Flexible cable shape construction and end positioning method and system based on gradient distribution prediction

Abstract

The application discloses a flexible cable shape construction and end positioning method and system based on gradient distribution prediction, and the method comprises the following steps: acquiring attitude data of each installation position based on an inertial measurement unit distributedly installed on a cable, and solving an attitude matrix of a position node; defining a unit gradient vector and converting to a navigation coordinate system; establishing a cable gradient change model; predicting a gradient change function of the cable through a cubic spline difference method, and then restoring an underwater flexible shape according to cable length integration, and positioning each point on the cable and the end.The application has low requirements on the number and precision of nodes, and the verification result shows that the relative positioning precision can be better than 2%, and the relative positioning precision can be as high as 0.05% in a high-precision environment.The application provides effective theoretical support for precision optimization of a deep-sea observation system based on a flexible cable, and lays a technical foundation for deep-sea positioning and exploration.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of flexible connection measurement, in particular to a flexible cable shape construction and end positioning method and system. BACKGROUND

[0002] The ocean observatory network is a new platform for human observation of the ocean, which can realize all-weather, in-situ, long-term, continuous, real-time, high-resolution and high-precision observation of the ocean from the seabed to the sea surface, and plays an important supporting role in the development of ocean science. With the promotion of modern sensors, underwater robots, submarine optical cables, Internet of Things, big data and other new technologies, the ocean observatory network presents the development trend of comprehensive three-dimensional observation, data deep excavation and comprehensive cross-fusion of various observation plans.

[0003] At present, China has initially formed a basic framework of the ocean observatory network covering the shore-based ocean observation system, off-shore ocean observation system and ocean and polar observation, which provides important support for the fields of disaster prevention and mitigation, scientific research and others. Among numerous observation networks, buoys, subsurface buoys and towed platforms are widely used, and flexible cables, as an important component, are responsible for connecting, fixing and guiding underwater equipment, playing an important role. The cable has the characteristics of long distance, small mass, high strength, low cost, portability and easy deployment, and is widely used in the ocean sensor observation system. The cable end is usually moored to the surface platform or the bottom anchor, and the other end is connected to the sensor equipment, however, the soft and curved nature of the mooring cable combined with the effect of ocean currents will cause the cable shape to change dynamically, and the end sensor position is uncertain. This has a great impact on the perception accuracy of the underwater observation system.

[0004] Underwater navigation and positioning technology has developed to the present, and can meet some underwater positioning needs by using methods such as acoustics, but the cost is high and the response speed is slow. For some short-distance and low-precision scenarios, the drift of the underwater mooring cable is usually ignored by technology. These problems need to be solved. SUMMARY

[0005] The purpose of the present application is to provide a flexible cable shape construction and end positioning method and system based on gradient distribution prediction to solve the problems of underwater mooring cable shape agnostic and end difficult to locate. The method is low in cost, simple in operation and high in precision, and is not only suitable for underwater observation, but also can be widely applied to other flexible connection measurement fields.

[0006] TECHNICAL SCHEME

[0007] In a first aspect, a flexible cable shape construction and end positioning method based on gradient distribution prediction includes the following steps:

[0008] The attitude data of each installation position is acquired based on the inertial measurement units distributedly installed on the cable, and an attitude matrix of a position node is solved based on the attitude data;

[0009] A length direction from a starting end to a terminal end of the cable is defined as a gradient direction, λ is a unit gradient vector, that is, a coordinate change caused by a unit length cable change, and a projection coordinate λ of the unit gradient vector in the carrier coordinate system is obtained according to the attitude matrix And a projection coordinate of the unit gradient vector in the navigation coordinate system is obtained according to the projection coordinate λ of the unit gradient vector in the carrier coordinate system b n represents the navigation coordinate system, and b represents the carrier coordinate system;

[0010] According to the continuity characteristic of the cable, a continuous cable structure model of an arbitrary shape is established, and the coordinates of any point on the cable are represented as a continuous function about the cable length l: Wherein, X(l), Y(l) and Z(l) are respectively an x coordinate, a y coordinate and a z coordinate of the cable at an arbitrary length l, A gradient change function is established according to the relationship between the unit gradient vector and the gradient change function

[0011] The gradient change function of the cable is predicted by a cubic spline difference method, and the underwater flexible shape is restored according to the cable structure model by cable length integration, and each point and the terminal end on the cable are positioned.

[0012] In a second aspect, a flexible cable shape construction and terminal positioning system based on gradient distribution prediction includes:

[0013] A node attitude calculation module is configured to acquire attitude data of each installation position based on inertial measurement units distributedly installed on the cable, and to solve an attitude matrix of a position node based on the attitude data;

[0014] A gradient definition and conversion module is configured to define a length direction from a starting end to a terminal end of the cable as a gradient direction, λ is a unit gradient vector, that is, a coordinate change caused by a unit length cable change, and a projection coordinate λ of the unit gradient vector in the carrier coordinate system is obtained according to the attitude matrix And a projection coordinate of the unit gradient vector in the navigation coordinate system is obtained according to the projection coordinate λ of the unit gradient vector in the carrier coordinate system b n represents the navigation coordinate system, and b represents the carrier coordinate system;

[0015] A gradient change model construction module is configured to establish a continuous cable structure model of an arbitrary shape according to the continuity characteristic of the cable, and to represent the coordinates of any point on the cable as a continuous function about the cable length l: ​​Wherein, X(l), Y(l), Z(l) are x coordinate, y coordinate, z coordinate of the cable at any length l respectively, is a gradient change function, and a relationship between a unit gradient vector and the gradient change function is established according to the definition of lambda

[0016] The solving calculation module is used for predicting the gradient change function of the cable through a cubic spline difference method, and restoring the underwater flexible shape of the cable through length integration of the cable according to the cable structure model, and positioning each point and the tail end of the cable.

[0017] In a third aspect, a computer device comprises: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs are executed by the processors to implement the steps of the flexible cable shape construction and tail end positioning method based on gradient distribution prediction as in the first aspect.

[0018] In a fourth aspect, a computer readable storage medium has a computer program stored thereon, and the computer program is executed by a processor to implement the steps of the flexible cable shape construction and tail end positioning method based on gradient distribution prediction as in the first aspect.

[0019] Beneficial effects: The cable is widely used in the marine field such as buoy, anchoring, and towing, and the dynamic change of the underwater sensor position caused by the flexible structure brings difficulties to marine observation. The present application provides a shape construction and tail end positioning method based on gradient distribution prediction, which provides a low-cost solution for the underwater position uncertainty problem of the flexible cable. The method uses a certain number of sensor nodes distributedly installed on the wet end of the cable to measure the posture of the cable at different positions, predicts the gradient change function of the cable through a cubic spline difference method, restores the underwater flexible shape of the cable through length integration of the cable according to the cable structure model, and positions each point and the tail end of the cable. The method is verified by simulating the underwater structure of the cable, and the results show that the method has low requirements for the number and accuracy of the nodes, the relative positioning accuracy can be better than 2%, and the relative positioning accuracy can be as high as 0.05% in a high-precision environment. This provides effective theoretical support for the precision optimization of the deep-sea observation system based on the flexible cable, and lays a technical foundation for deep-sea positioning and exploration. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 It is a schematic diagram of the underwater cable connection structure and use mode;

[0021] Figure 2 It is a flowchart of the method of the present application;

[0022] Figure 3 It is a simplified model of the towed sonar cable;

[0023] Figure 4 Gradient analysis for node diagram;

[0024] Figure 5 Towed sonar cable structure simulation example;

[0025] Figure 6 Cable simulation structure bottom view and side view;

[0026] Figure 7 Cable gradient prediction results (n = 21, attitude error is 0.1°) ;

[0027] Figure 8 Cable full segment positioning estimation error (n = 21, attitude error is 0.1°) ;

[0028] Figure 9 Cable gradient prediction results (n = 11, attitude error is 0.1°) ;

[0029] Figure 10 Cable full segment positioning estimation error (n = 11, attitude error is 0.1°) ;

[0030] Figure 11 Cable shape construction error comparison under different node numbers;

[0031] Figure 12 Cable gradient prediction results (n = 21, attitude error is 0.5° & 5°) ;

[0032] Figure 13 Cable full segment positioning estimation error (n = 21, attitude error is 0.5° & 5°) ;

[0033] Figure 14 Cable shape construction error comparison under different attitude accuracy. DETAILED DESCRIPTION

[0034] In order to have a clearer understanding of the features and advantages of the technical solutions of the present application, the composition and implementation of the specific schemes will be described below in conjunction with the drawings.

[0035] The present application is dedicated to solving the problem of determining the random change of the underwater shape of the mooring cable. For this purpose, the following three mooring cable underwater connection structures and use methods are summarized, as shown in Figure 1

[0036] 1) buoy suspension cable structure

[0037] ​Buoy plays an important role in ocean monitoring and underwater communication. It is widely used because of its light structure and easy deployment. The part above the water surface is called dry end, which is mainly composed of buoy, communication equipment and satellite positioning equipment, responsible for the function of buoy coordinate monitoring and data transmission and reception. The part below the water surface is called wet end, which carries different sensors to collect data, such as temperature, salinity, pressure, sonar and other equipment.

[0038] Global Ocean Observing Experiment Project Argo plan launched 3000 buoys in the world, which are used for measuring ocean subsurface temperature, salinity and depth profile. In order to measure the ocean parameters of different water layers in depth, the length of wet end is very large, with the maximum depth of 2km, so it is made of flexible cable structure, with sensors fixed at certain intervals to collect ocean parameters at corresponding depth, so that the profile distribution of hydrological data is obtained. Strictly speaking, this profile is not the vertical line below the GNSS(Global Navigation Satellite System, Global Navigation Satellite System) position of the dry end, because the bending deformation of the wet end makes the position of each sensor node underwater uncertain. Usually, the hydrological data and depth of these nodes are one-to-one corresponding and recorded, and the horizontal coordinates are ignored, one is because it is difficult to measure the horizontal position in real time underwater, and the other is that it is assumed that the local hydrological environment changes are small in horizontal direction. However, in severe sea conditions, the hydrological conditions at different positions may change suddenly, and the large deviation of the wet end nodes may lead to inaccurate profile data(2km long horizontal deviation can reach 1km). Therefore, fast and simple real-time horizontal positioning is very helpful for buoy detection.

[0039] Positioning sonar is also often deployed using buoy carrier. Sonar buoy is an important part of PNT(Positioning, Navigation, and Timing, Positioning, Navigation, and Timing), which is a relay for information exchange between underwater and water surface. At the same time, the combination of buoy sonar and underwater sonar anchor node forms a three-dimensional spatial positioning network, which can provide high-precision underwater positioning service. The transducer and hydrophone at the end of the wet end cable receive the sonar information of underwater targets, and then the positioning calculation is carried out, in which the deviation of the end from the dry end affects the positioning accuracy. In order to avoid interference and obtain good acoustic environment, the end hydrophone needs to be deep into the 200m below the sound channel axis remote sound channel layer. Therefore, long distance buoy sonar needs to solve the problem of relative deviation measurement of the end. Another passive detection buoy, the hydrophone is also placed at intervals on the wet end cable, which can distinguish the direction of arrival of the signal of the detected target, and the underwater deviation position of each node hydrophone can also improve the positioning accuracy.

[0040] 2) Subsea mooring structure

[0041] The seabed equipment deployment mode is divided into bottom sinking deployment and mooring deployment. The equipment deployed at the bottom sinks under the action of the weight and is fixed on the seabed, such as a seismic monitor, a bottom sinking mine and the like. The bottom sinking mode has the advantage of stable kinematic state, and the position coordinates are fixed and unchanged. The equipment deployed by mooring is connected by anchor chains, and the bottom end is anchored on the seabed, and the upper end is suspended in water. The advantage of the mooring deployment is that the equipment is far away from the seabed, and a good environment is created for sound signal transmission and reception. The underwater transponder and the semi-floating mine adopt this mode, and a large platform is stably moored by multiple anchor chains. However, due to the surge of underwater ocean current, the position and posture of the equipment deployed by mooring change greatly, and the coordinates of the transponder pre-deployed in the positioning array and the actual position will be different. The error can be ignored in long-distance positioning, but in the process of near-distance detection, the error has a greater influence on the positioning calculation. For the semi-floating mine and other pre-positioned platforms, the dynamically changing position and posture greatly interfere with the initial alignment process before execution. Therefore, real-time monitoring of the position of the underwater mooring deployed equipment can make its effect better.

[0042] 3) Water surface platform towed structure

[0043] Many underwater detection equipment do not have power sources and need to be towed by a water surface ship, such as a towed sonar and a side scan sonar. This towed structure is similar to a buoy, the dry end is regarded as fixed or has satellite positioning information, and the wet end is connected by a cable and is deep into the water for up to hundreds of meters. The towed sonar is used for passive detection of the direction of an enemy submarine, and its linear structure forms a baseline array and has a certain direction sensing ability, but is limited by its single structure and cannot eliminate the ambiguity problem of the left and right flanks. Once the underwater structure of the towed sonar can be accurately sensed in real time, the detection and recognition ability of the towed sonar will be greatly improved. The side scan sonar describes the terrain below after being released by a cable. Since the underwater shape of the cable is not a straight line, there will be a large deviation in the position of the side scan sonar only according to the length of the cable. Therefore, the underwater shape structure of the cable needs to be constructed.

[0044] The above problems can be summarized as real-time construction of the flexible shape of the cable underwater. Through the reconstruction of the structure, the accurate positioning of any node on the cable, including the tail end, is realized. In order to solve the above problems, the present application proposes a shape reconstruction and tail end positioning method based on gradient distribution prediction. The gradient change state of the cable is predicted by using the posture information of the distributed nodes on the cable, and the spatial structure of the entire cable is calculated by integrating the prior cable length, wherein the posture information is calculated in real time by the MEMS (Micro-Electro-Mechanical Systems) sensor installed at the node. The spatial structure of the cable provides the relative position of each point. Considering that the starting end generally has accurate GNSS position information, the relative position is added on this basis, and the real-time accurate positioning of the tail end is realized. Figure 2 The overall flowchart of the scheme is shown.

[0045] The flexible cable shape construction and end positioning method provided by the application is suitable for a cable structure with a certain bending freedom, can construct a spatial bending structure of the cable in real time, determine three-dimensional coordinates of any position on the cable according to anchor position coordinates of a starting end of the cable, and includes estimating a position of an end of the cable. The method can be used in scenarios such as positioning of a wet end of a buoy, positioning of an underwater mooring anchor chain, positioning of a towed sonar, and the like. In the embodiment, the towed sonar positioning is taken as an example for description. The same method is used for calculation and application in other scenarios.

[0046] The method obtains the attitude of each node by installing a certain number of 9-axis IMU (Inertial Measurement Unit) measurement units on the cable in a distributed manner, constructs a cable gradient change model through a series of attitude data, and finally reconstructs the overall spatial form according to the known cable length and calculates the end position. The node refers to the sensor and the position where the sensor is located, and the sensor has a measurement function for the related information of the position. Therefore, there are concepts of a sensor node, a measurement node and a position node in this paper. In the application, the sensor adopts an IMU measurement unit, and low precision is sufficient, so a MEMS inertial device is used.

[0047] The method is implemented as follows.

[0048] Suppose that in a spatial coordinate system oxyz, a simplified model of the towed sonar cable is as shown in Figure 3 The cable is released from a starting end P0(x0, y0, z0) position, and under the action of gravity, ocean current and buoyancy, the overall shape is a catenary, and in the local horizontal direction, a certain bending swing change occurs. The cable change has continuity, and large curvature deformation is excluded. The total length of the cable released by the towed sonar is L, and n measurement nodes a i (i=1, 2, …, n) are distributed at equal intervals on the cable, the first measurement node a1 is arranged at the position p0, and a terminal node a n is arranged at the end of the cable. The interval of the nodes is d, and the cable length l i of each node from the initial position is (i-1)d. The equal interval arrangement of the nodes can uniformly measure and facilitate the calculation of the length, and if the length l i of each node from the initial position is known, the equal interval arrangement is not necessary.

[0049] The node measures the acceleration f bi , the angular increment Δθ bi and the magnetic vector m bi of the position by the IMU, the static attitude of the node can be calculated from f bi and m bi , and the static attitude of the node a i is represented by an attitude matrix The relationship is shown below:

[0050]

[0051] The superscript n denotes the navigation coordinate system, and b denotes the vehicle coordinate system. g refers to Earth's gravity, m refers to the geomagnetic vector at that location, and the superscript n indicates the projection in the n-frame. The node α can be solved using the two-vector attitude determination principle. i pose matrix

[0052] For dynamic scenarios, the attitude matrix needs to be combined with the misalignment angle and the angle increment Δθ. bi Iterative updates will be performed.

[0053]

[0054] Where φ bi It is the horizontal misalignment angle. Represents the attitude matrix The third row vector. Obtain the calculated value of the misalignment angle φ. bi Then, combined with the gyroscope output Δθ bi It can calculate the attitude matrix. The numerical recursion algorithm is as follows, after updates and corrections:

[0055]

[0056] For node α before correction i The attitude matrix, For the corrected node α i The attitude matrix is ​​I, which is the identity matrix, and ()× indicates an antisymmetric matrix transformation on the vectors in parentheses.

[0057] Next, we predict the gradient. We define the gradient direction as the length of the cable from the start to the end, and λ as the unit gradient vector. At the node, the projection coordinates of λ in the b-frame are... b It can be pre-calibrated. Figure 4 For example, if λ is along the y-axis of the IMU, then:

[0058]

[0059] θ x and θ z It is a small angle error. In this invention, the gradient direction of the cable is defined along the y-axis. After the IMU device is installed, the small deviation angle between the coordinate system defined by the device and the coordinate system defined by the cable at that position.

[0060] Based on the attitude measured by the node, we can obtain:

[0061]

[0062] are the node pose matrices collectively, λ n is the projection of the unit gradient vector λ in the n-frame.

[0063] Let α1= (0, 0, 0), α i = (x i , y i , z i ), P(x, y, z) is any point on the cable. For any continuous cable structure at any time, its model can be represented by a continuous function as follows:

[0064]

[0065] X(l) is the x coordinate of the cable at any length l, Y(l) is the y coordinate of the cable at any length l, and Z(l) is the z coordinate of the cable at any length l. The first and second derivatives of this function are continuous, which meets the continuity characteristics of underwater cables. From the above formula, the coordinates of any point on the cable can be calculated using the length l of the cable. It is only necessary to master the differential function of the cable structure-length, i.e. the gradient change function Because according to the definition of λ, the coordinate change caused by the change of the unit length of the cable is the gradient, it can be known that, Combining equation (5), the gradient at node α i and the gradient change function are related as follows:

[0066]

[0067] λ ni , λ bi are the projections of the gradient at node α i in the n-frame and the b-frame.

[0068] The gradient at node α i can be calculated according to the measured value λ bi , and the gradient change function of the entire cable can be constructed by cubic spline interpolation as follows:

[0069]

[0070] where, and are the projections of the cable gradient change function on the three coordinate axes, l ∈ [l1, l2] represents the cable between l1 and l2, that is, between the first node and the second node. The rest is similar. δ = (δ i1 , δ i2 , δ i3 , δ i4 ), μ = (μi1 , μ i2 , μ i3 , μ i4 ) and v = (v i1 , v i2 , v i3 , v i4 ) are the spline interpolation parameters.

[0071] For a point P(x, y, z) at any length l on the cable, its coordinates can be obtained as:

[0072]

[0073] In the above formula, p is the length integral symbol.

[0074] To verify the feasibility and performance of the theory, the following simulation verification is performed. A towed sonar cable model is constructed.

[0075]

[0076] In the simulation, the cable is set to be a catenary in the vertical direction, with a catenary coefficient b = 3. In the horizontal direction, it is a multi-frequency sine superposition curve, with an amplitude parameter a = 0.2 and a frequency parameter f = 0.5π. The cable length L = 7. The underwater towed sonar cable structure and its top and side views are shown in Figure 5 and Figure 6 The circles in the figure are nodes, approximately uniformly distributed (with an interval of about 0.2), and the number of nodes n = 21. Considering that the positioning error is proportional to the length of the cable, the length unit is not particularly limited in this simulation.

[0077] First, to verify the feasibility of the algorithm, it is assumed that the node measurement accuracy is high, and the attitude measurement error of each node is 0.1°. The installation position of the end sonar is 6.37 units of length away from the starting point.

[0078] The cable gradient fitting function curve based on MEMS nodes is shown in Figure 7 , Figure 7 (a), (b), and (c) show the gradient fitting in the x, y, and z directions, respectively. The cubic spline interpolation has good restoration effect in each direction. The error after the entire cable is constructed is shown in Figure 8 The cable shape construction based on node attitude has good positioning effect, with an error of less than 0.02, about 0.135% of the rope length. In this experiment, the positioning error at the beginning and end of the cable grows faster in the x direction. This is because the cable shape is set to have large horizontal fluctuations, and the gradient of the cable in the x direction changes sharply, so the cubic spline interpolation has slightly poor agreement at the beginning and end.

[0079] The number of nodes is also a factor affecting the positioning accuracy. The more the number of sampling nodes, the more the function constructed will match the actual situation. However, the number of nodes is limited from the cost aspect, and therefore the influence of the number of nodes on the positioning accuracy needs to be evaluated. On the basis of the above experiment, the number of measurement nodes is reduced from 21 to 11, and the gradient prediction result is as shown in Figure 9 Fig. 3, (a), (b), (c) correspond to the gradient prediction of the xyz axis respectively. Figure 7 In comparison, the reduction in the number of nodes has a significant impact on the gradient prediction, especially in the x direction, which originally has a large change, and the result after interpolation has a large deviation from the actual situation. This also affects the shape construction of the cable, as shown in Figure 10 Fig. 4, the average error is enlarged by 6 times.

[0080] If the number of measurement nodes is increased to 41, it can be found that the gradient prediction and the positioning estimation error do not increase significantly, Figure 11 The error of the cable shape construction under different numbers of nodes is compared. This shows that excessive pursuit of the number of nodes not only does not increase the cost, but also the effect increases slowly. As long as the gradient function prediction is accurate, good construction accuracy can be obtained, which requires the number of nodes to be greater than the number of gradient change extremes and to be uniformly distributed in the characteristic position, so as to restore the gradient change with the least number of nodes. In this simulation, n = 21 is relatively economical and effective.

[0081] Finally, the influence of the IMU accuracy of the measurement node on the measurement is compared. The IMU of the measurement node usually uses a cheap and small MEMS sensor, and therefore the attitude accuracy is not high. In the above, the attitude accuracy of 0.1° is usually difficult to achieve by MEMS, especially in the heading based on the magnetometer. Conservatively, the horizontal attitude error is set to 0.5°, the heading error is 5°, and the number of nodes n = 21.

[0082] The gradient prediction result and the positioning estimation error are as shown in Figure 12 and Figure 13 Fig. 6, Figure 12 (a), (b), (c) are the gradient prediction of the xyz axis respectively. It can be seen that as the sensor accuracy decreases, the gradient function prediction error also increases, and further causes the cable positioning estimation to be less accurate. The average error is 0.025, and the percentage is 0.383%, which is one order of magnitude lower than that in the high-precision state simulation. Especially in the x direction, the error is larger than that in the other two directions, and the gradient distortion in this direction is also more serious, which is caused by the insufficient heading accuracy of the magnetometer, while the attitude accuracy measured by the accelerometer in the other two directions is slightly higher, and therefore the error is smaller.

[0083] The simulation test comparison of four groups of different accuracy IMUs is as shown in Figure 14As shown, the cable shape construction accuracy improves with the improvement of IMU accuracy. Even under the condition of 1° horizontal attitude error and 10° heading error, the average accuracy can still be better than 1%. This means that 21 low-precision sensors can be placed on a 1km underwater cable to achieve meter-level positioning.

[0084] The present application proposes a shape reconstruction and end positioning method based on gradient distribution prediction for the problem of underwater shape uncertainty of mooring cables in applications such as buoys and towed platforms. This method can predict the gradient change of the flexible structure only by using low-cost MEMS sensors distributed on the cable, and then complete the shape reconstruction of the cable. This makes the displacement of the underwater mooring cable be calculated in real time, and does not require complex solutions and expensive equipment. It provides an effective error compensation means for underwater detection and positioning equipment self-positioning. Comparative tests show that this method is feasible and can construct the shape of the freely curved cable underwater. The influence of the number of devices and device accuracy on the final shape construction and end positioning is discussed. The results show that a certain number (not too many) of node sensors can solve the construction of most underwater cable shapes, and low-precision sensors can also achieve prediction and construction. The positioning error of a 1k cable is only 18m, which can meet the use requirements of most scenarios. This method can solve the problems of buoy sonar wet end positioning, towed sonar structure reconstruction, semi-floating weapon underwater self-positioning, etc. in the industrial field, and can also provide non-line-of-sight measurement solutions for space measurement and other non-underwater environments.

[0085] Based on the same technical concept as the method embodiment, the present application also provides a flexible cable shape construction and end positioning system based on gradient distribution prediction, comprising:

[0086] A node attitude calculation module is configured to obtain attitude data of each installation position based on the inertial measurement units installed in a distributed manner on the cable, and solve the attitude matrix of the position node based on the attitude data.

[0087] A gradient definition and conversion module is configured to define the length direction of the cable from the starting end to the end as the gradient direction, λ as the unit gradient vector, i.e. the coordinate change caused by the change of the unit length cable, and obtain the projection coordinates of the unit gradient vector in the navigation coordinate system based on the attitude matrix and the projection coordinates of the unit gradient vector λ in the carrier coordinate system λ b . n represents the navigation coordinate system, and b represents the carrier coordinate system.

[0088] A gradient change model construction module is configured to establish a continuous cable structure model of any shape based on the continuity of the cable, and express the coordinates of any point on the cable as a continuous function about the rope length l: Wherein, X(l), Y(l), Z(l) are x coordinate, y coordinate, z coordinate of the cable at any length l respectively, is a gradient change function, and a relationship between a unit gradient vector and the gradient change function is established according to the definition of

[0089] The solving calculation module is configured to predict the gradient change function of the cable by using a cubic spline difference method, and to restore the underwater flexible shape of the cable by length integration according to the cable structure model, and to position each point on the cable and the tail end.

[0090] It should be understood that the flexible cable shape construction and tail end positioning system based on gradient distribution prediction in the embodiments of the present application can realize all the technical solutions in the above method embodiments, and the functions of each functional module can be realized according to the methods in the above method embodiments, and the specific implementation process can be referred to the related description in the above embodiments, which will not be described here.

[0091] The present application also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the program is executed by the processor to realize the steps of the flexible cable shape construction and tail end positioning method based on gradient distribution prediction as described above.

[0092] The present application also provides a computer readable storage medium having a computer program stored thereon, characterized in that the computer program is executed by the processor to realize the steps of the flexible cable shape construction and tail end positioning method based on gradient distribution prediction as described above.

[0093] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, device (system), computer device or computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0094] The present application is described with reference to flowcharts according to the method of the embodiments of the present application. It should be understood that each flow in the flowchart and the combination of the flows in the flowchart can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a method for implementing the functions described in the flowcharts. Figure 1an apparatus that performs the function specified in the flow or flows.

[0095] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flow Figure 1 an apparatus that performs the function specified in the flow or flows.

[0096] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 an apparatus that performs the function specified in the flow or flows.

Claims

1. A method for constructing the shape and locating the end of a flexible cable based on gradient distribution prediction, characterized in that, Includes the following steps: Attitude data at each installation location is acquired using inertial measurement units distributed on the cable, and the attitude matrix of the position node is solved based on the attitude data. The gradient direction is defined as the length of the cable from the start to the end. The unit gradient vector represents the coordinate change caused by a change in the length of the cable, based on the attitude matrix. and unit gradient vector Projected coordinates calibrated in the carrier coordinate system This yields the projected coordinates of the unit gradient vector in the navigation coordinate system. , Indicates the navigation coordinate system. Indicates the carrier coordinate system; Based on the continuity characteristics of cables, a cable structure model with arbitrary shape and continuity is established, and the coordinates of any point on the cable are represented as a continuous function with respect to the cable length l: ,in, , , For any length of cable The x, y, and z coordinates of the location , , Let be the gradient change function, according to The definition establishes the relationship between the unit gradient vector and the gradient change function. ; The gradient change function of the cable is predicted by the cubic spline interpolation method. Then, based on the cable structure model, the underwater flexible shape is restored by integrating the cable length, and the points on the cable and its end are located.

2. The method according to claim 1, characterized in that, Attitude data at each installation location is acquired using inertial measurement units (IMUs) distributed along the cable. The attitude matrix of each location node is then calculated based on this attitude data, including: Acquire the acceleration at the installation position measured by the inertial measurement unit. Angular increment and magnetic vector ,Depend on and Calculate the static pose of the location node, node The attitude matrix is ​​represented as Then we have: , where g refers to Earth's gravity, m refers to the geomagnetic vector at that location, and the superscript n of g and m indicates the projection in the n-frame; The nodes are solved using the two-vector attitude determination principle. pose matrix ; The nodes are calculated according to the following formula. Horizontal misalignment angle in the b-series : ,in Represents the attitude matrix The transpose of the third row vector; Obtain the calculated value of the misalignment angle Then, combined with the gyroscope output For calculating the attitude matrix Update and correct: ； in, The corrected attitude matrix, where I is the identity matrix. This indicates that an antisymmetric matrix transformation is performed on the vector within the parentheses.

3. The method according to claim 1, characterized in that, Unit gradient vector Projected coordinates calibrated in the carrier coordinate system Represented as: ； In the formula and This represents the angular error between coordinate systems along the x-axis and z-axis.

4. The method according to claim 1, characterized in that, Predicting the gradient change function of a cable using the cubic spline interpolation method includes: ； ； ； in, , and These represent the projections of the cable gradient change function onto the three coordinate axes. , and These are the interpolation parameters for each spline.

5. The method according to claim 4, characterized in that, The underwater flexible shape is reconstructed by integrating the cable length, including: For any length of cable Point at The coordinates are: ； in The coordinates of the starting end of the cable. It is the symbol for length integral.

6. The method according to claim 1, characterized in that, The inertial measurement units, which are distributed on the cable, use accelerometers and gyroscopes made up of MEMS sensors.

7. The method according to claim 1, characterized in that, The i-th position node on the cable The relationship between the unit gradient vector and the gradient change function at a given point is as follows: ； , It is a node The projection of the unit gradient vector at a given location onto the n-frame and b-frame.

8. A flexible cable shape construction and end-positioning system based on gradient distribution prediction, characterized in that, include: The node attitude calculation module is used to acquire attitude data of each installation position based on inertial measurement units distributed on the cable, and to solve the attitude matrix of the position node based on the attitude data. The gradient definition and transformation module is used to define the gradient direction along the length of the cable from the start end to the end end. The unit gradient vector represents the coordinate change caused by a change in the length of the cable, based on the attitude matrix. and unit gradient vector Projected coordinates calibrated in the carrier coordinate system This yields the projected coordinates of the unit gradient vector in the navigation coordinate system. , Indicates the navigation coordinate system. Indicates the carrier coordinate system; The gradient change model building module is used to establish a continuous cable structure model of arbitrary shape based on the continuity characteristics of the cable, and to represent the coordinates of any point on the cable as a continuous function of the cable length l: ,in, , , For any length of cable The x, y, and z coordinates of the location , , Let be the gradient change function, according to The definition establishes the relationship between the unit gradient vector and the gradient change function. ; The solution calculation module is used to predict the gradient change function of the cable using the cubic spline interpolation method, and then, based on the cable structure model, to reconstruct the underwater flexible shape by integrating the cable length, as well as to locate each point on the cable and its end.

9. A computer device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the method for constructing and positioning flexible cable shapes based on gradient distribution prediction as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for constructing and positioning the flexible cable shape based on gradient distribution prediction as described in any one of claims 1-7.

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