A variable speed trajectory planning method based on improved Dijkstra

Abstract

A variable speed trajectory planning method based on an improved Dijkstra is characterized by comprising the following steps: 1) specifying a planned sea area. 2) assessing the marine terrain. 3) assessing marine meteorological and hydrological risks. 4) setting constraints and starting and target points. 5) implementing a variable speed trajectory planning algorithm. 6) trajectory evaluation. The present invention improves the Dijkstra algorithm so that it can perform variable speed planning on the trajectory of surface ship operations, and avoid upcoming risks in the time dimension by accelerating in advance or reasonably decelerating or staying in place, thereby gaining advantages in the time dimension and avoiding the complexity of the route in the spatial dimension. In addition, 1) the algorithm itself includes an assessment of the marine terrain and pre-processing of the raster map, which greatly reduces the risk of a grounding in the route while taking into account the simplicity and effectiveness of the route. 2) After planning the time dimension of forecast data for several days, the optimal departure and arrival times can ultimately be given.

Description

Technical Field

[0001] The invention relates to a track planning technology, in particular to a variable speed track planning method based on an improved Dijkstra. Background Art

[0002] In the context of economic globalization, international trade in goods relies primarily on maritime transport, and trajectory planning plays a crucial role in ensuring the safety of ships at sea. Trajectory planning is also a crucial component of military oceanographic hydrographic support and has been widely used in the navigation systems of underwater robots, unmanned underwater vehicles, submarines, and other equipment. With the rapid development of information-based collection and analysis technologies such as big data, cloud computing, and the Internet of Things, trajectory planning based on oceanographic elements has become a key component in ensuring the safety of ships and a key technology for improving the combat effectiveness of weapons and equipment.

[0003] Existing trajectory planning methods focus on spatial risk avoidance, specifically altering the route so that the vessel maintains a certain curvature around the risk zone at a certain distance. For practical navigation support missions, the resulting paths are highly complex, with increased number of curves and length. Increased curves increase the risk of vessel pitching and even capsizing. The complex meteorological and hydrological environment at sea makes rare extreme weather events such as storm surges, typhoons, and small tsunamis difficult to accurately predict. This increased distance increases the actual time spent at sea compared to the budgeted time, potentially missing opportunities to avoid risk zones and increasing the risk of navigation safety. Furthermore, the speed of a vessel varies during actual navigation, while traditional trajectory planning algorithms typically assume a constant speed, reducing their practicality. When the ocean environment changes, the planned route may become untenable or require replanning. Because of the constant speed assumption, traditional trajectory planning algorithms cannot predict optimal departure and arrival times. Departure and arrival times are determined subjectively by decision-makers, leaving them susceptible to significant human influence. Trajectory planning efficiency needs to be further improved.

[0004] This article uses a relatively similar new technology as a comparative reference. This technology, titled "Dynamic Route Planning Method for Intelligent Ships Considering Complex Weather Changes," was published in the March 2021 issue of the Journal of Shanghai Maritime University (hereinafter referred to as Technology B). It's easy to see that the core of Technology B's solution is to construct an artificial threat field and then use the eight-direction A* algorithm for trajectory planning. The artificial threat field is derived through a series of risk assessments, quantifying risk into a value between 0 and 1 to facilitate path planning. The construction of the artificial threat field is largely similar, with minor differences arising from details such as the selected indicators and assessment methods. The final result is essentially the same: a standardized, positive risk value between 0 and 1. The true core of Technology B is the A* algorithm, which supports trajectory planning. The A* algorithm is a variation of the Dijkstra algorithm and can produce the same risk-minimizing path given the same artificial threat field. The only difference lies in theoretical search efficiency: A* uses a heuristic search method with a higher depth-first efficiency, while the Dijkstra algorithm uses a lower breadth-first search method with a lower efficiency. In actual applications of ship trajectory planning, the efficiency difference between the two is not significant. From the perspective of risk avoidance performance, A* is essentially the Dijkstra algorithm, and both have the same risk avoidance behavior. Therefore, when comparing it with Technique B, the comparison is actually with the Dijkstra algorithm. The Dijkstra algorithm's advantage is its stable performance and its ability to provide an optimal solution when a solution exists. However, its disadvantages are also quite obvious when applied to ship trajectory planning. It represents conventional risk avoidance behavior, namely, it only avoids risks in the spatial dimension, the planned daily speed cannot be changed, and it cannot provide optimal departure and arrival times.

[0005] In summary, the trajectory planning algorithm based on spatial dimension may increase the risk of ship navigation. The assumption of constant speed does not conform to the actual situation. The planned navigation has practical problems such as low accuracy and low efficiency. Summary of the Invention

[0006] In order to solve the above problems, the present invention proposes a variable speed trajectory planning method based on improved Dijkstra. First, the sea terrain of the grid map is evaluated and pre-processed so that the planned route can reduce the risk of running aground. Secondly, the improved Dijkstra algorithm comprehensively considers the spatial dimension and the time dimension to achieve variable speed planning. Risks are avoided by speeding up in advance or reasonably slowing down or staying in place, thereby gaining advantages in the time dimension and avoiding the complexity of the route in the spatial dimension. This method can also perform an identification and clipping operation on the variable speed route, and provide the optimal departure time and the optimal arrival time as a reference for decision-making.

[0007] The technical problem solved by the present invention is to provide a variable speed trajectory planning method based on an improved Dijkstra to solve the shortcomings of the above-mentioned background technology.

[0008] The technical solution of the present invention is: a variable speed trajectory planning method based on improved Dijkstra, comprising the following steps:

[0009] Step 1: Designate the planned sea area. Extract the sea area's latitude and longitude information and terrain information based on the task requirements. Determine the resolution of this information and construct a preliminary raster map, assuming it is a field of m×n matrix dimensions.

[0010] Step 2: Offshore terrain assessment. The extracted terrain data is processed and refined according to the definition section to obtain the terrain risk matrix R g , with dimensions of m×n.

[0011] Step 3: Marine meteorological and hydrological risk assessment. An evaluation index system is constructed using multiple methods, including satellite data, meteorological detector data, computer interpolation simulation, data collected during sea voyages, and historical data. The indicators are evaluated using, but not limited to, the analytic hierarchy process, fuzzy comprehensive evaluation, and projection pursuit methods, to normalize them to risk values ​​between 0 and 1. These are then rasterized into an indicator risk matrix R with dimensions of m × n × d for d days. f The information is thus converted into a form that is easy for computers to process so that it can be displayed on a grid map, laying the foundation for trajectory planning.

[0012] Step 4: Set the constraints and the starting point startPos = (x1, y1) and the target point goalPos = (x2, y2). The constraint is usually the maximum daily speed v, which must ensure that the navigation mission from the starting point to the target point can be completed.

[0013] Step 5: Implementing the variable-speed trajectory planning algorithm. Once these four steps are complete, trajectory planning can be performed with corresponding constraints for the specified sea area, starting point, and destination. The algorithm will generate a reasonable route and, based on this, assign a navigation plan to the route in the time dimension. This process is broken down into the following steps:

[0014] 1) Map preprocessing. Briefly, this involves comparing the indicator risk matrix and setting consistently high-risk points on the grid map as non-navigable. This creates a grid map (new_field) that allows for flexible daily navigation planning in the time dimension. The detailed operation is described in the definition above.

[0015] 2) Set the cost of each step of the eight-direction Dijkstra algorithm to the distance cost and the terrain risk cost, give the two appropriate weights according to the actual situation, and input the pre-processed raster map new_field, startPos=(x1,y1), goalPos=(x2,y2) and the terrain risk matrix R into the algorithm. gThe algorithm result is a reasonable and simple shortest path Path_opt1 = {z1,z2,···,z k}, which is a 1×k-dimensional row vector, each element of which is a linear index value of the raster map. This step records the basic information of the route.

[0016] 3) Extract the risk information on the shortest path and construct a time-risk-path matrix R with a dimension of d×k χ Specifically: According to the shortest path Path_opt1={z1,z2,···,z k}, starting from 1 and traversing the m×n×d indicator risk matrix R f For all values ​​of the third dimension d, we search for the indicator risk values ​​for the corresponding path points within d days. The vertical axis is sorted sequentially from day 1 to day d, and the horizontal axis is sorted sequentially from the starting point to the destination. For example, if the risk matrix is ​​122 × 133 × 11 and the shortest path is 1 × 120, then the time-risk-path matrix will be 11 × 120.

[0017] 4) Use the improved Dijkstra algorithm on the time-risk-path matrix to obtain a variable speed trajectory planning scheme. The improved Dijkstra algorithm is specifically as follows: the eight-direction search of the original algorithm is changed to a three-direction optimal search, namely the right, right and bottom directions. The search range is the time-risk-path matrix, and the search starting point is fixed to the upper left corner element of the time-risk-path matrix, that is, the element with a linear index value of 1, and the matrix coordinates are (1,1); the target point is fixed to the lower right corner element of the time-risk-path matrix, that is, the element with a linear index value of d·k, and the matrix coordinates are (d,k). The improved Dijkstra algorithm is run to obtain a variable speed trajectory planning scheme Path_opt2={Z1,Z2,···,Z l}, which is a 1×l-dimensional row vector, each element of which is a linear index value of the time-risk-path matrix, and each linear index value corresponds to a unique pair of matrix coordinates, that is, (r i ,c i ) represents the rth i The day should sail to c i waypoints.

[0018] 5) Linear index element Z of Path_opt2 i The corresponding matrix coordinates (r i ,c i) for identification, and then clipping, thereby defining an optimal departure time and arrival time. Specifically: set the counting variable count = 0, first find all matrix coordinates with the horizontal coordinate c1, stack their vertical coordinates in order into a column vector R, and traverse from the second element to the last element in R. The first element in R must be 1. Record the position of the first discontinuous element in the traversal process. If the element is continuous, set count plus 1. After the traversal is completed, clip the 1st to count linear index elements Z i , and get the new Path_opt′2={Z′1,Z′2,···,Z′ L}. Therefore, Path_opt′2 corresponds to a new speed change planning scheme for departure time. The optimal departure time recommended by the algorithm is The vertical coordinate r1′ is the r1′th day; similarly, set the counting variable and first find the horizontal coordinate c k All matrix coordinates are stacked into vectors and then flipped up and down for easy operation. Finally, they are traversed and clipped. After following the above steps, we get Path_opt″2={Z″1,Z″2,···,Z″ p}, the optimal arrival time recommended by the algorithm is The vertical coordinate c″ p , that is, c″ p Days. It should be noted that not every navigation mission planning will provide the optimal departure time. Sometimes the set time happens to be the optimal one. According to Path_opt″2={Z″1,Z″2,···,Z″ p}, which can be visualized as a three-dimensional space-time diagram (see the appendix of the manual Figure 7 ,8, and the related illustrations of the specification in the example part), which allows us to observe the decision-making situation more intuitively.

[0019] Step 6: Trajectory Evaluation. Due to the nature of the Dijkstra algorithm, if a solution exists, it will inevitably have an optimal solution. While there may be multiple equivalent solutions, the Dijkstra algorithm only provides one. Therefore, when evaluating a trajectory, the risk index values ​​of each shortest path point under the variable-speed trajectory plan can be extracted and averaged to gain a general understanding of the risk profile of the variable-speed trajectory plan.

[0020] The beneficial effects of the present invention are:

[0021] This invention improves the Dijkstra algorithm, enabling it to perform variable-speed planning for the trajectory of surface ship operations. This allows for the avoidance of impending risks in the temporal dimension by accelerating in advance, reasonably decelerating, or stopping in place, thereby achieving advantages in the temporal dimension and avoiding the complexity of the route in the spatial dimension. Furthermore: 1) The algorithm itself includes an assessment of the marine terrain and preprocessing of the grid map, which significantly reduces the risk of grounding while ensuring a simple and efficient route. 2) After temporal planning based on several days of forecast data, the optimal departure and arrival times can ultimately be determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 : A simple raster map example, Figure 1 This is a rasterized map. Unnavigable coasts are marked with yellow blocks, and navigable seas are marked with blue blocks.

[0023] Figure 2 : The risk matrix with each element value between 0 and 1 is obtained through the evaluation method, and the image is visualized using Matlab.

[0024] Figure 3 The terrain risk matrix is ​​visualized on a grid map, with values ​​ranging from 0 to 1. The closer to the shore, the higher the risk, colored red; the farther from the shore, the lower the risk, colored blue.

[0025] Figure 4 : Add new non-navigable point images to the original raster map according to map preprocessing. For comparison, the new non-navigable points are yellow, the old ones are green, and the navigable points are still blue.

[0026] Figure 5 : A simple 30x30 grid environment visualization map, with the magenta block as the starting point, the fluorescent green block as the target point, and the black path as the reasonable shortest path given by the algorithm.

[0027] Figure 6 : Atlas explaining the advance speed-up mode. The first two sub-graphs in the upper part are visualization diagrams of the indicator risk matrix for three days. The third sub-graph is a three-dimensional visualization diagram of the speed-changing trajectory planning. The z-axis represents the z-th day, and the fluorescent green is the speed-changing planning trajectory.

[0028] Figure 7 : Atlas explaining the early deceleration mode. The first two sub-figures in the upper part are visualization diagrams of the indicator risk matrix for three days. The third sub-figure is a three-dimensional visualization diagram of the speed change trajectory planning. The z-axis represents the z-th day, and the fluorescent green is the speed change planning trajectory.

[0029] Figure 8: Explanatory atlas of optimal departure time and optimal arrival time. The first two sub-graphs in the upper part are visualization diagrams of the indicator risk matrix for three days. The third sub-graph is a three-dimensional visualization diagram of the variable speed trajectory planning. The z-axis represents the z-th day, and the fluorescent green is the variable speed planning trajectory.

[0030] Figure 9 : Flow chart of the steps of the method of the present invention.

[0031] Figure 10 : 11-day heat map of the risk matrix obtained by projection pursuit evaluation of various indicators in the designated sea area.

[0032] Figure 11 : Resulting diagram of a reasonable route obtained by the eight-way Dijkstra algorithm. The shortest path planned by the example is shown as black scattered points, gray represents coasts or reefs, and blue represents unnavigable areas added by map preprocessing.

[0033] Figure 12 : 3D schematic diagram of the speed-varying trajectory planning of an example from a certain perspective, where the black part represents the speed-varying planned trajectory.

[0034] Figure 13 : A three-dimensional schematic diagram of the speed-varying trajectory planning of the example from another perspective, where the black part represents the speed-varying planned trajectory.

[0035] Figure 14 : The 11-day route planning map obtained by using technology B in the example. The white part is the planned route, the starting point and the end point are marked with five-pointed stars, and the daily route section is represented by the route between two hexagonal marks. DETAILED DESCRIPTION

[0036] This invention improves Dijkstra's algorithm twice. The first improvement can provide a reasonably risk-avoiding and simplest shortest path in the spatial dimension, and the second improvement can avoid risks in the temporal dimension. To introduce the content of this invention in detail, some concepts are explained or defined below:

[0037] Grid map. The grid map in this patent refers to a series of grid divisions of the planned sea environment, in which each grid is given a value to represent its status. For example, the value "1" indicates that the grid is navigable, and the value "2" indicates that the area is a reef or coast and is not navigable. Thus, a matrix can be used to describe the basic navigation status of the entire sea area. The grid map has the characteristics of strong flexibility and high precision, and is the basis of the track planning of this patent. An example of a grid map can be found in the appendix of the specification. Figure 1 .

[0038] Indicator risk matrix. The risk matrix refers to the indicators selected while fully considering the meteorological, natural, and artificial conditions of the sea area. After evaluating each navigable point in the sea area through risk assessment algorithms such as fuzzy comprehensive evaluation, hierarchical analysis method, and expert scoring method, a matrix with the same dimensions as the grid map is obtained. The risk matrix is ​​one of the bases for the track planning of this patent, and the risk value is generally normalized to a range of 0 to 1. This patent involves terrain risk matrix and indicator risk matrix. The visualization of a risk matrix is ​​shown in the appendix of the specification. Figure 2 .

[0039] Assessment of marine topography and map preprocessing. In traditional assessment activities, multiple indicators of the marine environment such as sea surface temperature, current velocity, wave height and sea surface salinity are often collected to assess the size of the risk. In reality, the factors of sea surface topography are often ignored, resulting in routes approaching reefs and coasts, increasing the risk of grounding. This patent conducts marine topography assessment,

[0040] Step 1: Collect the coordinate matrices of all navigable blocks and each non-navigable block.

[0041] Step 2: Calculate the Manhattan distance between each navigable block and each non-navigable block in turn.

[0042] Step 3: Find the farthest and closest non-navigable blocks from each navigable block, and record their Manhattan distance.

[0043] Step 4: Normalize the distance x obtained in Step 3, and then adjust the decay rate and indicator direction (the closer the x value is to 0, the closer the final risk value is to 1). A reasonable terrain risk matrix is ​​obtained, which can be input into the D-type pathfinding algorithm to assign weights to the affected path. Here, the function of the lower left quarter of the unit circle with the center at (1,1) is used. Perform attenuation to obtain the terrain risk matrix, see Figure 3 of the specification.

[0044] Map preprocessing: This also provides a basis for the subsequent use of the improved Dijkstra algorithm for time dimension planning. The grid map will be marked according to the indicator risk matrix. For example, grid points with a risk value exceeding 0.7 and occupying more than 10% of the forecast data days will be marked as non-navigable (these two 0.7 and 10% can be adjusted according to specific circumstances to obtain reasonable results, which are called map preprocessing parameters). This ensures that the path points on the track can be planned flexibly and effectively in the time dimension. See the attached manual. Figure 4 , gives an example of adding non-navigable state points on the basic grid point map (the sample data days are 11 days, and the map preprocessing parameters are 0.7 and 30%). Figure 1 Understand.

[0045] Grid Land Figure 8 Directional Dijkstra algorithm. The traditional Dijkstra algorithm uses a four-directional search mechanism: up, down, left, and right. In military operations, the eight-directional Dijkstra algorithm offers greater freedom and flexibility, adding four additional directions: upper left, lower left, and upper right and lower right. The algorithm only requires a starting point and an end point to determine the shortest path. In traditional applications of this algorithm, due to the dual requirements of risk avoidance and navigation, the cost of each step is defined as a weighted combination of distance, indicators, and terrain risk, combining indicators and a terrain risk matrix. Risk is a value between 0 and 1. Distance has the same value for up, down, left, and right, and for upper left, lower left, and upper right and lower right, with the specific value varying depending on the sea area. The algorithm itself seeks the shortest path, with the cost being solely the distance cost. By redefining the cost of each step, as described above, the risk cost is normalized to the same range as the distance. The algorithm results in the shortest path with the lowest risk given the current weighting. However, in the first implementation of Dijkstra in this patent, the cost of each step is simply the weighted combination of distance cost and terrain risk cost.

[0046] The optimal path properties obtained by Dijkstra. It's worth noting that there isn't necessarily a single shortest path, and the algorithm doesn't necessarily have a solution. However, when a solution exists, Dijkstra's algorithm performs a global breadth-first search, which will inevitably yield one of the shortest paths. Due to the different definitions of the cost of each step, Dijkstra can either obtain only the shortest path or the shortest path with the lowest risk given a weighted ratio. This property provides theoretical support for planning in the time dimension of this patent.

[0047] Time-risk-path matrix. This matrix refers to the shortest path points obtained by sorting out the raster map after the map preprocessing using the Dijkstra algorithm for the first time, and finding the values ​​corresponding to the indicator risk matrix at the path points of the multi-day forecast data. This constitutes a time-risk-path matrix with the vertical coordinate being time (the top of the vertical coordinate is the first day), the horizontal coordinate being the path point (the leftmost horizontal coordinate is the first path point), and the matrix element value being the indicator risk. This matrix is ​​the core analysis object of this patent and is the analysis object that provides the speed change planning path.

[0048] The Dijkstra algorithm is improved for time-based planning. The main improvement involves changing the Dijkstra algorithm's search direction to only three: due right, right-down, and down. The algorithm is then applied to the time-risk-path matrix, with the starting point always set to (1,1) and the ending point always set to (the last day of the forecast data, the total number of path points). Constraints are set to ensure that the number of grid points in the time-risk-path matrix occupied by the analyzed time-based path does not exceed the maximum daily speed. The three search directions are practically relevant: due right represents continued navigation to the next path point; down-right represents no navigation today, but navigation to the next path point the next day; and down-down represents no navigation today or the next day, but remaining at the current path point. Eliminating search directions and fixing the search start and end points does not alter the properties of the Dijkstra algorithm. The improved Dijkstra algorithm performs time-based secondary planning based on the path generated by the initial Dijkstra algorithm, achieving time-based allocation and speed-variable trajectory planning to avoid high-risk scenarios. The algorithm can provide a relatively simple and reasonable shortest path, and on this basis provide a speed-varying sailing plan with the least risk.

[0049] Speed ​​up, slow down or stop to avoid danger mode. Use two ideal examples to illustrate the two main avoidance modes of a variable speed trajectory planning method based on the improved Dijkstra. Given a 30x30 grid environment (see the attached manual) Figure 5 ), the starting point is the lower left corner block (magenta block), and the end point is the upper right corner block (fluorescent green block). This patented algorithm first gives a shortest path with a total of 30 path points. Then the maximum daily speed is set to 20 path points. According to the indicator risk matrix (see the indicator risk matrix visualization in the appendix of the manual), Figure 6 ,7 The first two sub-graphs) give a speed change sailing plan with the lowest risk, which can be divided into early speed increase and slow speed increase according to the characteristics (see the instruction manual). Figure 6 The last sub-graph), slow down or stop (instruction manual attached Figure 7 (The last sub-figure) Risk Avoidance Mode, where the fluorescent green represents the speed-variable route. Generally speaking, it's difficult for the algorithm to trigger Stop Risk Avoidance Mode. This is because most situations that can be handled by Stop Risk Avoidance Mode can also be avoided by premature deceleration. Preemptive deceleration offers greater flexibility and flexibility, so the algorithm defaults to using premature deceleration.

[0050] Optimal departure and arrival times. An ideal example visualization is shown in the appendix of the manual. Figure 8 The parameters are the same as those in the previous hedging mode, but the maximum daily speed is set to 29. This patented algorithm sets the time planning starting point from the first day of the forecast data by default, and the last day is the arrival point. However, after obtaining the indicator risk matrix, the algorithm will automatically analyze the optimal departure and arrival time. Figure 8In the first two subgraphs, the indicator risk matrix shows that on days 1 and 2, only the starting point is at low risk, while the rest of the area is at high risk. On day 3, the entire target area is at high risk. Therefore, the algorithm concludes that navigation should begin on day 2 and reach the target point on day 3.

[0051] In order to make the technical means, creative features, workflow, and usage methods of the present invention easy to understand and achieve the purpose and effect, the present invention is further explained below in conjunction with a specific sea area embodiment of a longitude: 110°~121° and latitude: 15°~25° used in the definition and explanation part.

[0052] Step 1: Specify the planned sea area, which is a sea area with longitude: 110°~121° and latitude: 15°~25°. The data accuracy is 1 / 12°, so the grid map is actually a field with a dimension of 121×133 matrix. Each grid to the left and right is about 4.8321 nautical miles, to the up and down directions is 5.0026 nautical miles, and the four diagonal directions are 6.9552 nautical miles. Figure 1 The lower sub-map is actually the visualization of the designated planned sea area.

[0053] Step 2: Offshore terrain assessment. The extracted terrain data is processed and refined according to the definition section to obtain the terrain risk matrix R g , dimensions are 121×133. Instructions attached Figure 3 It is actually a visualization of the terrain risk matrix.

[0054] Step 3: Marine meteorological and hydrological risk assessment. We selected various indicators for the designated sea area over 11 days, including sea temperature, sea surface velocity, sea visibility, and wave height, and used the projection pursuit method to normalize them to risk values ​​between 0 and 1. We then rasterized them into an indicator risk matrix R with a dimension of 121×133×11 for the 11 days. f . Instructions attached Figure 10 In fact, it is the 11-day risk matrix R f Visualization.

[0055] Step 4: Set the constraints and startPos = (100, 1) and goalPos = (11, 110). The estimated maximum distance between the two is 198 grid points. Assume a maximum daily speed of 20 grid points, meaning a maximum daily voyage of approximately 140 nautical miles, or a total of 220 grid points in 11 days. This ensures that the maximum daily speed will ensure the journey from the start point to the goal point is complete.

[0056] Step 5: Implementation of variable speed trajectory planning algorithm. It can perform trajectory planning with corresponding constraints on the designated sea area, starting point and target point. The algorithm will give a reasonable route (see the attached manual). Figure 11), and on this basis, assign a navigation plan to the route in the time dimension, and visualize the speed change planning plan as an appendix to the manual. Figure 12 and 13. It can be clearly seen that according to the instructions attached Figure 11 If the planned route doesn't properly plan daily speeds, it's highly likely that the route will pass through a large high-risk red zone on days 9 and 10, a potentially risky voyage. This is also the primary issue that needs to be avoided on this voyage. The algorithm allocates daily sailing plans for days 1 to 8, and by the end of day 8, the route has essentially passed through the high-risk red zone that existed on days 9 and 10. This is an example of the algorithm's early acceleration mode to avoid risks. Furthermore, on day 10, the route doesn't continue to reach the destination, but instead waits until day 11, when the entire ocean area appears to be significantly lower risk, before reaching the destination and completing the voyage. This is an example of the algorithm's early deceleration mode to avoid risks. Clearly, the algorithm performs well when handling real-world examples. For this planned mission, the algorithm doesn't provide additional optimal departure and arrival times; the default departure and arrival times provided by the algorithm are considered optimal.

[0057] Step 6: Track evaluation. Figure 11 If the planned route doesn't properly plan the daily speed, it's very likely that the route will pass through a large high-risk area on days 9 and 10. This is a potentially risky behavior during the voyage and a major issue that needed to be avoided during this voyage. The algorithm allocates daily sailing plans for days 1 to 8, and by the end of day 8, the high-risk area that existed on days 9 and 10 had already been largely cleared. This is an example of the algorithm's early acceleration mode, which avoids risk. Furthermore, on day 10, the route doesn't continue to reach the destination, but instead waits until day 11, when the entire ocean area appears to be significantly lower risk, before reaching the destination and completing the voyage. This is an example of the algorithm's early deceleration mode, which avoids risk. Clearly, the algorithm performs well when handling real-world examples. For this planning task, the algorithm doesn't provide additional optimal departure and arrival times; the default departure and arrival times provided by the algorithm are considered optimal.

[0058] For the algorithm of technique B, Figure 11As can be seen in Figure 11, the route planned for the entire 11 days primarily avoids risks through spatial deflections, with varying degrees of deflection. Days 9, 10, and 11 constitute a significant deflection, which increases distance and potential risks. Furthermore, the route planned for days 7-10 lies too close to the coastline, increasing the risk of grounding. Because the speed is fixed and cannot be changed, the planned route is less flexible, limiting sailing time when sea conditions are favorable and requiring detours to avoid risks when conditions are poor. Finally, the planned start and end times are artificially fixed, making it impossible to plan optimal departure and arrival times, a factor that lacks objectivity. In summary, while Technique B can solve trajectory planning problems in some simple cases, it still presents several challenges when dealing with situations such as the example presented here. These challenges are effectively addressed in the method presented in this paper.

[0059] Due to the nature of the Dijkstra algorithm, simply adding the indicator risk value and terrain risk value at each point on the shortest path, weighted by 0.5, and then taking the average, maximum, and minimum of this combined risk value provides a rough understanding of the speed allocation plan for the route. Calculations yield Table 1. The average risk value for the planned trajectory obtained by our algorithm is 0.2671, representing a low risk level. In contrast, the value for Technique B is 0.4347, approaching a medium risk level. The maximum risk value obtained by our algorithm is 0.6862, which is lower than that obtained by Technique B. The minimum risk value, 0.0393, is significantly lower than that obtained by Technique B. These results demonstrate the robust risk control capabilities of our algorithm, surpassing existing, comparable technologies in all respects. At average risk, our algorithm's risk control capability improves by approximately 38.56%.

[0060] In summary, the route provided by technology B has the disadvantages of high risk of grounding, high number of bends, poor flexibility in speed setting, etc. g 、R f After risk evaluation of the two matrices, technique B is obviously superior to technique B.

[0061] Table 1 Analysis of the average, maximum and minimum values ​​of comprehensive risk assessment of path points

[0062]

[0063] The above embodiment is a preferred technical solution, and the specific embodiment of the present invention shall be subject to the description in the claims.

Claims

1. A variable speed trajectory planning method based on improved Dijkstra, characterized in that: The following steps are involved: (1) Designated planning sea areas; (2) Marine terrain assessment; (3) Marine meteorological and hydrological risk assessment; (4) Setting constraints and starting and target points; (5) Implementation of variable speed trajectory planning algorithm; (6) Track evaluation; The trajectory planning algorithm in step (5) comprises the following steps: A. Map preprocessing: Based on the indicator risk matrix, some points that are always high-risk are set as non-navigable points on the grid map, and a grid map new_field is constructed to flexibly plan daily navigation in the time dimension; B. Set the cost of each step of the eight-direction Dijkstra algorithm to the distance cost and terrain risk cost. According to the weight ratio of the two, input the raster map new_field after map preprocessing, startPos=(x1,y1), goalPos=(x2,y2) and the terrain risk matrix R g ; Get the reasonable shortest path Path_opt1={z1,z2,…,z k }, which is a 1×k-dimensional row vector, each element of which is the linear index value of the raster map and records the basic information of the route; C. Extract the risk information on the shortest path and construct a time-risk-path matrix R with a dimension of d×k χ ; D. Apply the improved Dijkstra algorithm to the time-risk-path matrix to obtain a variable speed trajectory planning scheme; E. Linear index element Z of Path_opt2 i The corresponding matrix coordinates (r i ,c i ) for identification, and then clipping, specifying the sea area, starting point and target point for constrained track planning, giving a reasonable route, and on this basis assigning a navigation plan to the route in the time dimension, defining the optimal departure time and arrival time, as well as the speed change planning plan.

2. The variable speed trajectory planning method based on the improved Dijkstra according to claim 1, characterized in that: In step C, the time-risk-path matrix R χ Specifically: According to the shortest path Path_opt1={z1,z2,…,z k }, starting from 1 and traversing the m×n×d indicator risk matrix R f For all values ​​of the third dimension d, search for the indicator risk values ​​of the corresponding path points within d days. The vertical axis is arranged in sequence from the 1st day to the dth day, and the horizontal axis is arranged in sequence from the starting point to the target point.

3. The variable speed trajectory planning method based on the improved Dijkstra according to claim 1, characterized in that: The improved Dijkstra algorithm is specifically as follows: three-directional search, namely, right, right and down directions; the search range is the time-risk-path matrix, the search starting point is fixed to the upper left corner element of the time-risk-path matrix, that is, the element with a linear index value of 1, and the matrix coordinate is (1,1); the target point is fixed to the lower right corner element of the time-risk-path matrix, that is, the element with a linear index value of d·k, and the matrix coordinate is (d,k); the improved Dijkstra algorithm is run to obtain a variable speed trajectory planning scheme Path_opt2={Z1,Z2,…,Z l }, which is a 1×l-dimensional row vector, each element of which is a linear index value of the time-risk-path matrix, and each linear index value corresponds to a unique pair of matrix coordinates, that is, i=1,2,…,k;where(r i ,c i ) represents the rth i The day should sail to c i waypoints.

4. The variable speed trajectory planning method based on the improved Dijkstra according to claim 1, characterized in that: The step E is specifically as follows: set the counting variable count=0, first find all matrix coordinates with the horizontal coordinate c1, stack their vertical coordinates in order into a column vector R, traverse from the second element to the last element in R, and the first element in R must be 1; record the position of the first discontinuous element in the traversal process, and set count plus 1 if the element is continuous; after the traversal is completed, trim the first to count linear index elements Z i , and get the new Path_opt2′2={Z1′,Z2′,…,Z′ L }; Therefore, Path_opt2′ corresponds to the optimal departure time and arrival time.

5. The variable speed trajectory planning method based on the improved Dijkstra according to claim 4 is characterized in that: The optimal departure time is The vertical coordinate r1′ is the r1′th day; similarly, set the counting variable and first find the horizontal coordinate c k All matrix coordinates are stacked into vectors and then flipped up and down for easy operation. Finally, they are traversed and clipped. Then, the above steps are followed to obtain Path_opt2″={Z1′,′Z2″,…,Z p ″}, the optimal arrival time recommended by the algorithm is The vertical coordinate c′ p ′, that is, c′ p 'sky.

6. The variable speed trajectory planning method based on the improved Dijkstra according to claim 5, characterized in that: Set the Path_opt2″={Z1″, Z2″,…, Z′ p ′}, visualized as a three-dimensional space-time graph.

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