closed-loop system asymptotically stable through the Lyapunov method and the growth restriction condition, so as to achieve the accurate tracking of the load trajectory and complete the dynamic adjustment of the sling rope length; the matching developed sling rope length generator can autonomously manage the multi-rotor movement and the sling rope length change based on the system state constraints (such as the sling rope length range and the aircraft height limit), and completely abandon the traditional mode of manually presetting the sling rope trajectory. In addition, the simulation verifies the effectiveness of the control strategy in the trajectory tracking accuracy, the sling movement coordination and the load swing angle suppression, has important guiding significance for improving the task adaptability and operation autonomy of the variable sling aerial transportation system, and can be widely adapted to complex transportation scenes such as narrow space passing and dynamic target dropping. BRIEF DESCRIPTION OF DRAWINGS

[0025] The drawings accompanying the specification of this application are used to provide further understanding of the application, the illustrative embodiments of the application and the description thereof serve to explain the application, and do not constitute an improper limitation on the application.

[0026] Figure 1 A flow chart of the aerial transportation load trajectory tracking method based on the length optimization of a sling rope provided by the application is shown in the figure. Figure 2 A three-view of the running trajectory of Test 1 of the application is shown in the figure. Figure 3 A three-dimensional graph of the running trajectory of Test 1 of the application is shown in the figure. Figure 4 An error curve and a sling rope length and expected sling rope length curve of Test 1 of the application are shown in the figure. Figure 5 A control input curve and an unmanned aerial vehicle speed norm and rope length change speed curve of Test 1 of the application are shown in the figure. Figure 6 A three-view of the running trajectory of Test 2 of the application is shown in the figure. Figure 7 A three-dimensional graph of the running trajectory of Test 2 of the application is shown in the figure. Figure 8 An error curve and a sling rope length and expected sling rope length curve of Test 2 of the application are shown in the figure. Figure 9The control input curve of test 2 of the application and the unmanned aerial vehicle speed norm and rope length change speed curve; Figure 10 Three views of the running track of test 3 of the application, Figure 11 Three-dimensional view of the running track of test 3 of the application, Figure 12 Error curve of test 3 of the application and hoisting rope length and expected hoisting rope length curve diagram; Figure 13 Control input curve of test 3 of the application and unmanned aerial vehicle speed norm and rope length change speed curve. DETAILED DESCRIPTION

[0027] The application will be further described below in conjunction with the accompanying drawings and examples.

[0028] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0029] First, the application scenario of the air transportation load trajectory tracking method based on hoisting rope length optimization proposed by the application is described.

[0030] The air transportation load trajectory tracking method based on hoisting rope length optimization proposed by the application is applied to the load trajectory tracking and hoisting rope length adjustment control scenario of the multi-rotor unmanned aerial vehicle air transportation system with adjustable hoisting rope length.

[0031] With the continuous progress of electronic technology and control algorithm, unmanned aerial vehicles have become key equipment in many industries such as agriculture, logistics, and rescue. Among them, the use of multi-rotor unmanned aerial vehicles for hoisting rope suspension load transportation not only can significantly improve the efficiency of material delivery, but also can complete engineering construction and emergency rescue tasks in environments where ground vehicles are difficult to reach (such as post-disaster ruins and remote mountainous areas), so in recent years, hoisting rope suspension air transportation systems have become a research hotspot.

[0032] The core objective of existing research is to achieve efficient payload transportation in different scenarios through control and planning methods, which can be divided into two technical directions. One is to actively generate large payload swing angles to meet the requirements of obstacle avoidance or narrow space crossing. For example, Tang et al. estimated and captured the motion state of the payload using a downward-looking camera, and generated a large payload swing angle to achieve rapid crossing of the pile path. Yu et al. incorporated the direction constraint of the sling into the trajectory generator, constructed an aggressive payload swing trajectory, and efficiently completed the window crossing task. Wang et al. developed a planning and control framework with impact perception, combined agile flight and hybrid motion mode, and made the air transportation system able to cross narrow circular channels. The other is to suppress large payload swing to ensure transportation safety and payload protection. For example, Xian et al. designed a trajectory planning strategy that integrates target positioning and swing suppression modules, which can suppress the payload swing angle without iterative optimization. Lee et al. proposed a combination scheme of dynamic feasible trajectory generator and swing suppression tracking controller, which can effectively attenuate the payload oscillation while allowing short-term aggressive motion. Yu et al. also implemented a control framework that tracks a virtual point along the sling, which can cope with constant external disturbances and reduce payload swing. In addition, some research focuses on payload trajectory tracking rather than swing angle control: Cabecinhas et al. designed a backstepping control scheme based on the full dynamics model of the air transportation system to track the desired position of the point mass payload; Kong et al. developed an adaptive backstepping control strategy for systems with unknown payload mass, and set performance indicators for the payload position and sling direction.

[0033] However, the existing research still has the following key technical defects: 1) the limitations of fixed length hoisting rope system: most solutions focus on systems with fixed hoisting rope length, and the lifting movement of the load needs to rely entirely on the movement of the multi-rotor itself to achieve, which is difficult to complete tasks such as narrow tunnel crossing. Even if part of the fixed hoisting rope system can make the load swing through the narrow gap through a specific planning method, it cannot meet the task requirements if the length of the channel increases. At the same time, this type of system is not suitable for scenarios that require to maintain the distance between the multi-rotor and the load (such as load release, personnel near-suspension operation), and the way of adjusting the hoisting rope length by fixing the multi-rotor height can further improve the safety of personnel operation. 2) The shortcomings of variable length hoisting rope system: to solve the above limitations, in recent years, load transportation solutions using variable length hoisting ropes have emerged, which have significantly improved system flexibility, but existing solutions have two problems: one is that the control targets are mostly concentrated in multi-rotor movement tracking or load movement tracking, for example, Liang et al. achieved stable traversal and sample collection in narrow spaces by installing a motor under the multi-rotor to dynamically adjust the length of the hoisting rope in flight, but did not involve the movement coordination of the multi-rotor and the hoisting rope length. The second is that part of the load movement tracking solution, such as Zeng et al.'s geometric control solution, needs to predefine the hoisting rope length trajectory, which greatly limits the task flexibility of the system in complex dynamic scenarios. 3) Lack of coordination between multi-rotor and hoisting rope length: for variable length hoisting rope aerial transportation systems, the load position is determined by the movement of the multi-rotor and the length of the hoisting rope, and the same load trajectory can be achieved by different combinations of multi-rotor and hoisting rope length movements. For example, the load pickup and release stage needs to preferentially lengthen the hoisting rope to avoid ground effect and ensure personnel safety, while the long-distance transportation stage needs to preferentially improve transportation efficiency by multi-rotor movement, but the current research has not yet solved the problem of "how to coordinate the multi-rotor movement and the change of the hoisting rope length based on state constraints given the load trajectory, without manually predefining the hoisting rope trajectory", resulting in insufficient task efficiency and flexibility of load precise trajectory tracking.

[0034] In view of the above technical defects, it is urgent to develop a control scheme that can dynamically coordinate the movement of the multi-rotor and the length of the hoisting rope without predefining the hoisting rope trajectory, in order to break through the application limitations of existing variable length hoisting rope aerial transportation systems and achieve more efficient and flexible load trajectory tracking control.

[0035] To realize the load precise trajectory tracking and multi-rotor-hoist motion coordination control of the multi-rotor unmanned aerial vehicle air transportation system with adjustable hoist length, the embodiment of the present application adopts the multi-rotor unmanned aerial vehicle air transportation system with adjustable hoist length as the core carrier, combines a system tracking controller and a hoist length generator to build a complete control system, so as to solve the dynamic coupling and state constraint problems in practical applications. Due to the complex nonlinear dynamic coupling among the multi-rotor, the hoist and the load in the actual transportation scene, and the lack of flexibility caused by the manual predefinition of the hoist trajectory in the traditional scheme, the embodiment of the present application designs a nonlinear control scheme: the system tracking controller does not need to linearize the system dynamics model, and can ensure the closed-loop system asymptotically stable through the Lyapunov method and the growth restriction condition, so as to realize the precise tracking of the load trajectory and complete the dynamic adjustment of the hoist length; the hoist length generator developed in conjunction can autonomously manage the multi-rotor motion and the hoist length change based on the system state constraints (such as the hoist length range and the aircraft height limit), and completely abandon the traditional mode of manually presetting the hoist trajectory. In addition, the simulation verifies the effectiveness of the control strategy proposed in the embodiment of the present application in terms of trajectory tracking accuracy, hoist motion coordination and load swing angle suppression, which has important guiding significance for improving the task adaptability and operation autonomy of the variable hoist air transportation system, and can be widely adapted to complex transportation scenes such as narrow space traversal and dynamic target delivery.

[0036] Next, the air transportation load trajectory tracking method based on hoist length optimization proposed in the embodiment of the present application will be described in detail.

[0037] As shown in Figure 1 The air transportation load trajectory tracking method based on hoist length optimization proposed in the embodiment of the present application comprises: Obtaining the state information of the multi-rotor unmanned aerial vehicle air transportation system; Determining the control signal of the transportation system according to the state information of the system, the system tracking controller and the hoist length generator; wherein the system tracking controller is determined based on the dynamics model of the multi-rotor unmanned aerial vehicle air transportation system with adjustable hoist length through the backstepping method; the hoist length generator is determined according to the relationship between the motion of the multi-rotor unmanned aerial vehicle body and the change of the hoist length; Controlling the multi-rotor unmanned aerial vehicle air transportation system according to the control signal of the transportation system.

[0038] The obtained state information includes the unmanned aerial vehicle attitude information, the hoist length information, the hoist direction information and the load position information. The system tracking controller comprises a load position tracking controller, a hoist length tracking controller, a hoist direction tracking controller and a multi-rotor attitude tracking controller.

[0039] The existing flight hoisting system is mainly focused on the design of fixed hoisting rope length, and although it can complete tasks such as window crossing and obstacle avoidance, it needs to rely on aggressive trajectories and cannot meet the load demand of fragile goods and precision equipment that need to be transported smoothly. The air transportation load trajectory tracking method based on hoisting rope length optimization provided by the embodiment of the present application adopts a flight hoisting system with variable hoisting rope length, which can flexibly adjust the distance between the unmanned aerial vehicle and the load, efficiently complete related tasks under the premise of avoiding aggressive trajectories and ensuring the stability of the load, and the backstepping tracking controller strictly guarantees the asymptotic stability of the closed-loop system through Lyapunov stability analysis and growth restriction conditions, avoiding problems such as oscillation and divergence that are prone to occur in traditional control methods. It can effectively maintain system control accuracy and provide stable control support for load trajectory tracking and hoisting rope length adjustment, ensuring long-term reliable operation of the system. The method provided by the embodiment of the present application can be directly adapted to actual cargo transportation scenarios, such as delivering supplies to ground mobile platforms during post-disaster rescue, transferring packages to mobile delivery vehicles in the logistics field, and delivering components to high-altitude mobile platforms in engineering construction. Without the need for manual predefinition of hoisting rope trajectories, the method can dynamically coordinate the motion of multi-rotor and hoisting rope, significantly improve transportation efficiency, and reduce labor costs. It has important practical significance for promoting the development of air hoisting technology from laboratory research to industrial application, and can produce good economic and social benefits.

[0040] The embodiment of the present application establishes a dynamic model of a multi-rotor unmanned aerial vehicle air transportation system with adjustable hoisting rope length based on Newton's method; defines the error between the system state and the desired state and derives the open-loop dynamic equation; determines the load position tracking controller, the hoisting rope length tracking controller, the hoisting rope direction tracking controller, and the multi-rotor unmanned aerial vehicle attitude controller through backstepping.

[0041] The establishment process of the dynamic model of the multi-rotor unmanned aerial vehicle air transportation system with adjustable hoisting rope length is as follows: Unlike existing technologies, the embodiment of the present application regards the hoisting rope length as a non-constant system state and actively extends and retracts it through a motor-driven mechanism. Therefore, the control signals of the system not only include the thrust generated by the multi-rotor and the moment , but also include the hoisting rope axial force generated by the hoisting rope length adjustment mechanism for lifting and lowering the load.

[0042] Let and represent the mass of the multi-rotor and the load, respectively; represent the gravitational acceleration; represent the hoisting rope length; represent the moment of inertia matrix of the multi-rotor; represent the rotation matrix from the body system to the inertial system These represent the position and speed of the load, respectively. These represent the position and velocity of the multirotor, respectively. A unit vector representing the direction of the suspension rope; This indicates the angular velocity of the suspension rope; Indicating multi-rotor in-flight systems angular velocity at the bottom; This indicates the axial force in the lifting rope used to raise / lower the load; This represents the total thrust generated by the multi-rotor. This represents the torque generated by the multi-rotor. This represents a unit vector.

[0043] The kinematic equations of the multi-rotor UAV aerial transport system with adjustable sling length are as follows: (1) (2) (3) The geometric relationship between the multirotor and the load is as follows: (4) According to Newton's second law, the dynamic equations for the load and the multirotor are determined as follows: (5) (6) For equation (6) on both sides and Perform the inner product, and... Expressed using the second derivative of equation (4), we can obtain: (7) Substituting equation (5) into equation (7), we obtain the dynamics of the change in the length of the suspension rope: (8) Consider the multirotor as being relative to the center of mass of the load. point mass Its position vector is Then regarding point relative angular momentum for: (9) Based on acceleration reference points According to the angular momentum theorem: (10) in, For action on a multi-rotor, relative to a point The resultant torque, is the acceleration of the load's center of mass. Substituting equation (10) into the time derivative of equation (9), the dynamics equation in the direction of the tether is obtained as: (11) The multi-rotor rotational dynamics satisfy the Newton-Euler equation: (12) In summary, the dynamics model of the aerial transportation system with adjustable tether length can be established by solving equations (1)-(3), (5), (8), (11) and (12) simultaneously.

[0044] The process of defining the error between the system state and the desired state and deriving the open-loop dynamics equation is as follows: To facilitate subsequent control scheme design and analysis, the error between the system state and the desired state is first defined as follows.

[0045] where the error between the load position and the desired load position is the load position error, and the error between the load velocity and the desired load velocity is the load velocity error. The load position error and the load velocity error are defined as:

[0046] where is the desired load trajectory.

[0047] The error between the tether direction and the desired tether direction is the tether direction error, and the error between the tether angular velocity and the desired tether angular velocity is the tether angular velocity error . The tether direction error and the tether angular velocity error are defined as:

[0048] where and represent the desired tether direction and the desired tether angular velocity, respectively.

[0049] The error between the tether length and the desired tether length is the tether length error, and the tether length error is defined as:

[0050] where is the desired tether length.

[0051] The error between the multi-rotor attitude and the desired multi-rotor attitude is called the multi-rotor attitude error; the error between the multi-rotor angular velocity and the desired multi-rotor angular velocity is called the multi-rotor angular velocity error; and so on. and multi-rotor angular velocity error Defined as:

[0052] The control objective is to design a feedback control law that minimizes the error between the system state and the desired state, ensuring the load tracks its desired trajectory while simultaneously adjusting the length and direction of the suspension rope to achieve their respective desired states. Its mathematical description is as follows: Subsequently, by incorporating the aforementioned errors into the system's dynamic model and rearranging them, the open-loop error dynamics of the system can be obtained: (13) (14) (15) (16) The above forms the basis for subsequent closed-loop control law design and stability analysis.

[0053] The steps for determining the system tracking controller based on the backstepping method are as follows: First, the load position tracking controller is designed. The design is based on error dynamics (13). Following the hierarchical control concept, let... ,in The virtual control signal to be constructed. reflect Error with the direction of the suspension rope The coupling terms are decomposed as follows:

[0054] Using the triple product identity, we can obtain , and by We obtain the inequality: (17) Based on this, the load position tracking controller is designed as follows: (18) in, Virtual force is used to control the load position. , This is the positive definite gain matrix. The desired direction of the suspension rope can then be obtained: (19) From the decomposition relation, we can obtain:

[0055] The hoisting rope axial force of the hoisting rope is obtained: (20) Secondly, the hoisting rope length tracking controller design. From the error dynamics (14) and (15), we have which affects both the rope length and the hoisting rope direction. Define the virtual input as and decompose it as (21) Accordingly, the hoisting rope length tracking controller is constructed as (22) Subsequently, combining the decomposition and the error dynamics, the hoisting rope direction tracking controller is designed as (23) where is the configuration error, is the gain, is the upper bound of the hoisting rope direction error. The multirotor thrust input is obtained.

[0056] Finally, the multirotor attitude tracking controller design. The desired attitude is defined as (24) where and are not parallel; the desired angular velocity .

[0057] The multirotor attitude tracking controller is (25) where is the positive gain, . According to the singular perturbation theory, is used to ensure the convergence of and .

[0058] With the introduction of the variable rope length, the relative distance between the load and the multirotor can be freely adjusted. After the given load trajectory is given, the motion of the multirotor body and the change of the hoisting rope length can be coordinated and distributed according to the characteristics of the specific task. For example, in the load pickup and release stage, in order to ensure accurate control, the body movement of the multirotor should be minimized, and the load management should be mainly completed through the extension and contraction of the hoisting rope; while in the long-distance transportation stage, the body movement of the multirotor should be relied on more, and the change of the hoisting rope length should be minimized. Based on the above idea, the hoisting rope length generator is designed in this section. ​​

[0059] Based on the aforementioned backstepping control scheme, to ensure the smoothness of the control signal, the rope length trajectory is set to a fourth-order continuous path. To describe the relevant nonlinear optimization problem, a generalized state vector is introduced. ,in ; Let be the generalized expected rope length trajectory vector containing the expected rope length and its first to fourth time derivatives. Let be the generalized desired trajectory vector of the load. To obtain a reasonable rope length trajectory, the general form of the rope length generator is designed as follows: (26) (27) (28) (29) The sling length generator is designed in conjunction with the system tracking controller, based on the dynamic model of a multi-rotor UAV aerial transport system with adjustable sling length. Under the backstepping control framework, to ensure smooth control signals, the sling length trajectory must satisfy... Continuity; therefore, the fifth derivative of the desired rope length... The optimized output is selected. Given that the generator aims to coordinate the multirotor's motion and the rope length variation, the generalized dynamics shown in equation (27) are used as dynamic constraints; its state vector simultaneously includes the multirotor motion, rope length and its direction, and the desired rope length and its first to fourth derivatives. Based on the relationship between the multirotor and the load, the load position tracking controller (18), the rope length tracking controller (22), and the rope direction tracking controller (23) are substituted into the system dynamics models (5), (8), and (11) to obtain the specific expression of equation (27). Equation (27) gives the upper and lower bound constraints of the generalized desired rope length, where... These are the lower and upper bounds, respectively; Equation (29) specifies the upper and lower bounds of the optimized output, clearly defining... lower bound With the upper realm For different task requirements, the cost function... The design aims to enhance the synergy between multirotor motion and rope length variation, and to comprehensively balance the coupling with system state.

[0060] The method proposed in this embodiment of the invention is used to perform closed-loop system stability analysis, and the process is as follows: First, ignore coupling terms The stability of the subsystems for load location, suspension rope length, and suspension rope direction is proven separately. Then, based on the theory of cascaded systems, the stability of the overall system is guaranteed by proving that the coupling terms satisfy the growth constraint condition.

[0061] According to the load position control law, the following theorem is obtained: The designed load position control law (18) can make the load position and velocity errors asymptotically converge to zero, i.e.

[0062] To prove the above theorem, the following positive definite function is chosen as the Lyapunov candidate function: (30) where is the position gain vector, satisfying .

[0063] Taking the derivative of (30) and ignoring the coupling term , and substituting (13) and (18) into it, we get (31) From (18), (30), and (31), we have is non-increasing and bounded, so .

[0064] Further, let , , , then are all bounded, and the closed-loop error satisfies , so Integrating (31) gives Combining , which is uniformly continuous (obtained from ), according to the Barbalat lemma, we have (32) Since , we have , which is uniformly continuous; combining (32), we have . By the extended Barbalat lemma, we further have , so (33) In summary, from (32) and (33), the theorem is proved.

[0065] According to the length and direction control law of the hoisting rope, the following theorem is obtained: Consider the closed-loop system under the control laws (22) and (23). Define the potential barrier Lyapunov function on the safe set and , where , are constants. If the initial error satisfies and then there exists a positive control parameter such that: 1) for all , there exists such that ;} 2) the length and direction of the tether converge to zero, i.e.

[0066] Based on the singular perturbation model and time scale separation, the inner attitude loop is exponentially stable. Let on the slow subsystem, there exists , and the thrust direction satisfies , so that the tether length and direction dynamics are consistent with the commanded virtual force on the slow manifold.

[0067] Take , and select the potential Lyapunov candidate: (34) which is well-defined in . If , then , and by continuity, for all , there exists .

[0068] Let , then (35) where . Take the derivative of with respect to , substitute into (14) and (22), and obtain (36) where . The second term diverges when , thus ensuring the positive invariance of . By reasonably selecting and , the tether length can always be positive. Take , then (37) so that the tether length error exponentially converges.

[0069] Select the potential Lyapunov candidate related to the tether direction: (38) where , .

[0070] By , in , under (39) Let , we have (40) (41) where , . In , we have . Taking derivative of (42) where . The second term diverges when , which guarantees the positive invariance of . By properly choosing , we can guarantee that the direction of the cable always lies in the lower hemisphere when is located in the lower hemisphere, thus eliminating the a priori assumption that the payload must always be located below the multicopter.

[0071] Taking , we have (43) Thus the cable direction error index converges exponentially.

[0072] From (37) and (43), we have proved the above theorem.

[0073] Based on the above two theorems, the stability analysis of the closed-loop system is as follows.

[0074] Under the control law (18), (22), (23) and (25), the payload can be driven to the desired trajectory, and the cable length and cable direction can be adjusted to the desired value, i.e.

[0075] Consider the overall closed-loop system after coupling term . Let the generalized error vector be . Using , the virtual input (18) satisfies

[0076] where . Let , , then (44) From (44) and (17), we have (When ), which indicates that the coupling term satisfies the growth restriction condition.

[0077] Combining the above conclusions, the conclusion of the above theorem can be obtained.

[0078] After constructing the system tracking controller and the cable length generator, according to the specific form of the system tracking controller determined by the backstepping method, the unmanned aerial vehicle attitude information, the cable length information, the cable direction information and the load position information need to be obtained, and then the error between the system state and the expected state is closest to 0 as the target, the control signal of the transportation system is determined, the load position tracking controller, the cable length tracking controller, the cable direction tracking controller, the multi-rotor attitude tracking controller and the cable length generator are used to analyze the unmanned aerial vehicle attitude information, the cable length information, the cable direction information and the load position information, and the control signal of the multi-rotor unmanned aerial vehicle air transportation system is obtained.

[0079] According to the control signal of the transportation system, the multi-rotor unmanned aerial vehicle air transportation system is controlled, so that the multi-rotor unmanned aerial vehicle air transportation system completes the trajectory tracking of the expected trajectory, and realizes the automatic adjustment of the cable length.

[0080] To verify the effectiveness of the method proposed in the embodiment of the application, the embodiment of the application also carries out simulation experiments based on the acados library. All simulations are run on a desktop computer equipped with an AMD Ryzen 9 9950X processor and 64 GB of memory. The control frequency is 100 Hz, and the corresponding controller sampling period is . The system physical parameters are selected as: , , , . The control gain is set as: , , , , , , , , , , , .

[0081] The initial position of the load is set as , the initial direction of the cable is , and the initial length of the cable is . The expected trajectory of the load is selected as

[0082] In this embodiment of the invention, the focus is on basic performance verification. To coordinate multi-rotor motion with rope length variations, a cost function is used. Selected as in , These are weighting coefficients. By changing... and Set up three test groups: Test 1: ; Test 2: ; Test 3: .

[0083] All other weights are the same: , Generalized expectation vector of rope length With the fifth derivative The upper and lower bounds are set as follows: , , , .

[0084] Simulation results are as follows Figures 2 to 13 As shown. Among them, Figures 2-13 middle Indicates the location of the load. Indicates the location of the multi-rotor drone. This represents the expected trajectory of the load. Indicates the load position error. This indicates the error in the direction of the suspension rope. This indicates the error in the length of the suspension rope. Indicates the attitude error of the drone. This indicates the axial force of the lifting rope used to lift / lower the load. This represents the total thrust generated by the multi-rotor. This represents the torque generated by the multi-rotor. The velocity norm of a multi-rotor drone is represented. This indicates the rate of change of the length of the suspension rope.

[0085] Figure 2 , Figure 6 and Figure 10 Two-dimensional trajectory diagrams of three test loads and a multi-rotor are shown respectively; Figure 3 , Figure 7 and Figure 11Three-dimensional trajectories of three test loads and multicopters, respectively. Three sets of tests show that when the weight of the rope length in the cost function is higher, the change of the rope length is smaller, and the system tends to maintain an approximate constant length to achieve accurate tracking of the load trajectory; on the contrary, when the weight of the multicopter speed increases, the motion of the multicopter decreases, and the system compensates by increasing the rope length to ensure the tracking accuracy of the load trajectory. It is worth noting that, as shown in test 3, when the constraint is triggered (the upper limit of the rope length is reached), the system further completes the load trajectory tracking by reducing the height of the multicopter.

[0086] Figure 4 、 Figure 8 、 Figure 12 The tracking errors of the positions of the three test loads, the directions of the ropes, the lengths of the ropes, and the attitudes of the multicopters are shown, respectively, as well as the generated expected rope length and actual rope length curves. Although the initial error is non-zero, all error signals converge to zero within about 5s, verifying that the proposed control method can accurately track the expected trajectory for the aerial transportation system with variable rope length. Figure 5 、 Figure 9 、 Figure 13 The thrust and moment of the multicopter, the load lifting / dropping force, and the speed curves of the multicopter and the rope length are given, respectively, which intuitively reflect the coordination relationship between the motion of the multicopter and the change of the rope length under different weight settings.

[0087] The simulation verifies the effectiveness of the aerial transportation load trajectory tracking method based on the length optimization of the hoisting rope proposed in the embodiment of the present application in terms of trajectory tracking accuracy, hoisting rope motion coordination, and load swing angle suppression. It has important guiding significance for improving the task adaptability and operation autonomy of the variable hoisting rope aerial transportation system, and can be widely adapted to complex transportation scenarios such as narrow space traversal and dynamic target delivery.

[0088] The embodiment of the present application also proposes an aerial transportation load trajectory tracking system based on the length optimization of the hoisting rope, comprising: a state information acquisition unit for acquiring state information of the multicopter unmanned aerial transportation system; a system control signal determination unit for determining the control signal of the transportation system according to the state information of the system, the system tracking controller, and the hoisting rope length generator; wherein the system tracking controller is determined based on the dynamics model of the multicopter unmanned aerial transportation system with adjustable hoisting rope length through backstepping method; the hoisting rope length generator is determined according to the relationship between the motion of the multicopter unmanned aerial vehicle body and the change of the hoisting rope length; a system control unit for controlling the multicopter unmanned aerial transportation system according to the control signal of the transportation system.

[0089] The present application also discloses a computer device, which comprises: a processor adapted to execute a computer program; A computer readable storage medium, wherein a computer program is stored in the computer readable storage medium, and the computer program is executed by the processor to implement the load trajectory tracking method for aerial transportation based on the optimization of the length of the suspension rope.

[0090] The application further discloses a computer readable storage medium, wherein a computer program is stored in the computer readable storage medium, and the computer program is loaded by the processor and is used to implement the load trajectory tracking method for aerial transportation based on the optimization of the length of the suspension rope.

[0091] The application further discloses a computer program product, wherein the computer program product comprises a computer program, and the computer program is executed by the processor to implement the load trajectory tracking method for aerial transportation based on the optimization of the length of the suspension rope.

[0092] The above describes the specific embodiments of the application in combination with the drawings, but is not a limitation on the protection scope of the application, and those skilled in the art should understand that various modifications or changes made by those skilled in the art on the basis of the technical solutions of the application without creative labor are still within the protection scope of the application.

Claims

1. A method for tracking the trajectory of aerial transport loads based on optimized suspension rope length, characterized in that, include: Acquire status information of the multi-rotor UAV air transport system; The control signals of the transportation system are determined based on the system's status information, the system tracking controller, and the sling length generator. The system tracking controller is determined by backstepping based on the dynamic model of the multi-rotor UAV aerial transportation system with adjustable sling length. The sling length generator is determined based on the relationship between the motion of the multi-rotor UAV and the change in sling length. The multi-rotor UAV aerial transport system is controlled based on the control signals from the transport system.

2. The aerial transport load trajectory tracking method based on rope length optimization as described in claim 1, characterized in that, The acquired status information includes UAV attitude information, sling length information, sling direction information, and load position information; The system tracking controller includes a load position tracking controller, a sling length tracking controller, a sling direction tracking controller, and a multi-rotor attitude tracking controller.

3. The aerial transport load trajectory tracking method based on rope length optimization as described in claim 1, characterized in that, The load position tracking controller is: in, Virtual force is used to control the load position. For any vector Element-wise operations. For load position error, For load speed error, and It is a positive definite gain matrix. For the expected acceleration of the load, For load quality, It is the acceleration due to gravity. It is a unit vector. The rope length tracking controller is: in, For rope length controller, To account for the error in adjusting the length of the hoisting rope, To account for the error in the rate of change of the suspension rope length, It is a positive gain matrix. For the quality of drones, This refers to the length of the hoisting rope. It is the direction vector of the suspension rope. Let be the desired acceleration along the length of the suspension rope. The force required to lift / lower the load, This is the upper limit of the allowable error in rope length. The suspension rope direction tracking controller is: in, For rope direction tracking controller, For the quality of drones, This refers to the length of the hoisting rope. It is the direction vector of the suspension rope. To account for the error in the direction of the hoisting rope, This refers to the angular velocity error in the direction of the suspension rope. Defined as a two-dimensional spherical manifold The following configuration error, Positive control gain, It is the angular velocity in the direction of the suspension rope. For the desired angular velocity of the suspension rope, This is a positive constant used to specify the upper limit of the allowable deviation of the suspension rope direction. The multi-rotor attitude tracking controller is: in, For the attitude tracking error of the UAV, For the attitude error of the UAV, For the angular velocity error of the UAV, For the angular velocity of the drone, Here is the rotational inertia matrix of the UAV. It is a positive control gain. For the desired attitude of a multi-rotor drone, For the desired angular velocity, .

4. The aerial transport load trajectory tracking method based on rope length optimization as described in claim 1, characterized in that, The rope length generator is: Among them, the generalized state vector is introduced. To describe nonlinear optimization problems, i.e. Among them and It is the position and speed of the multi-rotor drone. It is the generalized expected trajectory of the suspension rope length, including and its first to fourth derivatives; It is the generalized expected trajectory vector of the load.

5. The aerial transport load trajectory tracking method based on rope length optimization as described in claim 1, characterized in that, The control signals for the transportation system are determined with the goal of minimizing the error between the system state and the desired state.

6. The aerial transport load trajectory tracking method based on rope length optimization as described in claim 1, characterized in that, The control signals of the transportation system include the thrust and torque generated by the multi-rotor, and the axial force of the hoisting rope generated by the hoisting rope length adjustment mechanism for lifting and lowering the load.

7. An aerial transport load trajectory tracking system based on rope length optimization, characterized in that, include: The status information acquisition unit is used to acquire the status information of the multi-rotor UAV air transport system. The system control signal determination unit is used to determine the control signals of the transportation system based on the system's state information, the system tracking controller, and the sling length generator. The system tracking controller determines the control signals based on the dynamic model of the multi-rotor UAV aerial transportation system with adjustable sling length using the backstepping method. The sling length generator determines the control signals based on the relationship between the motion of the multi-rotor UAV and the change in sling length. The system control unit is used to control the multi-rotor UAV aerial transport system according to the control signals of the transport system.

8. An electronic device, characterized in that, The device includes: A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the aerial transport load trajectory tracking method based on rope length optimization as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed by the aerial transport load trajectory tracking method based on rope length optimization as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the aerial transport load trajectory tracking method based on rope length optimization as described in any one of claims 1-6.

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