Cooperative method of submarine cable laying robot and optical cable laying ship

Abstract

The invention relates to a cooperation method for a submarine cable laying robot and an optical cable laying ship, and the method comprises the steps: setting a target route and a tension control interval at a ship end, and setting a task path at a robot end; the two parties respectively collect state data and establish state space models, and predict future trajectory and tension change trend; the robot and the ship exchange prediction information in real time as mutual constraint input; the robot side judges whether tension overrun or path conflict exists or not, and if yes, a local path is planned again, and prediction information is corrected; the ship side judges whether the cable laying rhythm is not matched or the tension early warning risk exists, and if yes, the navigational speed and the cable laying strategy are adjusted; and the two parties re-execute predictive control based on the corrected information to generate a final control quantity, and enter a next round of control cycle. According to the invention, by introducing a model prediction control mechanism based on double-end state prediction, tension dynamic adjustment in the submarine cable laying process is realized, and the stability and precision of operation are effectively improved.

Description

Technical Field

[0001] The present application relates to the field of submarine optical cable laying, and in particular to a method for coordinating a submarine cable laying robot with an optical cable laying vessel. Background Art

[0002] During the laying of submarine optical cables, the traditional operation mode usually relies on independent cable release operations by ships, supplemented by simple remote-controlled underwater equipment for path monitoring. However, with the development of deep-sea communications, energy, and sensing systems, the complexity of submarine terrain and the laying accuracy requirements have increased significantly. Traditional single-unit operation methods are prone to problems such as cable over-tension, floating, or dragging when dealing with complex terrain (such as deep-sea trenches, fault zones, and the interface between soft and hard terrain), which can lead to risks such as cable fatigue fracture, positioning deviation, and even construction failure.

[0003] To address these challenges, a master-slave collaborative laying system has been developed in recent years. In this system, the mother ship is responsible for overall propulsion and cable release, while auxiliary robots provide path guidance, tension adjustment, and localized intervention on the seabed. However, existing master-slave systems often employ sequential control strategies, where robots passively respond to ship decisions or rely on pre-set mission scripts for unidirectional execution. This makes it difficult to cope with real-time dynamic terrain changes, environmental disturbances, or sudden conflicts. This is particularly true during ship course adjustments or operations in confined waters, where the lack of a collaborative mechanism based on future state predictions makes it very easy for problems such as rhythm mismatch, sudden tension changes, or trajectory interference to occur. Summary of the Invention

[0004] In order to reduce the risk of cable damage caused by rhythm mismatch, path conflict or tension nonlinear disturbance in complex operating sea conditions, the present application provides a collaboration method between a submarine cable laying robot and an optical cable laying vessel.

[0005] In a first aspect, the present application provides a method for coordinating a submarine cable laying robot with an optical cable laying vessel, which employs the following technical solutions: A method for coordinating a submarine cable laying robot and an optical cable laying vessel, comprising the following steps: S1. The ship sets the target route, initial speed, and tension control range. The robot sets the current task type and simultaneously sets the control period T and the prediction time domain length N. S2. The ship and the robot collect data and establish their respective state-space models, executing a new round of predictive control cycles to derive trajectory and tension prediction information for the next N steps. S3. The ship and the robot transmit their respective prediction information to each other as constraint inputs for the other's state space model; S4. The robot determines whether the predicted trajectory poses a risk of excessive tension or conflicts with the vessel's trajectory. If so, it replans the local path and corrects the trajectory and tension prediction information. S5. The vessel determines whether the predicted cable-releasing strategy does not match the robot's predicted speed or whether the tension exceeds the warning threshold. If so, the vessel adjusts the speed and cable-releasing rhythm and corrects the trajectory and tension predictions. S6. The ship and the robot re-execute model predictive control based on each other's revised trajectory prediction information and tension prediction information to generate the final optimized control variable; S7. The ship and robot adjust their attitude, speed, and cable-releasing strategy based on the final optimized control variable, and use the current state feedback as the initial input of the state-space model in the next control cycle, entering a new round of control loops from S2 to S6.

[0006] By employing this technical solution, and based on a multi-round prediction and feedback mechanism, a collaborative closed-loop control of trajectory, tension, and cable payout behavior is achieved under different control entities at both ends. The design principle of this approach is to construct state-space models independently, incorporate trajectory and tension information within the prediction time domain, and exchange state prediction data within the control cycle, enabling each model to consider the other's behavior as a constraint or boundary input during prediction.

[0007] This collaborative mechanism is effective in two ways. First, when the ship's speed fluctuates due to waves or navigation adjustments, the robot can proactively adjust its speed and attitude based on the ship's predicted trajectory to avoid sudden increases in cable stress. Second, when the robot needs to temporarily adjust its path to avoid obstacles or reduce speed, the ship can instantly receive its predicted feedback and adjust the cable release rhythm to prevent cable tangles, floating, or low tension caused by excessive cable release.

[0008] Overall, by constructing a control structure centered on state prediction and supported by bilateral feedback, this solution can significantly reduce the risk of cable damage caused by rhythm mismatch, path conflict, or nonlinear tension disturbance in complex sea conditions, and improve path consistency and operational stability during long-term continuous laying.

[0009] Optionally, the S1 includes the following steps: S11. The vessel loads the mission planning data, including the track point sequence, target depth, obstacle area markings, and rhythm control area, based on the preset submarine cable planning path. S12. The vessel determines the initial heading angle, speed range, and preset tension control range; S13. The robot loads the current task type as a fault location task or a terrain-following cable laying task; S14. The ship and the robot jointly set the time window length N and the duration of each cycle T used for predictive control and establish communication.

[0010] By adopting the above technical solution, based on the unified parameter setting and trajectory information loading in the mission initialization phase, it is ensured that the two models use the same mission boundary conditions and time reference in the subsequent predictive control process, thus avoiding control strategy deviation and improving path prediction consistency.

[0011] Optionally, the S2 includes the following steps: S201. The robot collects real-time posture information, depth information, terrain contour information, current speed and acceleration, and current tension data; S202. Construct the current state variable and the historical state variable into an input vector; S203. Establish the robot's predicted state space model x r (t+1)=f r (x r (t),u r (t)); S204. Deducing the robot's posture trajectory in the next N steps based on the state model And use terrain features as prediction reference boundaries; S205. Predict the robot's tension change trend sequence based on the current task scenario

[0012] By adopting the above technical solution, by constructing a state space model on the robot side and using terrain information as boundary input, the foresight of its trajectory planning and tension prediction is enhanced, enabling the robot to have the ability to actively avoid risks and reduce tension in advance when paving tasks close to complex terrain.

[0013] Optionally, the S2 includes the following steps: S211. The vessel collects the current latitude and longitude position, speed, heading angle, current cable release speed, current cable tension, and the robot's real-time relative position and movement trend in real time; S212. Construct the current state variable and the historical state variable into an input vector; S213. Construct the ship's predicted state space model x s (t+1)=f s (x s (t),u s (t)); S214. Deducing the ship's position trajectory in the next N steps based on the state model S215. The task path, the track point sequence and the relative position of the robot are used as the prediction reference boundary; S216. Predict the ship's heading, speed, and tension change trend sequence for the next N steps

[0014] By adopting the above technical solution, the ship side introduces a fusion modeling of the robot's position, trend and its own tension, so that its trajectory prediction has the ability to perceive the behavior of the collaborative object, thereby improving the targetedness of the cable-releasing strategy and the accuracy of the tension control response.

[0015] Optionally, S4 includes the following sub-steps: S41. Set tension threshold T th , if present: Make T(t+k)>T th , it is determined that there is a risk of tension exceeding the limit; S42. Calculate the tension growth rate index If ΔT>δ T , it is determined to be a potential tension mutation risk; S43. Calculate the relative distance d between the ship and the robot at each moment in the future k =|x r (t+k)-x s (t+k)|, if present: It is judged as a path conflict, where d max is the maximum relative distance within the controllable tension range, θ diff (·) is the angle deviation; S44. If there is a risk of tension exceeding the limit, a potential risk of tension mutation, or a path conflict, replan the local path and update the predicted trajectory and tension sequence.

[0016] By adopting the above technical solution, the potential risks are triggered and judged using the dual criteria of tension threshold and spatial constraint, so that the system can intervene before the risk actually occurs, which has the effect of avoiding tension excess or trajectory conflict in advance and improving laying safety.

[0017] Optionally, the S44 includes the following sub-steps: S441. Preset path search window in front of the robot's current position, extract the current position to the future M meters of passable terrain area; S442. Generate multiple candidate path segments P1, ..., P n , each path satisfies the terrain traversability constraint, where each path P i Expressed as a set of continuous state point sequences {x i (t+1),…,x i (t+N)}; S443. For each candidate path P i, construct a multi-objective path evaluation function J(P i )=α1·D track (P i )+α2·R terrain (P i )+α3·T max (P i )+α4·S sync (P i ), where D track (P i ) is the average distance away from the original path; R terrain (P i ) is the slope risk of the terrain the path passes through; T max (P i ) is the maximum tension predicted along the path; S sync (P i ) is the degree of coordination between the path and the ship’s trajectory in time and space; S444. Select the path P with the smallest evaluation function opt As a final alternative path; S445. Select the path P opt Input to the robot's state-space model: The constraint is x r (t+k)∈P opt ; S446. Based on P opt A new round of trajectory and tension prediction is performed to obtain an updated trajectory prediction sequence and updated tension prediction sequence S447. Update auxiliary parameters related to path planning; S448. The data is transmitted back to the ship to participate in the next round of collaborative optimization.

[0018] By adopting the above technical solution, when risks occur, local closed-loop correction can be achieved through path replanning and tension update prediction. Under the constraint of effective path passability, an optimized alternative path that takes into account terrain, tension and coordinated rhythm can be selected, thereby enhancing the robot's path adaptability.

[0019] Optionally, S5 includes the following sub-steps: S51. Obtain the forward velocity sequence at each moment in the robot's predicted trajectory: V r (t+k), k=1…N; S52. Obtain ship's predicted cable-releasing speed sequence: V s cable (t+k), k=1…N; S53. Calculate the difference between the two at each prediction step: Δv k =V s cable (t+k)-V r (t+k), if present: It is determined that the cable release rhythm does not match the robot; where v th is the maximum acceptable speed difference threshold; S54. Obtain the predicted tension sequence at the ship end If present: or It is considered that there is a risk of sudden increase in tension or it is about to exceed the limit; where T is the upper limit of tension warning (usually lower than the tension limit warn T max ), δT is the tension change rate threshold.

[0020] S55. If it is determined that the cable release rhythm does not match the robot, or if it is believed that there is a risk of a sudden increase in tension or that the tension is about to exceed the limit, the objective function is optimized, wherein the objective function is optimized as min(β1·(v s cable -V r ) 2 +β2·ΔT 2 +β3·(θ sync ) 2 ), v s is the ship speed, ψ s is the heading angle, v scable is the cable release speed, β1·(v scable -V r ) 2 Used to constrain the cable rhythm fitting robot, β2·ΔT 2 To suppress tension fluctuations, β3·(θ sync ) 2 Used to control the deviation from the robot's heading; S56. Update the control quantity Input the ship end state space model: To re-predict heading and speed trajectory and tension change trend

[0021] By adopting the above technical solution, by comparing the robot's predicted speed with the ship's cable-releasing speed sequence and judging the tension warning status, feedback drive of the ship's control behavior is achieved, thereby ensuring that the movement states of the two are continuously synchronized in a dynamic environment, avoiding local cable breakage or accumulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1A flowchart illustrating a method for coordinating a submarine cable laying robot and an optical cable laying vessel according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0023] The present application will be further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application.

[0024] In the following description, for the purpose of explanation, many specific details are set forth in order to provide a thorough understanding of the inventive concepts. Some of the figures in the drawings of the present disclosure, which are part of this specification, represent structures and devices in block diagram form to avoid making the disclosed principles complicated and obscure. For the sake of clarity, not all features of an actual implementation are necessarily described. In addition, the language used in this disclosure has been selected primarily for readability and instructional purposes and may not have been selected to delineate or limit the subject matter of the invention, thereby resorting to the necessary claims to determine such inventive subject matter. References in this disclosure to "one embodiment" or "an embodiment" mean that the specific features, structures or characteristics described in conjunction with that embodiment are included in at least one embodiment, and multiple references to "one embodiment" or "an embodiment" should not be understood to necessarily all refer to the same embodiment.

[0025] Unless expressly limited, the terms "a", "an" and "the" are not intended to refer to a singular entity, but rather to include a general class of which a specific example may be used for illustration. Thus, the use of the term "a" or "an" may mean any number of at least one, including "one", "one or more", "at least one", and "one or more than one". The term "or" means any of the alternatives and any combination of the alternatives, including all, unless the alternatives are expressly indicated to be mutually exclusive. The phrase "at least one of" when combined with a list of items refers to a single item in the list or any combination of the items in the list. The phrase does not require all of the listed items unless expressly limited to that.

[0026] The embodiment of the present application discloses a method for coordinating a submarine cable laying robot with an optical cable laying vessel. Figure 1 The method includes the following steps S1-S7.

[0027] S1. The ship sets the target route, initial speed, and tension control range. The robot sets the current task type and simultaneously sets the control period T and the predicted time domain length N.

[0028] This step is used to complete the initial parameter setting, task mode loading and time synchronization of the ship and robot ends, and establish a unified predictive control framework.

[0029] First, the ship needs to set the target route, initial speed and tension control range. The target route is generated based on the pre-planned submarine cable laying path and consists of multiple track points. Each point has the target depth, heading angle and possible terrain restriction information. These data will be used as path reference items for the subsequent ship state prediction model. In implementation, the target route can be imported using the standard GeoJSON path format, and the system converts it into a discretized path node list {P1, P2, ..., P n The initial speed determines the vessel's desired propulsion speed before entering the operating section and also influences the initial setting of the tension adjustment strategy. The tension control range [T_{"{min}}, T_{"{max}}] is used to limit the dynamic tension response during cable release, ensuring sufficient traction for the robot's synchronous navigation without exceeding the cable's maximum load capacity. This tension range serves as the boundary condition input in the tension prediction model and is embedded in the vessel-side objective function weight scheduling module.

[0030] At the same time, the robot side loads the "fault location path" or "terrain tracking task" according to the task type. The former is suitable for performing current signal tracking and fine positioning when a breakpoint or signal anomaly occurs in the submarine cable line, and the latter is used for terrain-adaptive operations along a predetermined path during normal laying. The path input can be the local cable direction or the regional elevation map index, and the control system will automatically extract the pose reference sequence therein. The task type not only affects the navigation logic, but also determines the prediction item structure of the control model - the fault location task focuses more on the signal strength gradient prediction, and the terrain tracking task emphasizes the climbing angle, local slope change and wheel grip model.

[0031] Next, the ship and the robot need to collaboratively set the time window length N and the duration of each cycle T used for predictive control. T is the rolling cycle of the MPC controller, generally set between 1 and 3 seconds, and N is the step size for future state prediction. For example, setting it to 10 means that the state evolution within the next 10 cycles will be predicted. Taking the control cycle T = 2 seconds and the prediction step size N = 10 as an example, the system will continuously perform preview estimates of heading, tension, and posture in a 20-second look-ahead window as the input source for the optimization objective function. The prediction time window parameters directly affect the iteration overhead and convergence speed of the model solver, and are also an important basis for communication bandwidth scheduling and data packaging.

[0032] To support the interactive and real-time requirements of the aforementioned initialization parameters, a bidirectional communication link must be established between the vessel and the robot. This is typically achieved using the Ethernet channel within the underwater umbilical cable, supplemented by UDP or the low-latency TCP transport protocol, to ensure the stable synchronization of structured data such as position, predictions, and tension feedback. During the initialization phase, a communication handshake is performed to establish a standardized data frame format, ensuring consistent bidirectional transmission interfaces for both prediction and status data.

[0033] Specifically, S1 includes the following steps S11-S15.

[0034] S11. The vessel loads the mission planning data including the track point sequence, target depth, obstacle area marking and rhythm control area according to the preset submarine cable planning path.

[0035] S12. The ship determines the initial heading angle, speed range and preset tension control range.

[0036] S13. The robot loads the current task type as a fault location task or a terrain-following cable laying task; S14. The ship and the robot jointly set the time window length N and the duration of each cycle T used for predictive control and establish communication.

[0037] The vessel first loads the complete mission planning data based on the preset submarine cable planning path. The data includes the path's trackpoint sequence, the corresponding target depth, obstacle area annotations in the terrain information, and the rhythm control area containing variable cable release rhythm or speed segment switching prompts. These data items are parsed into path reference items and boundary inputs for the state space model. The trackpoint sequence will provide the expected state input for the target heading in the future prediction cycle, which is used to construct the model's reference trajectory x sre f (t+k); the obstacle area information is used to construct soft constraint functions or penalty factors in the subsequent prediction process, corresponding to the feasibility area under the constraints of the seabed topography; and the switching information of the rhythm control area affects the scheduling value of the expected cable release speed or tension change speed in the state model control quantity prediction process. The set initial heading angle and speed range are not used in isolation. On the one hand, they determine the initial value x of the state space model. s (t0), on the other hand, provides the upper and lower limits of the control quantity for the model predictive controller (MPC), such as the control quantity constraint set The value boundary of tension control interval [T min ,T max ] is used as a hard constraint boundary term in the tension prediction model and is embedded as an inequality constraint in the optimization problem, so that the system avoids outputting solutions that do not meet the mechanical safety requirements.

[0038] There are two main types of current tasks loaded on the robot side: one is the fault location task, and the other is the terrain following cable laying task. These two types of tasks will directly affect key components such as the state dimension, prediction target function structure, and path judgment logic in the subsequent state space model. Taking the terrain following task as an example, the state model will introduce the terrain profile height information z(x,y) as an external interference factor affecting the state transition, and the prediction target will focus on trajectory smoothness and tension stability; in the fault location task, the state transition equation needs to add the electric signal intensity gradient change. As the basis for path advancement, the position of the path target point is no longer a fixed track point sequence, but the center coordinates of the breakpoint candidate area inferred from the signal strength.

[0039] In different embodiments, the task-related data loaded during initialization may vary depending on the type of sensor. For example, a robot equipped with a water flow sensor may also initialize the current water flow velocity vector field v curr (x, y, z) as reference conditions for future attitude maintenance or thrust adjustment. For example, robots with image recognition capabilities can also load labels for bottom texture recognition areas for fine-tuning path strategies. Once imported, these data can be used as boundary inputs, control parameter corrections, or external disturbance inputs in state-space models for modeling and prediction. For example, water flow velocity can be added as an additional disturbance term to the equation of motion: the state transfer function x(t+1)=f(x(t),u(t),d(t)), where d(t) represents the environmental disturbance term.

[0040] It should be noted that the initialization data content and structure mentioned in this application are only examples used to illustrate the input dimensions and model adaptability supported by this method, and do not limit the scope of protection of the technical solution.

[0041] After completing initialization steps S11 to S14, the ship and robot each perform a single-step predictive simulation to verify that the established state-space model can converge to a feasible solution within the control cycle. This simulation includes a trajectory prediction and a tension trend prediction, outputting metrics such as whether the peak tension in the predicted trajectory is within the tension control range and whether the posture change conforms to the posture change constraints. If the predicted value exceeds the tension limit or the path does not converge, the system automatically rolls back to the initialization process and prompts for initial parameter adjustments. Simulation results also determine if there is a conflict between the control boundaries of both parties, such as whether the robot's planned path deviates beyond the ship's tension control range. Only when all test indicators meet safety, controllability, and synchronization requirements will the system enter the first formal control cycle and execute the subsequent prediction-judgment-execution process from S2 to S6, forming a truly closed-loop collaborative control.

[0042] S2. The ship and the robot collect data and establish their own state space models, executing a new round of predictive control cycles to deduce trajectory prediction information and tension prediction information for the next N steps.

[0043] In this step, the initial heading angle and speed range constitute the initial conditions for the ship's state variables, while the preset tension control range constitutes the hard constraint boundary in the model, limiting the scope of the optimizer's solution space. A state-space model is a mathematical form of describing a dynamic system. Its core is to characterize the system's current state using a set of state variables and describe how this state evolves over time under the influence of input controls through difference equations or continuous-time models.

[0044] The predictive control cycle is the controller's rolling update period. During this period, the controller uses the current state and the predictive model to predict the system's evolution trajectory over a period of time (usually N steps) into the future and generates the optimal control instructions for the current moment. This control cycle is typically 1 to 3 seconds and needs to be set based on the controller's processing speed and real-time execution requirements.

[0045] Trajectory prediction information refers to the future trajectory sequence deduced by the model given the current state and control sequence. Tension prediction information is formed by adding a tension prediction function to the state model and converting control actions into tension change responses through polynomial fitting, physical tension simulation, or machine learning models (such as BP neural networks).

[0046] For the robot side, S2 includes the following steps S201-S205.

[0047] S201. The robot collects posture information, depth information, terrain contour information, current speed and acceleration, and current tension data in real time.

[0048] S202. Construct the current state variable and the historical state variable into an input vector.

[0049] S203. Establish the robot's predicted state space model x r (t+1)=f r (x r (t),u r (t)); The essence of the state space model is to model the evolution of the control system as a set of state variables that progress over time. Its standard form is x r (t+1)=f r (x r (t),u r (t)). Where x r(t) is the state vector of the robot at time t, which includes its three-dimensional posture (such as pitch angle, roll angle, and heading angle), depth value, terrain perception result (such as the ground elevation difference 5 meters ahead), current cable tension, forward speed, vertical speed, acceleration, and tension change rate in adjacent time periods; u r (t) is the control input of the robot at that moment, such as propeller power distribution, attitude adjustment, etc. Function f r (·) is the state transfer function obtained through system identification or kinematic modeling. It can be a nonlinear model based on empirical equations or a trained small neural network to capture the effects of nonlinear disturbances.

[0050] During the implementation, the current state variable x r (t) is composed of real-time collected data, while historical state variables are state records of several control cycles in the past, such as x r (t-1),x r (t-2),…,x r (th), where h is the history window length, usually 3 to 5 control cycles. These historical states are concatenated with the current state to form a complete state input vector X r =[x r (t),x r (t-1),…,x r (th)] as the input to the predictive state space model. The historical state is introduced because the robot's dynamic response in environments with strong disturbances (such as seafloor fluctuations or tidal currents) has inertial lags. Using only the current state is insufficient to capture the true trend of the system's evolution. Introducing past state sequences can enhance the model's memory capacity and improve prediction accuracy. This modeling approach is equivalent to introducing "extended states" into the state space framework, expanding the model from a Markov state model (which relies solely on the current state) to a non-Markov prediction network with memory properties.

[0051] In specific form, if the state variables include the three-dimensional angle of posture (φ, θ, ψ), depth z, tension T, velocity v, acceleration a, and terrain height difference Δz terrain , then the current state vector is expressed as: x r (t)=[φ(t),θ(t),ψ(t),z(t),T(t),v(t),a(t),Δz terrain (t)] Add the state vectors of the three historical cycles and concatenate them to form the input vector: X r =[x r (t),x r (t-1),x r(t-2),x r (t-3)] Its dimension is 8×4=32. If a small neural network is used for state transition prediction, the input vector can be used as the input layer of the network, and the output layer of the network is the predicted state estimate for the next moment. The model structure is in Represents the neural network structure. The number of hidden layers and units can be set according to the computing power and task complexity. For example, a 2-layer fully connected network with 64 units per layer is used. If a non-neural network model is used, such as a motion equation with a perturbation term, then X r It will be used for parameter updating and adaptive parameter adjustment process.

[0052] Ultimately, the output of the predicted state space model is the robot's next state estimate, which is used to construct the future trajectory.

[0053] S204. Deducing the robot's posture trajectory in the next N steps based on the state model And the terrain features are used as the prediction reference boundaries.

[0054] This step refers to using the state space model established in the previous step to gradually predict the dynamic response of the robot under a given control sequence and generate a continuous posture trajectory sequence in the future time window.

[0055] The deduction process is based on the state vector x known at the current moment r (t) is the initial condition, and the state value of each future step is recursively calculated in a rolling manner. In each step k∈[1,N], the state is calculated by the state transfer function, that is: x r (t+k)=f r (x r (t+k-1),u r (t+k-1)) Among them, f r The state transfer function constructed in S203 can be a nonlinear system equation based on kinematics and hydrodynamics modeling, or a neural network predictor trained by machine learning. r (t+k) is the thrust, yaw rate, attitude adjustment amplitude, etc. to be optimized or temporarily given. In implementation, a baseline control sequence, such as uniform speed and uniform direction propulsion, can be set to initially generate a predicted trajectory, which is then iteratively adjusted through the optimizer.

[0056] Taking the terrain following task as an example, the current state of the robot is x r (t)=[x,y,z,φ,θ,ψ,v,a,T] The first three items are position, the next three are attitude angles, v is forward velocity, a is acceleration, and T is tension. Initially, the robot is at the beginning of a path with a continuously rising seabed slope. If the control sequence is set to a small-angle climbing propulsion (maintaining constant thruster power and slightly adjusting the attitude), the position x(t+k), attitude θ(t+k), and velocity v(t+k) calculated at each moment according to the state model will show a continuously climbing trend, ultimately forming an ascending trajectory that roughly matches the slope of the terrain.

[0057] In order to avoid the predicted trajectory entering an inaccessible area or generating dangerous behaviors that do not match the terrain profile, this step also requires the terrain feature data to be input as a reference boundary to participate in the verification and screening of the predicted trajectory. Terrain features usually exist in the form of discrete elevation points, represented as a two-dimensional scalar field Z(x,y), where each coordinate point corresponds to an elevation value. The robot will use the current predicted position coordinate x in each prediction step. r (t+k),y r (t+k) corresponds to the terrain height z terrain (t+k)=Z(x r (t+k),y r (t+k)) is compared with its own predicted depth z(t+k) to determine whether the accessibility constraint is met.

[0058] If the predicted trajectory has a step where the bottom position of the robot is lower than the terrain surface, that is, z(t+k) <z terrain (t+k)+∈, where ∈ is the ground clearance tolerance threshold, this trajectory will be assigned a higher penalty factor or directly eliminated in subsequent optimization. At the same time, the terrain slope can also be calculated from the local elevation difference to constrain the robot's maximum allowable climbing angle or turning radius.

[0059] For example, when the robot advances along the path for 20 seconds (i.e., N = 10, T = 2 seconds) and predicts that the path is located on a rock surface with a steep slope, the system will automatically extract the maximum slope value in the path segment. This is then compared to the robot's maximum stable slope (e.g., 20 degrees). If the safe upper limit is exceeded, the optimizer increases the penalty weight for that path segment in the objective function or switches to a smoother alternative path. This combination of "state prediction + terrain constraints" enables the robot to proactively assess path feasibility and avoid local obstacles.

[0060] S205. Predict the robot's tension change trend sequence based on the current task scenario

[0061] This step builds a tension prediction model that can be combined with the current task scenario to deduce the tension change trend sequence experienced by the robot in the future prediction window (length N)

[0062] Tension is a response variable generated by the interaction of multiple factors. It is not only constrained by the robot's posture and velocity, but is also significantly affected by terrain undulations, seabed obstacles, current disturbances, cable payout rate and angle, and the relative motion of the vessel. To capture these complex coupled effects, tension prediction models typically employ data-driven nonlinear modeling approaches, primarily using multi-input small neural networks or ensemble regression models.

[0063] In the specific implementation, the tension prediction model is constructed in the following form: Among them, x r (t+k) represents the state vector of the robot at step k, Δz terrain (t+k) represents the topographic gradient of the seabed at that location, θ(t+k) is the pitch angle, v(t+k) is the forward velocity, and d s (t+k) is the relative distance between the robot and the ship at that moment, and α(t+k) is the angle of the cable out of the water. All the above quantities are calculated from the trajectory prediction results completed in S204, forming a multi-dimensional feature input vector, which is then input into the trained tension prediction network. The output of this network is the predicted tension value

[0064] For example, in a terrain tracking scenario, if the robot is expected to pass through an area with significant undulations and a slope of about 15 degrees in its future predicted trajectory, and the seabed in this area is hard sandstone, the robot will experience increased propulsion resistance when climbing and fluctuations in the cable trench depth, resulting in discontinuous cable burial, which will cause the cable tension to rise rapidly within seconds. At this time, the prediction model will use the robot's current speed (such as 0.4m / s), forward acceleration (such as negative 0.1m / s) and the acceleration of the forward direction (such as negative 0.1m / s). 2 ), attitude change trend (pitch angle continues to increase), and terrain slope It is inferred that a rapid increase in tension will occur at t+5 seconds, and the prediction result is output as follows: For the ship side, S2 includes the following steps S221-S216.

[0065] S211. The vessel collects the current latitude and longitude position, speed, heading angle, current cable release speed, current cable tension, and the robot's real-time relative position and movement trend in real time.

[0066] S212. Construct the current state variable and the historical state variable into an input vector.

[0067] S213. Construct the ship's predicted state space model x s (t+1)=f s (x s (t),u s (t)); First, in S211, the ship control system collects the current dynamic and environmental status data at a fixed period, including but not limited to the longitude and latitude position P of the ship body. s (t) = [lat(t), lon(t)], speed v s (t), heading angle ψ s (t), cable release speed v sca bl e (t), real-time tension T s (t), and the relative position of the robot Δx measured by the posture sensor and the underwater acoustic positioning system rs (t), relative speed Δv rs (t). These state data represent the basis of the dynamic interaction between the ship and the robot and are the original input source for constructing the state space model.

[0068] Entering S212, in order to enable the prediction model to have time series learning capabilities, not only the current state quantity is required, but also the historical data of the previous several cycles must be introduced to form an input structure that includes time memory. Therefore, the system splices the states of the past L moments into an input vector to form an input sequence: ipt=[x s (t),x s (t-1),…,x s (t-L+1)] Where each state vector x s (t) includes the above-mentioned multiple state variables, such as: x s (t)=[v s (t),ψ s (t),v sca bl e (t),T s (t),Δx rs (t),Δv rs (t)] By constructing such a time series stacking structure, we can capture the inertial characteristics and short-term trends of state evolution and effectively enhance the stability of prediction.

[0069] In S213, the state space prediction model constructed based on this input sequence is in the form of: x s (t+1)=f s (x s (t),u s (t)) Among them, f s (·) represents the ship's dynamic function, which can be an explicit physical model (such as the acceleration equation derived from the propulsion and resistance model) or a black box model obtained through system identification (such as recursive neural network, LSTM, nonlinear autoregressive neural structure NARX, etc.), and u s (t) is the control input variable, which mainly includes the speed command, heading angle command, and cable-releasing speed change command to be adjusted in this cycle.

[0070] For example, if the NARX structure is used, the model can be formalized as: The function It is trained through historical operation data. The output of the model is the predicted state x at the next moment. s (t+1), further iterative calculation of the state sequence within the next N steps Provide a predictive basis for subsequent trajectory evaluation and tension control optimization.

[0071] For example, during the laying of submarine cables, when the robot enters a steep terrain area, the ship needs to reduce its forward speed and maintain a certain cable length payout rhythm to relieve the increase in tension. In the previous cycle, if the input of the ship is deceleration (u s (t)=-0.3m / s 2 ) maintains the heading (Δψ=0) and reduces the cable-releasing speed (-0.1m / s), the model will output the predicted future speed sequence to slow down and the tension trend to be stable, which will be reflected in the future state vector.

[0072] S214. Deducing the ship's position trajectory in the next N steps based on the state model

[0073] S215. Use the task path, the track point sequence, and the relative position of the robot as the prediction reference boundary.

[0074] In step S214, the ship side constructs the state space model x s (t+1)=f s (x s (t),u s (t)) performs trajectory deduction for the next N steps. This process is based on the current state x s(t) is used as the initial input, combined with the control input u set in the current cycle s (t), and gradually generate the pose prediction results for each moment in the future through recursion. The prediction output of each step is used as the state input for the next step, and the iterative form is: x s (t+1)=f s (x s (t),u s (t)),x s (t+2)=f s (x s (t+1),u s (t+1)),…,x s (t+N) =f s (x s (t+N-1),u s (t+N-1)) Among them, each state vector x s (t+k) contains the longitude and latitude coordinates [lat(t+k),lon(t+k)], and the heading angle ψ s (t+k), speed v s (t+k), cable release speed v sca bl e (t+k), cable tension prediction value T s (t+k) and other elements. The control quantity sequence {u s (t),u s (t+1),…,u s (t+N-1)} can be set to a constant value or the control input generated by the previous round optimization according to the current rhythm control strategy.

[0075] In S215, the obtained future pose trajectory Limited by the mission path, track point sequence and the real-time relative position information of the robot, the system introduces predicted reference boundaries for constraints to ensure that the future trajectory of the ship is not only dynamically achievable but also complies with the mission planning constraints and collaborative boundary conditions.

[0076] The mission path is a polyline trajectory consisting of preset track points [P1, P2, ..., P M ], where each point carries information such as target position, target depth, and path tangent direction. The track point sequence defines the target trajectory segment, while the rhythm control area specifies additional control requirements such as speed and tension limits within certain segments.

[0077] The reference boundary introduction method can adopt soft constraint or hard constraint. The commonly used method is to construct a virtual path tunnel, that is, the ±R range on both sides of the task path is set as the effective passage area. In the trajectory prediction process, it is required have: in represents the set of task path segments, and distance(·) represents the minimum Euclidean distance between the current position and the path.

[0078] In addition, considering the requirements of collaborative control, the current and predicted positions of the robot need to be added to the trajectory prediction reference boundary. rs (t) is used as a reference. A coordinated offset zone is constructed within each prediction step, restricting the ship to a rectangular area extending from L1 meters in front of the robot to L2 meters behind it, and W meters to the left and right. This area serves as a flexible coordination constraint to prevent the robot from exceeding the tension control coverage of the ship.

[0079] For example, if the mission path contains a water depth abrupt change section, the corresponding track point is [P 20 ,P 21 ], a straight line segment in the coordinate system, which requires the ship to pass through the segment at a speed lower than 1.2m / s and a tension no greater than 1.5kN. At this time, in the k=8th step of trajectory deduction (corresponding to 8 seconds later), the predicted trajectory point If it falls within this range, the corresponding control weight should be introduced and the v in the control input should be appropriately lowered. s (t+8) to avoid violating the constraint boundaries.

[0080] S216. Predict the ship's heading, speed, and tension change trend sequence for the next N steps

[0081] In this step, the ship side is based on its predicted trajectory And control input sequence, further predict the tension change trend in the next N steps to form a tension prediction sequence

[0082] The mathematical realization of tension prediction relies on the state-control mapping relationship of multi-variable coupling, and its core lies in establishing a tension function model. Among them, x s (t+k) represents the predicted position of the ship, u s (t+k) represents the control input (including ship speed and cable release speed), Represents the relative velocity of the robot at the predicted time step. This function reflects the mechanism by which tension changes due to the combined effects of trajectory changes, relative displacement, velocity differences, and environmental resistance.

[0083] Specifically, cable tension can usually be simplified to the sum of the following three terms: T s (t+k)=T grav (t+k)+T drag (t+k)+T sync (t+k) Among them, T grav is the vertical tension component caused by the cable's own gravity and laying depth, which can be calculated from the current water depth z(t+k) and the cable length; T drag represents the cable drag tension caused by the difference between the ship speed and the current direction, which can be modeled by the relative speed and current parameters; T sync It represents the additional tension disturbance term caused by inconsistent longitudinal or lateral motion trends between the ship and the robot, and is usually calculated from the speed difference and angle between the predicted trajectories of the two.

[0084] For example, in a mission segment, the ship is currently in a curved channel section, where the water depth drops sharply from 50m to 70m. According to the pose trajectory generated by S214 The ship will enter the water depth change area at step t+4. Due to the lag in the adjustment of the cable release speed, if the current v is maintained at step t+5 sca bl e =0.8m / s, the vertical tension of the cable will surge. At this time, the tension model is used to calculate T s (t+5)=2.1kN, and the upper limit of tension in this section is 1.8\kN. Therefore, an over-limit point appears in the tension prediction sequence, providing a pre-judgment basis for subsequent S5 determination and optimization.

[0085] In the implementation, It can be obtained by physical model calculation or data-driven model fitting. In the data-driven scenario, historical trajectory-tension pairs can be used to construct prediction functions, such as multivariate regression models or neural network structures T s =φ(x,u), where the input includes continuous state variables and control inputs within the time window, and the output is the tension sequence prediction value.

[0086] S3. The ship and the robot transmit their respective prediction information to each other as constraint inputs of the other party’s state space model.

[0087] The ship and the robot will respectively use the prediction results obtained based on their own state space models, that is, the posture trajectory prediction information within the next N steps. And the tension change trend sequence It is transmitted to the other party's control end in real time through the communication system and used as the external constraint input of the other party's state space model.

[0088] In the traditional single-model predictive control architecture, the control optimization of the system usually relies only on its own dynamic model and constraints. In the dual-end collaborative control framework of this application, the prediction and optimization of each control subject need to refer to the prediction behavior of the other party, so as to dynamically adjust its own control variables to avoid conflicts, balance tension or synchronize rhythm. For example, the state space model x constructed on the ship side s (t+1)=f s (x s (t),u s (t)), its optimization goal is not only to minimize its own control error or tension fluctuation, but also to constrain the predicted path not to deviate too far from the robot's predicted trajectory, so as to avoid problems such as tension pulling or communication loss. and It will be introduced into the control optimization model on the ship side as a prediction reference boundary or additional cost term.

[0089] Specifically, when the ship performs the next step of solving the control variables, its cost function can be expanded to the following form: Where ΔT s (t+k) is the rate of change of tension, d sr (t+k)=|x s (t+k)-x r (t+k)| is the predicted relative distance between the ship and the robot at step k. If this distance is too large, the cost function will increase the penalty value, forcing the ship to adjust its speed or direction to catch up with the robot's forward pace or reduce the risk of excessive cable tension. Similarly, the robot incorporates the ship's predictions as a state reference or speed synchronization constraint when formulating its control optimization problem.

[0090] For example, consider a specific application scenario. Suppose, at time t, the ship predicts that it will travel northeastward along a pre-set path at a speed of 1.2 m / s, with a cable-releasing speed of 0.9 m / s. Furthermore, the tension is predicted to reach 1.8 kN at step t+4. Upon receiving this prediction sequence, the robot discovers that its relative speed at the same time step is 1.0 m / s, with its path direction slightly deviating to the northeast. Continuing along this path would result in a tension growth curve that is inconsistent with that of the ship. In this case, the robot can incorporate a tension consistency constraint into its control optimization and reconstruct its cable-releasing tension model or fine-tune its path based on the ship's predicted tension curve, making the overall coordinated operation more compact and safer.

[0091] S4. The robot determines whether the predicted trajectory has a risk of exceeding the tension limit or a path conflict with the ship's trajectory. If so, the robot replans the local path and corrects the trajectory prediction information and tension prediction information.

[0092] Specifically, S4 includes the following sub-steps S41-S44.

[0093] S41. Set tension threshold T th , if present: Make T(t+k)>T th , it is determined that there is a risk of tension exceeding the limit.

[0094] S42. Calculate the tension growth rate index If ΔT>δ T , it is determined to be a potential tension mutation risk.

[0095] S43. Calculate the relative distance d between the ship and the robot at each moment in the future k =|x r (t+k)-x s (t+k)|, if present: It is judged as a path conflict, where d max is the maximum relative distance within the controllable tension range, θ diff (·) is the angular deviation.

[0096] S44. If there is a risk of tension exceeding the limit, a potential risk of tension mutation, or a path conflict, replan the local path and update the predicted trajectory and tension sequence.

[0097] In S41, the system sets a tension upper limit threshold T th , and predict tension sequence Each prediction moment in is compared and judged one by one. If there is any time step k∈[1,N] that satisfies T r (t+k)>T th , it is considered that there is a risk of tension exceeding the limit. This judgment mechanism is based on the traditional tension tolerance analysis principle and quickly captures potential over-tension points through the maximum value comparison method. In order to improve the sensitivity and foresight of the system response, S42 further introduces the tension growth rate indicator Used to detect the trend of tension mutation. When the tension growth rate of a certain continuous step in the prediction sequence exceeds the pre-set change rate threshold δ T When the tension is greater than 0.05, the system will consider that there is a risk of sudden change in tension, which may indicate that the robot's current path may pass through complex terrain, high-slope areas, or have a tendency to separate from the direction of the ship.

[0098] In addition to the tension risk, S43 further evaluates the spatiotemporal coordination between the robot and the ship in the predicted trajectory, calculating the relative spatial distance between the two at each future time step: d k =|x r (t+k)-x s (t+k)| And the heading angle difference θ can be further calculated diffk =|θ r (t+k)-θ s (t+k)|. If there exists any prediction step that satisfies d k >d max or This indicates spatial deviation between paths, potentially causing the robot to leave the tension coverage area, deviate from the paving direction, or create potential risks such as signal disconnection and coordination failure. The above three criteria (tension limit excess, tension sudden change, and path conflict) constitute the present invention's three-tiered judgment system for robot trajectory prediction evaluation, which is comprehensive and targeted.

[0099] Once any of the criteria from S41 to S43 is triggered, S44 enters the trajectory correction phase, calling the local path replanning module to re-search the current path within the window range and update the predicted trajectory and tension sequence in a linked manner. With tension sequence It will replace the original prediction output and provide a safer control reference in subsequent control cycles.

[0100] For example, in a certain task segment, the robot predicts that it will enter a terrain area with a sharp slope change in the next step t+5. The predicted tension will rise rapidly from 1.2kN to 1.9kN, exceeding the set tension limit T th =1.8kN. At the same time, the ship's trajectory shows that it will deflect to the north at step t+6, while the robot predicts that it will continue to advance eastward, resulting in the relative distance between the two at step t+7 being predicted to be d7 = 15m, which exceeds the maximum allowable controllable tension range d max =10m. At this point, the system determines that both tension and path risks exist. S44 immediately calls the search module to regenerate multiple navigable paths within the terrain area 30 meters ahead of the robot's current position. After selecting the optimal path through a multi-objective function, it updates its prediction model and transmits the correction results back to the ship in real time for coordinated adjustment.

[0101] Specifically, the S44 includes the following sub-steps S441-S448.

[0102] S441. Preset a path search window in front of the robot's current position and extract the passable terrain area from the current position to M meters in the future.

[0103] S442. Generate multiple candidate path segments P1, ..., P n , each path satisfies the terrain traversability constraint, where each path P i Expressed as a set of continuous state point sequences {x i (t+1),…,x i (t+N)}.

[0104] In S441, the system presets a path search window of a certain length in front of the robot based on its current spatial posture state. The value is usually 20 to 30 meters in the future. The specific length can be dynamically adjusted according to the task requirements and the complexity of the seabed terrain. The search window is based on the current velocity vector direction as the main axis to construct a conical or rectangular area, and the local terrain information in the area is intercepted from the built three-dimensional terrain map. The terrain surface is then sampled point by point according to the grid resolution in the map to determine whether each grid unit meets the passability conditions, such as the slope is lower than the threshold, there are no fault obstacles, and the area is not covered by underwater buildings. Finally, a boundary set of a spatially feasible area is obtained, which is recorded as It is the range of traversable space allowed for subsequent path searches.

[0105] Entering S442, the system uses a sampling-based path generation algorithm in Ω feasible Construct multiple candidate paths {P1,…,P n}. Each path P i It consists of a continuous sequence of state points in the form of: P i ={x i (t+1),x i (t+2),…,x i (t+N)} where each x i (t+k) is a set of elements in the state space, containing the robot's 3D position (x, y, z), velocity v, and attitude angles (θ, φ, ψ) at step t+k. Path generation can use the A* algorithm, avoiding impassable areas while maintaining a close fit to the target path shape. Alternatively, the RRT (Rapidly-Exploring Random Tree) algorithm can be used to construct trajectory segments in the search space that satisfy maximum steering angle and maximum acceleration constraints.

[0106] For example, in a scenario with an underwater protrusion 10 meters ahead, the original trajectory would cross the protrusion. The robot would then determine that there is a risk of excessive tension at step t+4. The search window is now set to 25 meters ahead, and the system removes the protrusion from the terrain map, generating a valid grid set at a resolution of 0.5 meters. Five candidate paths are then constructed using a sampling strategy. Path P_2 bypasses the protrusion and turns along a gently sloping area. This pathpoint sequence satisfies all kinematic and terrain feasibility constraints, making it a candidate for the next evaluation phase.

[0107] S443. For each candidate path P i , construct a multi-objective path evaluation function J(P i )=α1·D track (P i )+α2·R terrain (P i )+α3·T max (P i )+α4·S sync (P i ), where D track (P i ) is the average distance away from the original path; R terrain (P i ) is the slope risk of the terrain the path passes through; T max (P i ) is the maximum tension predicted along the path; S sync (P i ) is the degree of coordination between the path and the ship trajectory in time and space.

[0108] S444. Select the path P with the smallest evaluation function opt As a final alternative path.

[0109] Path evaluation function J(P i ) consists of four weighted indicators, reflecting the candidate path P i The mathematical expressions for the deviation from the original mission path, the risk level of the terrain traversed by the path, the peak tension induced along the path, and the temporal and spatial consistency between the path and the predicted trajectory of the ship are as follows: J(P i )=α1·D track (P i )+α2·R terrain (P i )+α3·T max (P i )+α4·S sync (P i ) Among them, D track (Pi ) represents the path P i The average Euclidean distance between each point in the original target path is used to measure the degree of path deviation; R terrain (P i ) reflects the average or maximum slope of the terrain in the area where the path passes, and is used to evaluate terrain risk; max (P i ) is the maximum value of the tension prediction value of each step in the predicted trajectory corresponding to the path, reflecting the impact of the path on the tension safety; S sync (P i ) is constructed based on the relative position error and relative heading difference between the robot and the ship at each prediction step, and is used to measure the collaborative performance of the path.

[0110] For example, in one scenario, the robot is located at the edge of a submarine ridge. The original path would cross a slope approximately 3 meters high, causing the estimated tension to reach 820N at step t+5, exceeding the tension threshold. In step S442, the system constructs five candidate paths. Path P1 is the shortest but requires crossing a high slope. Path P2, which detours along the eastern side of the ridge, is longer but has a gentler slope. Path P3 deviates approximately 1.2 meters downward from the original path to avoid the risk zone. The evaluation function calculates each path as follows: J(P1)=1.8, mainly due to T max =820N; J(P2)=1.3, although the path is long but R terrain and T max Lower; J(P3) = 1.1, achieving a balance between deviation and terrain, and good synchronization; J(P4)=1.6, poor synchronization; J(P5)=1.5, the path is too far, D track Larger.

[0111] Finally, the system selects P according to the minimum evaluation function value. opt =P3, and input it as an alternative path into the next step of model prediction and control process.

[0112] S445. Select the path P opt Input to the robot's state-space model: The constraint is x r (t+k)∈P opt .

[0113] S446. Based on P opt A new round of trajectory and tension prediction is performed to obtain an updated trajectory prediction sequence and updated tension prediction sequence

[0114] After completing the optimal candidate path P opt After screening, the core work of S445 is to formally constrain the path into the robot's state space model, so that the robot can gradually advance along the path in the next control cycle. To achieve this constraint, the path P opt The discrete state point sequence {x (t+1) ,x (t+2) ,…,x * (t+N)} is embedded into the Model Predictive Control (MPC) framework to form the target evolution trajectory of the state variables. The original state space model of the robot is: x r (t+1)=f r (x r (t),u r (t)) Among them, x r (t) is the current state, including the robot's position, posture, speed and other factors, u r (t) is the control input, which usually includes thrust, rudder angle, etc. To ensure that the trajectory strictly follows P opt , soft constraints or hard constraints are introduced in the predictive control optimization process: In actual calculation, the state x of each step of the predicted trajectory is r (t+k) and path point x * The Euclidean distance of (t+k) is controlled within the tolerable error ε, that is: |x r (t+k)-x * (t+k)|≤ε Such constraint design ensures the feasibility of the trajectory and at the same time solves the control sequence {u r (t),u r (t+1),…,u r (t+N-1)}, the MPC solver based on quadratic programming can be used to optimize the control quantity.

[0115] After entering S446, the robot uses P opt As a preset path, the trajectory and tension prediction process is re-executed. Essentially, the new path sequence is input into the prediction model, and the existing state-space model and control input are combined to simulate the system's dynamic response over a period of time. Regarding tension prediction, a mechanical or empirical model is used to construct a tension estimation function based on the interaction between each step in the path and the terrain, the robot's propulsion acceleration, posture changes, and relative motion with the ship: This function represents the tension value T predicted by the robot at the t+kth prediction moment. r (t+k), the calculation result of which is a multivariable nonlinear function Decision. Among them, x r (t+k): Represents the robot's position at step t+k, including its three-dimensional position (e.g., longitude, latitude, depth) and attitude (e.g., pitch, roll, and heading). This parameter determines the spatial geometry of the cable at that position and has a direct impact on the cable's curvature and tension distribution.

[0116] v r (t+k): The robot's forward velocity at step t+k. Its changes directly affect the cable's pulling rate. If the robot accelerates or decelerates suddenly without releasing the cable simultaneously, it can easily cause a sudden increase in tension or cable slack.

[0117] Indicates the current position x r The gradient of the seafloor topography at (t+k) (i.e., topographic slope) is typically calculated from the gradient of the topographic elevation function Z(x) with respect to a two-dimensional horizontal coordinate. When ascending or descending a steep slope, the cable attachment angle and gravity distribution change, significantly disturbing the tension distribution. For example, gravity-assisted pulling reduces tension when descending a slope, while increasing the tension load when ascending a slope.

[0118] x s (t+k): Represents the vessel's position at step t+k, reflecting its spatial relationship with the robot. Because the optical cable connects the vessel and the robot, the distance and angle between them directly affect the tension. For example, if the vessel drifts more relative to the robot, the cable stretches more, increasing the tension.

[0119] function These can be analytical models based on physical laws or regression models trained through data-driven training, such as neural networks or Gaussian process regression models. Analytical models are typically based on mechanical equilibrium formulas for tension, such as the catenary model of the cable, bending stiffness, and gravity terms. Data-driven models, on the other hand, use extensive historical operational data to fit the nonlinear mapping relationship between input parameters and tension output.

[0120] For example, if the tension distribution mechanics model is used It can be described by the following simplified formula: T r (t+3)=T g +T v +T θ in: T g is the gravity tension component along the terrain slope direction, and the calculation formula can be T g =ρ·g·L·sin(θ z ), where ρ is the unit mass of the cable, L is the cable length, and θ z is the slope angle; T v is the velocity tension term caused by the asynchrony between the robot speed and the ship’s cable-releasing speed; T θ It is the correction term of the lateral tension caused by the spatial angle.

[0121] Finally, we get a new predicted trajectory sequence: And the tension prediction sequence: S447. Update auxiliary parameters related to path planning.

[0122] S448. The data is transmitted back to the ship to participate in the next round of collaborative optimization.

[0123] Auxiliary parameters include path risk weight parameters, key node location indexes, path curvature change, tension prediction rate of change scalars, terrain complexity indicators, and the corresponding environmental confidence score for the path, which are used to support subsequent control optimization and collaborative path coordination calculations. These auxiliary parameters include but are not limited to path execution tags, control granularity adjustment coefficients within the prediction cycle, and tension weight dynamic factors, all of which are used to ensure path execution consistency and control strategy consistency within subsequent control cycles. For example, after reselecting a path, the system will synchronously update the current path number, path segment index, and its alignment within the global task path, and remap the start and end time windows of the path segments to the global timeline. In addition, the parameters used to construct the weight matrix in the predictive control model must also be updated accordingly. For example, the weight of the tension prediction error term, \rho_T, is increased to 1.5 times the original weight to strengthen the tension stability constraint in the initial section of the path, thereby avoiding the initial tension jump caused by switching paths.

[0124] After completing the above parameter update, S448 will re-predict the trajectory sequence and tension change trend The data is transmitted to the ship’s control system in real time via a communication link. After receiving the data, the ship uses it as the reference boundary and constraint input of the state space model in the next predictive control cycle to construct the constrained optimization problem on the ship. For example, if the robot feedback It is shown that the tension will rise to 860N at step t+5, which is close to the upper limit of the safety tension set by the ship. The ship will automatically introduce tension smoothing constraints when optimizing its cable release speed trajectory, giving priority to the speed scheme with smaller tension fluctuations. In terms of path synchronization, the ship will also The robot trajectory trend in the robot is readjusted, and its own heading change amplitude and inflection point buffer distance are readjusted to avoid the cable release rhythm jump caused by excessive posture adjustment in a short period of time.

[0125] S5. The ship determines whether the predicted cable-releasing strategy does not match the robot's predicted speed or whether the tension exceeds the warning threshold. If so, the ship adjusts the speed and cable-releasing rhythm and corrects the trajectory prediction information and tension prediction information.

[0126] Specifically, the step S5 includes the following sub-steps S51-S56.

[0127] S51. Obtain the forward velocity sequence at each moment in the robot's predicted trajectory: V r (t+k),k=1…N.

[0128] S52. Obtain ship's predicted cable-releasing speed sequence: V sca bl e (t+k),k=1…N.

[0129] S53. Calculate the difference between the two at each prediction step: Δv k =V sca bl e (t+k)-V r (t+k), if present: It is determined that the cable release rhythm does not match the robot; where v th is the maximum acceptable speed difference threshold.

[0130] In S51, the robot forward velocity sequence V is obtained. r (t+k), k=1…N is the prediction result output by the state space model on the robot side, and each V r (t+k) corresponds to the robot's motion speed at the t+kth step. This speed is usually determined by the robot's trajectory prediction sequence Derived from this, the calculation method is: V r (t+k)=‖x r (t+k)-x r (t+k-1)‖ / T Where ‖·‖ represents the Euclidean norm, and T is the duration of the control cycle. This speed reflects the robot's path advancement within the prediction cycle and accurately characterizes its relative cable payout speed requirements.

[0131] In S52, the ship extracts its predicted cable-releasing speed sequence as V sca bl e (t+k), k=1…N. This speed is generally generated by the cable-releasing control module or tension prediction model, derived by combining the ship's motion state and the tension control mechanism. In the control framework, the cable-releasing speed can be calculated as follows: V s cable (t+k)=||x s (t+k)-x s (t+k-1)||| / T+η k The first term represents the propulsion speed of the ship at time t+k, η k This is a correction term for the speed based on tension feedback. Its design goal is to make the cable payout rhythm and the robot's movement speed as close as possible in time series to avoid over- or under-payout.

[0132] Finally, in S53, the system compares the two speed sequences step by step and calculates the difference at each prediction step: Δv k =V s cable (t+k)-V r (t+k) If there exists a prediction step k that satisfies |Δv k |>v th , then the cable release incoordination judgment is triggered. th The maximum allowable velocity difference threshold is set empirically and is usually adjusted according to the buffer length of the cable body and the response capability of the system.

[0133] For example, suppose the robot's velocity sequence in the prediction period is [0.85, 0.83, 0.80, 0.82, 0.81] m / s, and the ship's cable-releasing velocity sequence is [0.90, 0.91, 0.88, 0.84, 0.82] m / s, and set v th =0.05m / s, then the difference under each prediction step is: Δv=[0.05,0.08,0.08,0.02,0.01] It can be seen that the difference between the second and third prediction steps (i.e. k=2,3) has exceeded the threshold. At this moment, the system triggers the judgment result as "the cable release rhythm does not match the robot movement" S54. Obtain the predicted tension sequence at the ship end If present: or It is considered that there is a risk of sudden increase in tension or it is about to exceed the limit; where T is the upper limit of tension warning (usually lower than the tension limit T), warn maxδT is the tension change rate threshold.

[0134] First, predict the tension sequence is the state space model of the ship x s (t+1)=f s (x s (t),u s (t)) is generated by combining the tension estimation function, and the model is usually in the form of: in, Represents the tension calculation function, the input variables include the current position of the ship x s (t+k), robot relative position x r (t+k) and terrain slope The output is the dynamic tension between the cables at that step. This function can be constructed by constructing a force balance equation based on the cable's unit length weight, hydrodynamic forces, and tension conduit feedback.

[0135] For example, suppose that at the prediction time t+k, the state between the ship and the robot is as follows: The ship's position is (x s ,y s )=(0,0), the cable release speed is v s cable =1.0m / s; The robot position is (x r ,y r )=(10,-10), the speed of movement is v r =0.8m / s; The terrain slope at the robot's current position is That is, the depth decreases by 5 cm for every meter of advance; The tension estimation model in a simplified setting is defined as follows: in: T0=500N: basic tension; |x r -x s |: horizontal distance between the ship and the robot; absolute value of terrain slope; α=10N / m: distance gain coefficient; β=8000N: slope gain coefficient; Substitute the numerical calculation: Then we have: T s (t+k)=500+10×14.14+8000×0.05=500+141.4+400=1041.4N The system performs two types of abnormal risk analysis on the predicted tension sequence: first, it determines whether there is a tension value exceeding the upper warning limit T, which is usually set about 10%-15% below the tension limit T as a safety margin; second, it calculates the maximum tension change rate of the warn max in the sequence: Take the maximum rate of change If it exceeds the tension change rate threshold δ T , it is considered that the system has the hidden danger of sudden tension fluctuation.

[0136] For example, suppose the predicted tension sequence is [9.3, 9.7, 10.5, 10.8, 11.2] kN, and set T warn =11.0kN,δ T =0.5kN / s, Δt=1s. System detection found: T s (t+5)=11.2>T warn , there is an overrun; At the same time, the tension changes from step 3 to step 4 by 0.8 kN, exceeding the change rate threshold δ T .

[0137] Since the existence of tension risk can be determined if any judgment condition is met, it is judged as a "tension abnormality warning" during this prediction period, and the system will enter the strategy correction and optimization calculation process in the next step.

[0138] S55. If it is determined that the cable release rhythm does not match the robot, or if it is believed that there is a risk of a sudden increase in tension or that the tension is about to exceed the limit, the objective function is optimized, where the objective function is Among them, v s is the ship speed, ψ s is the heading angle, v scable is the cable release speed, β1·(v scable -V r ) 2 Used to constrain the cable rhythm fitting robot, β2·ΔT 2 To suppress tension fluctuations, β3·(θ sync ) 2Used to control the deviation from the robot's heading.

[0139] The optimization objective function is defined as follows: Among them, v sca bl e Indicates the ship's cable-releasing speed, V r is the forward velocity of the robot during the prediction period; ΔT is the maximum rate of change in the predicted tension sequence, defined as: And θ sync Indicates the current heading angle of the ship ψ s and the robot's current heading angle ψ r The angle difference is: θ sync =|ψ s -ψ r | The three weight parameters β1, β2, and β3 correspond to speed matching, tension stability, and posture synchronization, respectively. Their values can be adjusted according to specific task requirements. For example, in tasks where tension control is prioritized, β2 can be set to a higher value to suppress tension mutations.

[0140] In practical applications, assuming that during the current forecast period, the average forward velocity of the robot at time t+k is V r =1.2m / s, and the initial cable-releasing speed of the ship is Leading to Δv k =0.4m / s, the maximum rate of change in the tension prediction sequence is ΔT = 0.85kN / s, and the current heading difference between the ship and the robot is θ sync =12°. If the weight coefficients are set to β1=1.5, β2=2.0, and β3=0.8, the objective value of the optimization function is: J=1.5·0.4 2 +2.0 0.85 2 +0.8·(12·π / 180) 2 ≈0.24+1.445+0.035=1.72 The ship control system will search for a control solution that can minimize the function in the control variable space through numerical optimization algorithms such as gradient descent, particle swarm or Newton iteration. This control variable is then input into the state space model Used for a new round of state prediction and trajectory generation.

[0141] S56. Update the control quantity Input the ship end state space model: To re-predict heading and speed trajectory and tension change trend

[0142] The state space model is of the form: Among them, x s (t) represents the state vector of the ship at the current moment, including current position, speed, heading angle, cable release speed, cable tension, etc. represents the set of control variables obtained through the optimization function (see S55), usually including the speed v s , cable release speed v sca bl e and heading angle ψ s wait.

[0143] Based on this model, the ship motion state for the next step and the next N steps is recursively deduced to obtain the predicted trajectory sequence. Each element is a state vector, which covers the geographic location, motion parameters and control state at the future moment.

[0144] At the same time, according to the predicted cable release speed and ship speed changes, the cable tension needs to be re-estimated to obtain the revised tension change trend sequence Tension prediction is usually achieved by establishing a tension response model related to the cable release speed, ship motion state, seabed slope and the relative position of the robot, for example: in is the tension estimation function based on physical modeling and regression correction, Indicates the seabed slope gradient at the current location. The tension change is constrained by the terrain change and the relative position of the robot.

[0145] For example, in a certain actual simulation, the updated control quantity obtained by the ship side through S55 optimization is the speed v s =1.3m / s, cable release speed v s cable =1.2m / s, heading angle ψ s = 270°. This set of control variables was incorporated into the state-space model for a forward simulation. The resulting trajectory showed that the vessel would move approximately 78 meters westward at a constant speed within the 60-second prediction time domain. The tension curve fluctuations were significantly reduced, with the maximum value reduced to 85% of the original prediction.

[0146] After completing this step, the ship's forecast information (including ) will be used as one of the next round of ship-engine collaborative inputs and will participate in the iteration of model predictive control again in the next control cycle S6. The ship and the robot re-execute the model predictive control based on each other's revised trajectory prediction information and tension prediction information to generate the final optimized control quantity.

[0147] The state space model of the ship is expressed as x s (t+1)=f s (x s (t),u s (t)), and the model of the robot side is x r (t+1)=f r (x r (t),u r (t)). In this step, the ship and the robot will obtain the corrected predicted trajectory from each other. and predicted tension sequence The respective control optimization processes are introduced as soft or strong constraints.

[0148] Taking the ship end as an example, its goal is to adjust the control variable u s (t), so that the state sequence of the next N steps can meet the following optimization objectives as much as possible: in: v sca bl e (t+k) is the predicted cable-releasing speed of the ship; V r (t+k) is the robot’s predicted forward velocity; ΔT s (t+k)=T s (t+k+1)-T s (t+k) is the change in tension; θ sync Indicates the relative heading angle deviation between the ship and the robot; β1, β2, β3 are the weight coefficients of each loss term.

[0149] The robot side also performs a similar form of optimization process. The difference is that its optimization focuses more on path safety and tension stability. Its objective function may include more constraints on terrain adaptability or penalty terms for local path planning.

[0150] In actual implementation, for example, when laying a cable across a shallow sea terrain with gentle slopes and rock masses, the robot's predicted trajectory adjustment showed that the future tension would increase significantly at step t+4, and there was a risk of intersecting the ship's trajectory. The ship then re-optimized the cable release speed and course control, adjusting the cable release rhythm to achieve tension release while ensuring avoidance. Ultimately, both parties obtained a set of updated control variables. The execution quantities such as speed, heading angle, attitude angle, propulsion force and cable winch speed are controlled separately, and the motion behavior in the subsequent control cycle is guaranteed to maintain global consistency with tension constraints and path coordination.

[0151] It should be noted that the prediction information exchanged in S3 is used in S4 and S5, but this does not mean that the prediction updates in S4 and S5 are repeated in the predictive control in S6. This is because S4 / S5 and S6 belong to two different stages of predictive control. S4 / S5 is based on the current prediction and the prediction of the other party, abnormal analysis + local strategy adaptation → update the prediction amount, but does not output the final control action. This stage belongs to the prediction recalibration stage and is still an intermediate state in the operation of the controller. S6 is based on the latest two-way prediction. After both parties complete self-correction, collaborative constraint optimization is performed → output the final control amount. In other words, this stage is the real joint optimization control action output stage, and it is the only stage that outputs the control instruction u' r ,u s steps.

[0152] S7. The ship and robot adjust their attitude, speed, and cable-releasing strategy based on the final optimized control variable, and use the current state feedback as the initial input of the state-space model in the next control cycle, entering a new round of control loops from S2 to S6.

[0153] In step S7, the ship side and the robot side adjust their respective execution behaviors based on the final optimized control quantity calculated in the previous step, and use the current state after execution as the initial input of the next control cycle to enter a new round of predictive control cycle, thereby realizing an adaptive and continuously optimized closed-loop control mechanism.

[0154] Specifically, the control variables include the ship's speed, heading angle, and cable-releasing speed, as well as the robot's propulsion speed, attitude control variables, and path-following instructions. These control variables are jointly optimized by a model predictive controller, taking into account multiple objective trade-offs such as tension limits, relative position coordination, and path planning results, achieving phased optimality.

[0155] After the control quantity is issued, the ship adjusts the speed and heading by updating the traction speed of its cable winch and adjusting the propeller output power, so that its actual movement trend is towards the predicted trajectory. Get closer and try to maintain the forecast tension The robot realizes posture adjustment and forward propulsion based on its motor control module, and Performs a cabling operation for a trajectory constraint.

[0156] In this process, when each cycle T reaches the end, the system collects the state quantities (such as current position, speed, attitude angle, tension value) obtained through actual sensor feedback to form the initial state vector x of the state space model in the next control cycle. s (t+1), x r (t+1). This state feedback mechanism ensures that the model predictive control can perform rolling optimization based on the latest system dynamics in each cycle, thus having strong disturbance adaptability and real-time correction capabilities.

[0157] For example, during a deepwater optical cable laying mission in the South China Sea, the vessel detected tension approaching a boundary during the kth cycle. Adjustments were made to obtain new cable payout speed and heading angle control commands, while the robot simultaneously converged to the new target path while avoiding intersections with seabed terrain boundaries. After completing adjustments, both systems collected tension values, GPS, and IMU data, recombined them into new state inputs, and jointly entered the next control cycle.

[0158] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0159] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A method for coordinating a submarine cable laying robot and an optical cable laying vessel, characterized in that: The following steps are involved: S1. The ship sets the target route, initial speed, and tension control range. The robot sets the current task type and simultaneously sets the control period T and the prediction time domain length N. S2. The ship and the robot collect data and establish their respective state-space models, executing a new round of predictive control cycles to derive trajectory and tension prediction information for the next N steps. S3. The ship and the robot transmit their respective prediction information to each other as constraint inputs for the other's state space model; S4. The robot determines whether the predicted trajectory poses a risk of excessive tension or conflicts with the vessel's trajectory. If so, it replans the local path and corrects the trajectory and tension prediction information. S5. The vessel determines whether the predicted cable-releasing strategy does not match the robot's predicted speed or whether the tension exceeds the warning threshold. If so, the vessel adjusts the speed and cable-releasing rhythm and corrects the trajectory and tension predictions. S6. The ship and the robot re-execute model predictive control based on each other's revised trajectory prediction information and tension prediction information to generate the final optimized control variable; S7. The ship and robot adjust their attitude, speed, and cable-releasing strategy based on the final optimized control variable, and use the current state feedback as the initial input of the state-space model in the next control cycle, entering a new round of control loops from S2 to S6.

2. The method for coordinating a submarine cable laying robot with an optical cable laying vessel according to claim 1, characterized in that: Said S1 comprises the following steps: S11. The vessel loads the mission planning data, including the track point sequence, target depth, obstacle area markings, and rhythm control area, based on the preset submarine cable planning path. S12. The vessel determines the initial heading angle, speed range, and preset tension control range; S13. The robot loads the current task type as a fault location task or a terrain-following cable laying task; S14. The ship and the robot jointly set the time window length N and the duration of each cycle T used for predictive control and establish communication.

3. The method for coordinating a submarine cable laying robot with an optical cable laying vessel according to claim 2, characterized in that: The S2 comprises the following steps: S201. The robot collects real-time posture information, depth information, terrain contour information, current speed and acceleration, and current tension data; S202. Construct the current state variable and the historical state variable into an input vector; S203. Establish the robot's predicted state space model x r (t+1)=f r (x r (t),u r (t)); S204. Deducing the robot's posture trajectory in the next N steps based on the state model And use terrain features as prediction reference boundaries; S205. Predict the robot's tension change trend sequence based on the current task scenario 4. The method for coordinating a submarine cable laying robot and an optical cable laying vessel according to claim 3, characterized in that: The S2 comprises the following steps: S211. The vessel collects the current latitude and longitude position, speed, heading angle, current cable release speed, current cable tension, and the robot's real-time relative position and movement trend in real time; S212. Construct the current state variable and the historical state variable into an input vector; S213. Construct the ship's predicted state space model x s (t+1)=f s (x s (t),u s (t)); S214. Deducing the ship's position trajectory in the next N steps based on the state model S215. The task path, the track point sequence and the relative position of the robot are used as the prediction reference boundary; S216. Predict the ship's heading, speed, and tension change trend sequence for the next N steps 5. The method for coordinating a submarine cable laying robot with an optical cable laying vessel according to claim 4, characterized in that: The S4 includes the following sub-steps: S41. Set tension threshold T th , if present: Make T(t+k)>T th , it is determined that there is a risk of tension exceeding the limit; S42. Calculate the tension growth rate index If ΔT>δ T , it is determined to be a potential tension mutation risk; S43. Calculate the relative distance d between the ship and the robot at each moment in the future k =|x r (t+k)-x s (t+k)|, if present: or θ diff (k)>θ th , then it is judged as a path conflict, where d max is the maximum relative distance within the controllable tension range, θ diff (·) is the angle deviation; S44. If there is a risk of tension exceeding the limit, a potential risk of tension mutation, or a path conflict, replan the local path and update the predicted trajectory and tension sequence.

6. The method for coordinating a submarine cable laying robot and an optical cable laying vessel according to claim 5, characterized in that: The S44 includes the following sub-steps: S441. Preset path search window in front of the robot's current position, extract the current position to the future M meters of passable terrain area; S442. Generate multiple candidate path segments P1, ..., P n , each path satisfies the terrain traversability constraint, where each path P i Expressed as a set of continuous state point sequences {x i (t+1),…,x i (t+N)}; S443. For each candidate path P i , construct a multi-objective path evaluation function J(P i )=α1·D track (P i )+α2·R terrain (P i )+α3·T max (P i )+α4·S sync (P i ), where D track (P i ) is the average distance away from the original path; R terrain (P i ) is the slope risk of the terrain the path passes through; T max (P i ) is the maximum tension predicted along the path; S sync (P i ) is the degree of coordination between the path and the ship’s trajectory in time and space; S444. Select the path P with the smallest evaluation function opt As a final alternative path; S445. Select the path P opt Input to the robot's state space model: x r ′(t+1) =f r (x r (t),u r (t)), the constraint is x r (t+k)∈P opt ; S446. Based on P opt A new round of trajectory and tension prediction is performed to obtain an updated trajectory prediction sequence and updated tension prediction sequence S447. Update auxiliary parameters related to path planning; S448. The data is transmitted back to the ship to participate in the next round of collaborative optimization.

7. The method for coordinating a submarine cable laying robot with an optical cable laying vessel according to claim 6, characterized in that: The S5 comprises the following sub-steps: S51. Obtain the forward velocity sequence at each moment in the robot's predicted trajectory: V r (t+k), k=1…N; S52. Obtain the ship's predicted cable-releasing speed sequence: S53. Calculate the difference between the two at each prediction step: If present: It is determined that the cable-releasing rhythm does not match the robot; Among them, v th is the maximum acceptable speed difference threshold; S54. Obtain the predicted tension sequence at the ship end If present: or It is considered that there is a risk of sudden increase in tension or it is about to exceed the limit; where T is the upper limit of tension warning (usually lower than the tension limit warn T max ), δT is the tension change rate threshold.

8. S55. If it is determined that the cable release rhythm does not match the robot, or if it is determined that there is a risk of a sudden increase in tension or that the tension is about to exceed the limit, the objective function is optimized, where: The objective function is optimized as v s is the ship speed, ψ s is the heading angle, is the cable release speed, Used to constrain the cable rhythm fitting robot, β2·ΔT 2 To suppress tension fluctuations, β3·(θ sync ) 2 Used to control the deviation from the robot's heading; S56. Update the control quantity Input the ship end state space model: To re-predict heading and speed trajectory and tension change trend

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