Off-road intelligent vehicle global path planning method based on bidirectional alternate search A*

Abstract

The application is suitable for the technical field of intelligent vehicle path planning, and provides an off-road intelligent vehicle global path planning method based on bidirectional alternate search A*; the method adopts a hierarchical processing architecture: the first layer generates a global original polyline path through bidirectional alternate search A* algorithm; the second layer performs node filtering and smoothing processing on the path, eliminates redundant nodes and meets the kinematic constraints of the vehicle. The method effectively solves the problems of low path planning efficiency, poor terrain adaptability and insufficient path smoothness in off-road environment, and realizes safe, efficient and feasible global path planning. The planning path of the application not only maintains the terrain passing optimality, but also has continuous and derivable geometric characteristics, and can be directly used for vehicle tracking control, significantly improving the autonomous driving capability of off-road vehicles in complex terrain.

Description

Technical Field

[0001] This invention belongs to the field of intelligent vehicle path planning technology, and particularly relates to a global path planning method for off-road intelligent vehicles based on bidirectional alternating search A*. Background Technology

[0002] Path planning is one of the core functions for autonomous navigation in intelligent vehicles. In structured road scenarios, path planning methods based on high-precision maps and lane constraints are relatively mature. However, off-road environments, with their unstructured characteristics such as lack of clear road markings, varied terrain, and complex ground properties, pose significant challenges to path planning algorithms. Currently, the most widely used algorithm in global path planning is the A* algorithm. It guides the search direction through a heuristic function and can quickly generate a path from the starting point to the destination in a rasterized map, combining completeness and optimality, and is widely used in mobile robot path generation tasks.

[0003] The standard A* algorithm suffers from three significant drawbacks in large-scale off-road map applications: First, the massive number of nodes leads to low search efficiency, making it difficult to meet real-time requirements. Second, the heuristic function only considers Euclidean distance or simple obstacle distances, failing to effectively quantify the real impact of terrain factors such as slope resistance and rolling resistance on vehicle passage, resulting in a geometrically shortest but physically infeasible planned path. Third, the algorithm outputs a polyline path with numerous sharp turning points, requiring post-processing (such as Bézier curve fitting) for smoothing. Existing post-processing methods separate geometric continuity from kinematic constraints; when the smoothed path fails to meet minimum turning radius or terrain safety constraints, repeated corrections or even replanning are necessary, resulting in overall low efficiency.

[0004] To address the aforementioned issues, existing research proposes two improvement directions: one incorporates attitude costs such as terrain slope and roll angle into the A* cost function to improve path terrain adaptability, but fails to solve the search efficiency problem; the other uses a hybrid A* algorithm with embedded kinematic constraints, which, while taking into account vehicle dynamics, suffers from excessively high computational complexity, making it difficult to support large-scale off-road global planning. Neither existing solution achieves simultaneous high search efficiency, terrain adaptability, and synergistic optimization of kinematic constraints, resulting in persistent technical bottlenecks in off-road path planning due to low efficiency and poor feasibility. Summary of the Invention

[0005] The purpose of this invention is to provide a global path planning method for off-road intelligent vehicles based on bidirectional alternating search A*, aiming to solve the problems mentioned in the background art.

[0006] The embodiments of the present invention are implemented as follows: a global path planning method for off-road intelligent vehicles based on bidirectional alternating search A*, comprising the following steps:

[0007] Step 1: Establish a global grid map, which contains elevation information, and calculate the slope and rolling resistance coefficient of each grid based on the elevation information;

[0008] Step 2: Based on the slope and rolling resistance coefficient, calculate the terrain field of the rugged terrain and determine the actual cost from the starting point to the current node in the A* algorithm. And the heuristic function from the current node to the target node. ;

[0009] Step 3: Use a bidirectional alternating search (BAS) strategy to perform path search, starting from the starting point. Begin forward search, starting from the endpoint. Start the reverse search. During the forward and reverse search processes, exchange information on the current optimal boundary nodes between the two sides in real time to guide each other's search direction.

[0010] Step 4: When a forward search node meets a backward search node, perform path concatenation to generate a path starting from the origin. To the finish line The original polyline path;

[0011] Step 5: Filter the original polyline path by key nodes, remove redundant nodes, and generate a sparse polyline path composed of key nodes.

[0012] Step 6: Based on the key nodes in the sparse polyline path, Bézier curves are used for path smoothing. During the smoothing process, turning constraints, terrain constraints, and connection constraints are applied simultaneously. Under the premise of ensuring path traversability and terrain adaptability, the curvature continuity and smooth transition of the global path are achieved.

[0013] In a further technical solution, step 1 includes the following specific steps:

[0014] Step 1.1: Digital Elevation Model (DEM) Construction;

[0015] A DEM is used to describe the three-dimensional terrain features of the off-road environment. The DEM is constructed as follows: the study area is divided into squares of equal size, and each square records an elevation value. The continuous curved terrain is transformed into a two-dimensional matrix composed of squares, and each element in the matrix represents the elevation value corresponding to that square.

[0016] Step 1.2: Ground feature analysis;

[0017] Step 1.2.1: Calculate the terrain slope;

[0018] The terrain of the off-road environment was assessed based on the DEM. To calculate the surface slope, a 3D model was used. 3. The moving window method is used to process raster data; taking the raster to be calculated as the center, the elevation values ​​of the eight surrounding adjacent raster cells are taken to calculate the east-west elevation change rate. and the rate of change of elevation in the north-south direction :

[0019] (1)

[0020] (2)

[0021] in, It is the grid side length. The elevation value of the raster;

[0022] Slope angle of the middle grid for:

[0023] (3)

[0024] slope Expressed as a percentage, equation (3) becomes:

[0025] (4)

[0026] Here, 40% is taken as the median value as the slope constraint threshold. Grid cells with a slope exceeding this value are assigned an infinite passage cost.

[0027] Step 1.2.2: Calculate the surface travel cost based on the rolling resistance coefficient;

[0028] Introducing the rolling resistance coefficient as a traffic cost indicator to quantify the traffic difficulty of different road surface types; Rolling resistance coefficient Defined as the ratio of the traction force required for a vehicle to overcome road surface deformation to the vehicle's normal load, it is used to characterize the softness of the road surface and the ease of passage; thus, the surface passage cost of a grid cell. Defined as:

[0029] (5).

[0030] In a further technical solution, step 2 includes the following specific steps:

[0031] Step 2.1: Calculate the terrain field of the rugged terrain;

[0032] Introducing the artificial potential field method, for any grid cell Its total repulsive potential field value Defined as:

[0033] (6)

[0034] In the formula, This is the repulsive force intensity coefficient, used to adjust the overall magnitude of the repulsive force; For grid cells To the An undulating grid The distance; It is a very small positive number, and a fixed constant of 0.001 is used to prevent the denominator from being equal to 0 when the distance is 0; For grid cells The total number of surrounding undulating grid cells;

[0035] Step 2.2: Improve the evaluation function;

[0036] Introducing the BAS strategy for heuristic functions An exponential decay weighting mechanism is introduced; simultaneously, based on the aforementioned slope calculation and the calculation of surface travel cost based on the rolling resistance coefficient, as well as the construction of the terrain field, the cost function is set as follows:

[0037] (7)

[0038] In the formula, Represents the total cost; This represents the repulsive potential field value of the current node; , and These are the weighting coefficients for each cost, which add up to 1. For index weighting factors;

[0039] 1) Actual cost In the iterative process of improving the A* algorithm, starting from the current node... Extend to child nodes At that time, the actual cost of updating the child nodes. The update method is the actual cost from the starting point to the current node. Adding the terrain traversal cost from the current node to its extended child nodes, the actual cost function is thus improved to:

[0040] (8)

[0041] in, For the current node; for The extended child nodes of a point; The Euclidean distance between grid cells; The slope of the grid;

[0042] 2) Heuristic function Design two sub-functions and , To meet vehicle kinematic constraints, the shortest path that ignores collision factors is selected. The shortest path that satisfies obstacle avoidance constraints but ignores vehicle dynamics constraints; for and The maximum value, using and The calculated values ​​naturally differ at different distances, and the maximum value is taken to achieve dominance at different stages; at the same time, the additional cost of obstacles in the predicted path is considered. The improved heuristic function is as follows:

[0043] (9)

[0044] (10)

[0045] in, As a fundamental estimator of the heuristic function; Implemented based on Reeds-Shepp curves; Implemented by an improved ant colony algorithm, based on a grid map, obstacle areas are set as impassable areas, and the shortest path without collision is searched through the positive feedback mechanism of ant colony pheromones, and the length of the path segment is taken as the function value. Used to correct and improve the estimated cost of the heuristic function; This represents the number of obstacle points on the line connecting the current node and its parent node whose Euclidean distance to the line is less than a set threshold. This is the unit obstacle cost coefficient, used to quantify the impact of a single eligible obstacle point on the estimated path cost.

[0046] In a further technical solution, step 3 includes the following specific steps:

[0047] Initialization phase: Initialize the forward open list Reverse open list and the corresponding closed list , Initialize the forward and reverse parent node pointer table;

[0048] Termination condition judgment: If and If all values ​​are empty, the path does not exist, the search fails, and the algorithm terminates.

[0049] Forward expansion: If If not empty, the evaluated function value will be displayed. The smallest node is selected as the current forward node. Move it into ;examine Does it exist in If they exist, it is determined that they meet in both directions, and the process proceeds to step 4; otherwise, for All 8-neighbor feasible neighbor nodes ,like Calculate its cost according to the evaluation function formula and update it. ;

[0050] Reverse expansion: Starting from the current forward node For the search target, the search steps are the same as for forward expansion.

[0051] A further technical solution, the specific steps of step 5 are as follows:

[0052] 1) Initialization: Starting from the beginning As the current anchor point And add it to the set of key nodes. ;

[0053] 2) Forward search: from the current anchor point Begin by connecting subsequent nodes sequentially. ,judge Did it collide with an obstacle?

[0054] 3) Multi-constraint collision detection: for line segments Perform four joint tests, including geometric collision test, safety margin test, terrain cost test, and turning capability test; if all four tests pass, continue to expand backward; if any one of them fails, stop the expansion of the current anchor point.

[0055] 4) Key node extraction: Extract the last collision-free node. As a key node, add it to the key node set. and set it as the new current anchor point. ;

[0056] 5) Iterative execution: Repeat steps 2) to 4) until the current anchor point. Reach the finish line and will Add to key node set ;

[0057] 6) Path Reconstruction: Connect the key node sets sequentially. Each node in the graph generates a filtered sparse polyline path.

[0058] In a further technical solution, step 5 involves four joint tests:

[0059] Geometric collision check: A straight-line grid traversal method is used to ensure that no obstacle grid is crossed;

[0060] Safety margin check: Ensure that the line segment maintains a safe distance of at least one grid cell from the outer edge of all obstacle expansion areas;

[0061] Terrain cost check: Calculate the average unit terrain cost of the area traversed by the line segment. If it exceeds 1.5 times the average cost of the corresponding section of the original path, it is determined to be impassable.

[0062] Steering ability test: Predict the vehicle's position at the current anchor point The change in heading angle formed by the previous critical node ensures that the single steering angle does not exceed the vehicle's maximum steering angle.

[0063] A further technical solution involves introducing a third-order Bézier curve and control parameters that determine the control point positions in step 6, parameterizing the intermediate control points into the form of "start point / end point ± proportional coefficient × segment length × heading vector"; for key nodes... , and The control points for the resulting third-order Bézier curve segment are generated as follows:

[0064] (11)

[0065] (12)

[0066] (13)

[0067] (14)

[0068] in, This indicates the direction of travel when entering the current segment; This indicates that you are about to leave the current direction of travel; Represents the distance from the start to the end of the current segment; and This is the proportionality coefficient;

[0069] Control points are introduced to incorporate turning constraints, terrain constraints, and connection constraints, where:

[0070] Turning constraints: After the Bézier curve is generated, the curve is sampled at equal intervals to ensure the curvature at any point. If the limit is exceeded, the curvature of the curve will be reduced by adaptively adjusting the control point parameters until the constraint is met.

[0071] Terrain constraints: Define the path-terrain deviation cost, which is the weighted slope and resistance integral value of the area traversed by the curve; if the deviation cost exceeds the preset threshold, tighten the control points to move closer to the original polyline to prevent the smooth path from encroaching on steep slopes or high resistance areas.

[0072] Connection constraints: Adjacent Bézier curve segments must satisfy positional continuity and tangential continuity at the connection point to ensure a smooth transition of the global path heading; by forcing the collinearity of control points of preceding and following segments, natural connection between segments is achieved, avoiding abrupt changes in steering.

[0073] Further technical solutions, proportional coefficient and The initial value is 0.5 by default. If the curvature exceeds the preset threshold, it will be reduced in a normal step size of 0.05 to 0.1. and The curve is then regenerated until the constraint is met or the lower limit engineering experience value of 0.1 is reached, and 0.1 is taken as the minimum value. and The minimum value.

[0074] The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* provided in this invention has the following beneficial effects:

[0075] (1) Improve search efficiency: The bidirectional alternating search strategy is adopted, and mutual guidance is achieved by exchanging the optimal node information in the forward and reverse directions in real time. This significantly reduces the number of node expansions, accelerates convergence, and solves the problem of low search efficiency of the traditional A* algorithm in large-scale off-road maps.

[0076] (2) Enhance terrain adaptability: Construct a comprehensive terrain cost model, and incorporate both slope resistance and rolling resistance into the actual cost and heuristic function to make the planned path truly reflect the difficulty of vehicle passage and energy consumption characteristics; the heuristic function integrates Reeds-Shepp curves and improved ant colony algorithm to take into account kinematic constraints and obstacle avoidance requirements, and ensure the physical feasibility of the path.

[0077] (3) Suppress search oscillations: Introduce an exponential decay weighting mechanism to dynamically adjust the heuristic weights based on the distance between the current node and the other party's search node. Strengthen the direction guidance at long distances and reduce the weights at close distances to get closer to the real cost, so as to avoid detours or oscillations caused by fixed weights and improve convergence stability.

[0078] (4) Output a traceable smooth path: By filtering out redundant turning points through key nodes, and by applying minimum turning radius, terrain safety and continuity constraints simultaneously with the third-order Bézier curve, a path with continuous curvature and kinematic constraints is generated, which can be directly used for local tracking control without secondary interpolation.

[0079] (5) Integrated smooth design: Abandoning the traditional “search-post-processing” fragmented mode, the terrain cost and turning capability are used as internal constraints in curve generation to ensure that the smooth path does not deviate from the low cost area, avoid the risk of terrain intrusion caused by geometric smoothness, and improve path safety and passability.

[0080] (6) Enhance autonomous navigation capability: While maintaining the completeness and optimality of the A* algorithm, comprehensively optimize search efficiency, terrain adaptability, path smoothness and kinematic feasibility, and comprehensively enhance the global path planning capability of intelligent vehicles in complex off-road environments, which has high engineering practical value. Attached Figure Description

[0081] Figure 1 A flowchart of the global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* provided in an embodiment of the present invention;

[0082] Figure 2 This is a diagram illustrating the movement of a window;

[0083] Figure 3 This is a schematic diagram of the dynamic update of positive and negative targets in a synchronous bidirectional alternating search (where a is the initial state, b is the forward expansion, c is the reverse expansion, and d is the meeting process). Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0085] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0086] like Figure 1 As shown, this invention provides a global path planning method for off-road intelligent vehicles based on bidirectional alternating search A*, which employs a hierarchical processing architecture: the first layer generates a global original polyline path using an improved bidirectional alternating search A* algorithm; the second layer performs node filtering and smoothing on the path, eliminating redundant nodes and satisfying vehicle kinematic constraints. Details are as follows:

[0087] First layer: Global path planning based on bidirectional search A*;

[0088] Since the A* algorithm is only suitable for urban environments with flat roads and clearly defined obstacles, it is necessary to consider terrain factors and create an environmental map that includes slope and undulations to make it effective in off-road environments with varying road types and undulations. Considering that raster maps can better store environmental elevation information and can assign different passage costs to raster cells based on different ground types to measure the impact of ground types on vehicle performance, a raster method is adopted, using a DEM as the basis to comprehensively consider information on different ground types to create the map.

[0089] Step 1: Create a global raster map;

[0090] (1) DEM Construction: The three-dimensional terrain features of the off-road environment are described using a DEM. The DEM is constructed as follows: the study area is divided into squares of equal size, and each square records an elevation value. In this way, the continuous curved terrain is transformed into a two-dimensional matrix composed of squares, and each element in the matrix represents the elevation value corresponding to that square.

[0091] (2) Ground feature analysis:

[0092] ① Calculate the terrain slope:

[0093] The terrain of the off-road environment was assessed based on the DEM. To calculate the surface slope, a 3D model was used. 3. The moving window method is used to process raster data. Figure 2 A calculation illustration of this method is provided. Taking the grid cell to be calculated as the center, the elevation values ​​of the eight surrounding adjacent grid cells are used to calculate the east-west elevation variation rate. (Equation 1) and the rate of change of elevation in the north-south direction (Equation 2):

[0094] (1)

[0095] (2)

[0096] in, It is the grid side length. This represents the elevation value of the raster.

[0097] The slope angle of the middle grid for:

[0098] (3)

[0099] slope When expressed as a percentage, equation (3) becomes:

[0100] (4)

[0101] The maximum climbing gradient for most off-road vehicles is 30%. Between 60% and 40%, the middle value is taken as the slope constraint threshold. Grid cells with a slope exceeding this value are assigned an infinite passage cost.

[0102] ② Calculate the surface travel cost based on the rolling resistance coefficient:

[0103] In off-road environments, terrain type directly impacts vehicle passability. To quantify the difficulty of traversing different terrain types, a rolling resistance coefficient is introduced as an indicator of passability cost. Rolling resistance coefficient Defined as the ratio of the traction force required for a vehicle to overcome road surface deformation to the vehicle's normal load, this is a physical quantity characterizing the softness of the road surface and the ease of passage. A larger coefficient indicates a softer road surface and a higher difficulty for vehicles to pass. Therefore, the surface passage cost of a grid cell... Defined as:

[0104] (5)

[0105] in, For specific values, please refer to the experimental data given in relevant literature on vehicle ground mechanics (such as "Automotive Theory").

[0106] Step 2: Calculate the terrain field of the rugged terrain;

[0107] The aforementioned slope and rolling resistance coefficient calculations only reflect the passability of a single grid cell and cannot describe the impact of regional terrain undulations on path selection. In actual off-road environments, even if the slope of each grid cell is within the passable range, continuously undulating terrain can still lead to a decrease in vehicle ride comfort. Therefore, an artificial potential field method is introduced to construct a repulsive potential field for areas with severe undulations. This potential field does not depend on the slope or road surface type of the grid cell itself, but is based on a comprehensive consideration of the elevation fluctuation characteristics of some terrain features, enabling the planned path to proactively avoid areas with large undulations at the global level. For any grid cell... Its total repulsive potential field value Defined as:

[0108] (6)

[0109] In the formula, This is the repulsive force intensity coefficient, used to adjust the overall magnitude of the repulsive force, and is typically taken from the conventional range of 5 in this field. 10. The simulation calibration is adapted to the terrain undulations and uses "balance between obstacle avoidance safety and search efficiency" as the indicator. For grid cells To the An undulating grid The distance is calculated using Euclidean distance based on coordinates; the closer the distance, the greater the repulsive force. It is a very small positive number, and a fixed constant of 0.001 is used to prevent the denominator from being equal to 0 when the distance is 0; For grid cells The total number of surrounding undulating grid cells is calculated from DEM data: First, the undulation of each grid cell (e.g., elevation root mean square deviation) is calculated. Grid cells exceeding a set threshold (determined based on off-road vehicle terrain accessibility and the "Digital Elevation Model Specification," etc.) are marked, and the number is counted. .

[0110] Step 3: Improve the evaluation function;

[0111] By introducing the BAS strategy, when the forward and backward search paths meet, if there are obstacles near the meeting area that are perpendicular to the path direction and difficult to bypass, traditional heuristic functions tend to guide the search to oscillate back and forth on both sides of the obstacle, causing the algorithm to repeatedly explore unnecessary nodes. This phenomenon not only fails to leverage the expected advantages of bidirectional search but may even lead to a total number of expanded nodes exceeding that of the original A* algorithm, severely reducing path planning efficiency. To address these issues, this step modifies the heuristic function... An exponential decay weighted mechanism is introduced. This mechanism dynamically adjusts the heuristic values ​​by adjusting their weights, making the search direction more stable when approaching obstacles or encounter areas. This avoids search oscillations caused by fluctuations in cost estimation, thus significantly improving the convergence speed and planning efficiency of bidirectional alternating search in complex off-road terrain. Furthermore, based on the aforementioned slope calculation, the calculation of surface travel cost based on the rolling resistance coefficient, and the construction of the terrain field, the cost function is set as follows:

[0112] (7)

[0113] In the formula, Represents the total cost, The actual cost from the starting point to the current node. This is the heuristic function (i.e., cost estimate) from the current node to the target node. This represents the repulsive potential field value at the current node. , and The weighting coefficients for each cost are set to sum to 1, adapted to terrain complexity, and calibrated using a balance between traversability and convergence speed as the criterion. (Introduction) The core idea is to adaptively adjust the weights of the heuristic function based on the distance between the current node and the current best node searched by the other node, thereby optimizing the search direction and convergence speed. Specifically, when the current node is far from the current best node searched by the other node, it leads to... The index weighting factor is relatively large at this time. The corresponding increase makes the heuristic function The enhanced dominance of the current node in the evaluation function prompts the forward search to rapidly advance towards the target direction, accelerating the meeting process of the bidirectional paths. Conversely, as the current node gradually approaches the current optimal node of the other path's search, Consequently, the exponential weighting factor decreases. It also decays exponentially, and the weights of the heuristic function are dynamically reduced. At this point, More dependent on actual costs The reflected real terrain cost makes the estimated cost closer to the actual travel cost, avoiding local path distortion or detours caused by excessive heuristic value dominance. Through the above-mentioned exponential decay weighting mechanism, this method effectively suppresses search oscillations and node redundancy caused by fixed heuristic function weights while retaining the high efficiency of bidirectional alternating search. It achieves adaptive search characteristics of rapid long-distance guidance and accurate short-distance evaluation, significantly improving the efficiency of global path planning in complex off-road terrain.

[0114] 1) Actual cost In the iterative process of improving the A* algorithm, starting from the current node... Extend to child nodes At that time, the actual cost of updating the child nodes. The update method is to calculate the actual cost from the starting point to the current node. Adding the terrain traversal cost from the current node to its extended child nodes, the actual cost function can be improved to:

[0115] (8)

[0116] in, For the current node; for The extended child nodes of a point; The Euclidean distance between grid cells; The slope of the grid.

[0117] 2) Heuristic function Considering that the heuristic cost in the traditional A* algorithm is represented only by the Euclidean distance from the current node to the target node, which not only fails to reflect the actual driving environment of off-road intelligent vehicles but also completely ignores terrain factors in the cost estimation, two sub-functions are designed. and , To meet vehicle kinematic constraints, the shortest path that ignores collision factors is selected. The shortest path that satisfies obstacle avoidance constraints but ignores vehicle dynamics constraints. for and The maximum value, when the distance from the target node is far, Dominant, guiding the search rapidly towards the destination and avoiding obstacle areas; when close to the target node, Dominant, satisfying vehicle kinematic constraints, ensuring the path can be executed by the vehicle, accurately reaching the target node, without needing to set additional distance thresholds, utilizing and The calculated values ​​naturally differ at different distances. By taking the maximum value, the dominance of different stages is achieved, ensuring the adaptability of the heuristic function. At the same time, the additional cost of obstacles in the predicted path is considered. The improved heuristic function is as follows:

[0118] (9)

[0119] (10)

[0120] in, As a basic estimate of the heuristic function. It is implemented based on the Reeds-Shepp curve, which is a well-known curve in the field of path planning that is adapted to the two-degree-of-freedom kinematic model of the vehicle and satisfies the minimum turning radius constraint. Its length can be directly solved by the fixed formula of the curve. Implemented by an improved ant colony algorithm, based on a grid map, obstacle areas are set as impassable areas, and the shortest path without collision is searched through the positive feedback mechanism of ant colony pheromones, and the length of the path segment is taken as the function value. Used to correct and improve the estimated cost of the heuristic function; This is the number of obstacle points on the line connecting the current node and its parent node whose Euclidean distance to the line is less than a set threshold (path safety distance, which should be half the width of the vehicle based on the vehicle's geometry and path safety avoidance principles). This is the unit obstacle cost coefficient, used to quantify the impact of a single eligible obstacle point on the estimated path cost. Its value is positively correlated with the side length of a single grid cell in the raster map, and is preferably 0.5 of the side length of the single grid cell. The size can be adjusted adaptively based on map accuracy and obstacle density; the denser the obstacles, the larger the map grid. The larger the value, the better.

[0121] Step 4: Implement a bidirectional alternating search strategy;

[0122] The improved evaluation function can be obtained from the first three steps. Based on this, the dynamic update diagram is as follows: Figure 3 As shown, the complete process for further implementing bidirectional alternating search A* is as follows:

[0123] ① Initialization phase: Initialize the forward open list Reverse open list and the corresponding closed list , Initialize the forward and reverse parent node pointer table;

[0124] ② Termination condition judgment: If and If all values ​​are empty, the path does not exist, the search fails, and the algorithm terminates.

[0125] ③ Forward expansion: If If not empty, the evaluated function value will be displayed. The smallest node is selected as the current forward node. Move it into .examine Does it exist in If they exist, it is determined that they meet in both directions, and the process proceeds to step ⑤; otherwise, for... All 8-neighbor feasible neighbor nodes ,like Calculate its cost according to the evaluation function formula and update it. ;

[0126] ④ Reverse expansion: Starting from the current forward node For the search target, the search steps are the same as for forward expansion.

[0127] ⑤ Path concatenation and output: Using the meeting node as the connection point, backtrack from the meeting node to the starting point along the forward parent pointer. Backtrack along the parent pointer to the end point By splicing the two paths together, a path is formed from... arrive The complete planning path.

[0128] Second layer: Global path smoothing based on Bézier curves;

[0129] Step 1: Path node filtering;

[0130] While the first-layer bidirectional alternating search A* global path planning significantly reduces path planning time and turning angles, it also introduces problems such as increased path length and redundant turning nodes. The generated path exhibits obvious jagged, broken-line characteristics with discontinuous curvature, failing to meet the requirements of smoothness, continuity, and terrain adaptability in actual off-road environments, and also hindering smooth vehicle steering and speed control. To address these issues, a key node filtering process is introduced in the second layer to post-process and optimize the original broken-line path planned in the first layer. The specific steps are as follows:

[0131] 1) Initialization: Starting from the beginning As the current anchor point And add it to the set of key nodes. ;

[0132] 2) Forward search: from the current anchor point Begin by connecting subsequent nodes sequentially. ,judge Did it collide with an obstacle?

[0133] 3) Multi-constraint collision detection: for line segments Perform the following four joint tests:

[0134] ① Geometric collision check: A straight-line grid traversal method is used to ensure that no obstacle grid is crossed;

[0135] ② Safety margin check: Ensure that the line segment maintains a safe distance of at least one grid cell from the outer edge of all obstacle expansion areas;

[0136] ③ Terrain cost check: Calculate the average unit terrain cost of the area traversed by the line segment. If it exceeds 1.5 times the average cost of the corresponding section of the original path (this value refers to the commonly used safety factor of 1.5 in engineering design, which can be calibrated according to the actual scenario), it is determined to be impassable.

[0137] ④ Steering ability test: Estimate the vehicle's performance at the current anchor point The change in heading angle formed by the previous critical node ensures that the single steering angle does not exceed the vehicle's maximum steering angle;

[0138] If all four checks pass, the process continues to expand; if any check fails, the expansion of the current anchor point stops.

[0139] 4) Key node extraction: Extract the last collision-free node. As a key node, add it to the key node set. and set it as the new current anchor point. ;

[0140] 5) Iterative execution: Repeat steps 2) to 4) until the current anchor point. Reach the finish line and will Add to key node set ;

[0141] 6) Path Reconstruction: Connect the key node sets sequentially. Each node in the graph generates a filtered sparse polyline path.

[0142] This step involves segment-by-segment visibility assessment and redundant node removal, retaining necessary terrain avoidance points and turning points while eliminating unnecessary intermediate turning points. This significantly shortens the path length, reduces the number of turns, and optimizes the turning angle distribution without altering path traversability. After critical node filtering, the path shape is optimized from a jagged, obstacle-edge-hugging line to a sparser line closer to the ideal driving trajectory. This provides a high-quality initial control point sequence for subsequent Bézier curve smoothing, ensuring the final global path possesses curvature continuity, terrain adaptability, and vehicle tracing capability, comprehensively enhancing the autonomous driving ability of off-road vehicles in complex terrain.

[0143] Step 2: Curve smoothing and constraint;

[0144] The optimized path generated after filtering by key nodes, while significantly reducing redundant turning points, still retains a broken line segment shape, exhibiting issues such as curvature discontinuity and abrupt steering changes, failing to meet the requirements of off-road vehicles for ride smoothness and terrain adaptability. Therefore, a third-order Bézier curve and control parameters determining the control point positions are introduced. To ensure the Bézier curve's starting point has the correct departure direction and the ending point has the correct arrival direction, and that the curve's curvature is adjustable and constrained, intermediate control points are parameterized as "start point / end point ± proportional coefficient × segment length × heading vector". For paths generated by key nodes... , and The control points for the resulting third-order Bézier curve segment are generated as follows:

[0145] (11)

[0146] (12)

[0147] (13)

[0148] (14)

[0149] in, This indicates the direction of travel when entering the current segment; This indicates that you are about to leave the current direction of travel; This represents the distance from the start to the end of the current segment. To prevent control points from being too close or too far from nodes, a scaling factor is introduced. and The initial value is 0.5 by default. If the curvature exceeds the preset threshold, it will be reduced by a normal step size of 0.05 to 0.1, calibrated with "smoothness and kinematic constraint adaptation" as the indicator. and The curve is then regenerated until the constraints are met or the curve is less than the lower limit of the empirical engineering value of 0.1. If the scaling factor is less than 0.1, the control points will be too close to the start or end point, and the generated curve will be too close to the broken line segment, losing its smoothness. Therefore, 0.1 is taken as the acceptable minimum value. Control points are introduced only to incorporate the following three types of constraints:

[0150] Turning constraint: The vehicle has a minimum turning radius. Physical limitations. This method, after generating the Bézier curve, performs equally spaced curvature sampling on the curve to ensure curvature at any point. If the limit is exceeded, the curvature of the curve is reduced by adaptively adjusting the control point parameters until the constraint is met.

[0151] Terrain Constraints: The smooth path must not significantly deviate from areas with low original terrain cost. This invention defines path-terrain deviation cost as the weighted slope and resistance integral value of the area traversed by the curve. If the deviation cost exceeds a preset threshold, the control points are tightened to revert to the original polygonal line, preventing the smooth path from encroaching on steep slopes or high-resistance areas.

[0152] Connection constraints: Adjacent Bézier curve segments must satisfy positional and tangential continuity at their connection points to ensure a smooth transition in the global path heading. This invention achieves natural connection between segments and avoids abrupt changes in direction by forcing collinear adjustment of control points between preceding and following segments.

[0153] By introducing third-order Bézier curves and triple constraints on turning, terrain, and connectivity, the curvature continuity and smooth heading transition of the global path are achieved while ensuring path traversability and terrain adaptability. The maximum curvature of the smoothed path strictly satisfies the vehicle's minimum turning radius constraint, eliminating the jagged lines and abrupt steering changes of traditional A* paths. Simultaneously, the terrain constraint mechanism effectively prevents the smoothed path from encroaching on steep slopes or high-resistance areas in pursuit of geometric smoothness. The resulting path curvature information can be explicitly extracted without secondary interpolation or local replanning, significantly improving the ride comfort, tracking accuracy, and control stability of off-road vehicles in actual driving.

[0154] As a preferred embodiment of the present invention, a bidirectional Dijkstra algorithm can be used instead of the A* framework. A cost boundary is maintained for both the forward and reverse directions. Each time, the direction with the smaller accumulated cost in the current boundary is selected for expansion until the two directional boundaries intersect. This method does not depend on the design of the heuristic function.

[0155] In a preferred embodiment of the present invention, the node expansion method can be replaced with jump-point search, utilizing the symmetry of the grid environment to achieve long-distance jump expansion. This scheme can be embedded in a bidirectional search framework, employing a jump-point expansion strategy in both forward and reverse directions, significantly reducing the number of expanded nodes.

[0156] As a preferred embodiment of the present invention, B-spline curves can be used instead of Bézier curves for path smoothing. B-spline curves have local support characteristics, and adjusting a single control point only affects the local shape of the curve, which facilitates fine-tuning of local road sections.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A global path planning method for off-road intelligent vehicles based on bidirectional alternating search A*, characterized in that, Includes the following steps: Step 1: Establish a global grid map, which contains elevation information, and calculate the slope and rolling resistance coefficient of each grid based on the elevation information; Step 2: Based on the slope and rolling resistance coefficient, calculate the terrain field of the rugged terrain and determine the actual cost from the starting point to the current node in the A* algorithm. And the heuristic function from the current node to the target node. ; Step 3: Use the BAS strategy for pathfinding, starting from the origin. Begin forward search, starting from the endpoint. Start the reverse search. During the forward and reverse search processes, exchange information on the current optimal boundary nodes between the two sides in real time to guide each other's search direction. Step 4: When a forward search node meets a backward search node, perform path concatenation to generate a path starting from the origin. To the finish line The original polyline path; Step 5: Filter the original polyline path by key nodes, remove redundant nodes, and generate a sparse polyline path composed of key nodes. Step 6: Based on the key nodes in the sparse polyline path, Bézier curves are used for path smoothing. During the smoothing process, turning constraints, terrain constraints, and connection constraints are applied simultaneously. Under the premise of ensuring path traversability and terrain adaptability, the curvature continuity and smooth transition of the global path are achieved.

2. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 1, characterized in that, Step 1 includes the following specific steps: Step 1.1: DEM construction; A DEM is used to describe the three-dimensional terrain features of the off-road environment. The DEM is constructed as follows: the study area is divided into squares of equal size, and each square records an elevation value. The continuous curved terrain is transformed into a two-dimensional matrix composed of squares, and each element in the matrix represents the elevation value corresponding to that square. Step 1.2: Ground feature analysis; Step 1.2.1: Calculate the terrain slope; The terrain of the off-road environment was assessed based on the DEM. To calculate the surface slope, a 3D model was used.

3. The moving window method is used to process raster data; taking the raster to be calculated as the center, the elevation values ​​of the eight surrounding adjacent raster cells are taken to calculate the east-west elevation change rate. and the rate of change of elevation in the north-south direction : （1） （2） in, It is the grid side length. The elevation value of the raster; Slope angle of the middle grid for: （3） slope Expressed as a percentage, equation (3) becomes: （4） Here, 40% is taken as the median value as the slope constraint threshold. Grid cells with a slope exceeding this value are assigned an infinite passage cost. Step 1.2.2: Calculate the surface travel cost based on the rolling resistance coefficient; Introducing the rolling resistance coefficient as a traffic cost indicator to quantify the traffic difficulty of different road surface types; Rolling resistance coefficient Defined as the ratio of the traction force required for a vehicle to overcome road surface deformation to the vehicle's normal load, it is used to characterize the softness of the road surface and the ease of passage; thus, the surface passage cost of a grid cell. Defined as: （5）。 3. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 2, characterized in that, Step 2 includes the following specific steps: Step 2.1: Calculate the terrain field of the rugged terrain; Introducing the artificial potential field method, for any grid cell Its total repulsive potential field value Defined as: (6) In the formula, This is the repulsive force intensity coefficient, used to adjust the overall magnitude of the repulsive force; For grid cells To the An undulating grid The distance; It is a very small positive number, and a fixed constant of 0.001 is used to prevent the denominator from being equal to 0 when the distance is 0; For grid cells The total number of surrounding undulating grid cells; Step 2.2: Improve the evaluation function; Introducing the BAS strategy for heuristic functions An exponential decay weighting mechanism is introduced; simultaneously, based on the aforementioned slope calculation and the calculation of surface travel cost based on the rolling resistance coefficient, as well as the construction of the terrain field, the cost function is set as follows: (7) In the formula, Represents the total cost; This represents the repulsive potential field value of the current node; , and These are the weighting coefficients for each cost, which add up to 1. For index weighting factors; 1) Actual cost In the iterative process of improving the A* algorithm, starting from the current node... Extend to child nodes At that time, the actual cost of updating the child nodes. ; The update method is the actual cost from the starting point to the current node. Adding the terrain traversal cost from the current node to its extended child nodes, the actual cost function is thus improved to: （8） in, For the current node; for The extended child nodes of a point; The Euclidean distance between grid cells; The slope of the grid; 2) Heuristic function Design two sub-functions and , To meet vehicle kinematic constraints, the shortest path that ignores collision factors is selected. The shortest path that satisfies obstacle avoidance constraints but ignores vehicle dynamics constraints; for and The maximum value, using and The calculated values ​​naturally differ at different distances, and the maximum value is taken to achieve dominance at different stages; at the same time, the additional cost of obstacles in the predicted path is considered. The improved heuristic function is as follows: （9） （10） in, As a fundamental estimator of the heuristic function; Implemented based on Reeds-Shepp curves; Implemented by an improved ant colony algorithm, based on a grid map, obstacle areas are set as impassable areas, and the shortest path without collision is searched through the positive feedback mechanism of ant colony pheromones, and the length of the path segment is taken as the function value. Used to correct and improve the estimated cost of the heuristic function; This represents the number of obstacle points on the line connecting the current node and its parent node whose Euclidean distance to the line is less than a set threshold. This is the unit obstacle cost coefficient, used to quantify the impact of a single eligible obstacle point on the estimated path cost.

4. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 1, characterized in that, Step 3 includes the following specific steps: Initialization phase: Initialize the forward open list Reverse open list and the corresponding closed list , Initialize the forward and reverse parent node pointer table; Termination condition judgment: If and If all values ​​are empty, the path does not exist, the search fails, and the algorithm terminates. Forward expansion: If If not empty, the evaluated function value will be displayed. The smallest node is selected as the current forward node. Move it into ;examine Does it exist in If they exist, it is determined that they meet in both directions, and the process proceeds to step 4; otherwise, for All 8-neighbor feasible neighbor nodes ,like Calculate its cost according to the evaluation function formula and update it. ; Reverse expansion: Starting from the current forward node For the search target, the search steps are the same as for forward expansion.

5. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 1, characterized in that, The specific steps of step 5 are as follows: 1) Initialization: Starting from the beginning As the current anchor point And add it to the set of key nodes. ; 2) Forward search: from the current anchor point Begin by connecting subsequent nodes sequentially. ,judge Did it collide with an obstacle? 3) Multi-constraint collision detection: for line segments Perform four joint tests, including geometric collision test, safety margin test, terrain cost test, and turning capability test; if all four tests pass, continue to expand backward; if any one of them fails, stop the expansion of the current anchor point. 4) Key node extraction: Extract the last collision-free node. As a key node, add it to the key node set. and set it as the new current anchor point. ; 5) Iterative execution: Repeat steps 2) to 4) until the current anchor point. Reach the finish line and will Add to key node set ; 6) Path Reconstruction: Connect the key node sets sequentially. Each node in the graph generates a filtered sparse polyline path.

6. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 5, characterized in that, In step 5, the four joint tests are specifically as follows: Geometric collision check: A straight-line grid traversal method is used to ensure that no obstacle grid is crossed; Safety margin check: Ensure that the line segment maintains a safe distance of at least one grid cell from the outer edge of all obstacle expansion areas; Terrain cost check: Calculate the average unit terrain cost of the area traversed by the line segment. If it exceeds 1.5 times the average cost of the corresponding section of the original path, it is determined to be impassable. Steering ability test: Predict the vehicle's position at the current anchor point The change in heading angle formed by the previous critical node ensures that the single steering angle does not exceed the vehicle's maximum steering angle.

7. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 5, characterized in that, In step 6, a third-order Bézier curve and control parameters determining the control point positions are introduced, and the intermediate control points are parameterized into the form of "start point / end point ± proportional coefficient × segment length × heading vector"; for key nodes , and The control points for the resulting third-order Bézier curve segment are generated as follows: (11) (12) (13) (14) in, This indicates the direction of travel when entering the current segment; This indicates that you are about to leave the current direction of travel; Represents the distance from the start to the end of the current segment; and This is the proportionality coefficient; Control points are introduced to incorporate turning constraints, terrain constraints, and connection constraints, where: Turning constraints: After the Bézier curve is generated, the curve is sampled at equal intervals to ensure the curvature at any point. If the limit is exceeded, the curvature of the curve will be reduced by adaptively adjusting the control point parameters until the constraint is met. Terrain constraints: Define the path-terrain deviation cost, which is the weighted slope and resistance integral value of the area traversed by the curve; if the deviation cost exceeds the preset threshold, tighten the control points to move closer to the original polyline to prevent the smooth path from encroaching on steep slopes or high resistance areas. Connection constraints: Adjacent Bézier curve segments must satisfy positional continuity and tangential continuity at the connection point to ensure a smooth transition of the global path heading; by forcing the collinearity of control points of preceding and following segments, natural connection between segments is achieved, avoiding abrupt changes in steering.

8. The global path planning method for off-road intelligent vehicles based on bidirectional alternating search A* according to claim 7, characterized in that, proportionality coefficient and The initial value is 0.5 by default. If the curvature exceeds the preset threshold, it will be reduced in a normal step size of 0.05 to 0.

1. and The curve is then regenerated until the constraint is met or the lower limit engineering experience value of 0.1 is reached, and 0.1 is taken as the minimum value. and The minimum value.

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