Route planning method in radiation environment based on Riemannian manifold

Abstract

The invention discloses a Riemannian manifold-based path planning method in a radiation environment, and belongs to the technical field of robot path planning in a nuclear environment, and the method comprises the following steps: S1, modeling an environment in which a robot moves, and establishing a Riemannian manifold influenced by environmental factors; s2, performing path search on the Riemannian manifold through an RRT * algorithm to generate an initial optimal path; and S3, performing path smooth optimization on the initial optimal path through collision-free constraint and non-incremental radiation constraint to generate a final smooth path. By introducing Riemannian measurement, the influence of environmental factors such as radiation risk on path selection is reflected more truly, efficient and safe path planning of the robot in a complex nuclear environment is effectively achieved, and the problem that an existing method depends on Euclidean distance as heuristic measurement, and the path selection accuracy is poor is solved. And the influence of environmental factors such as radiation risk on path selection cannot be truly reflected, so that path generation is unsafe.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of robot path planning in nuclear environment, and particularly relates to a path planning method in a radiation environment based on Riemannian manifold. BACKGROUND

[0002] Nuclear facilities need to perform frequent inspection, maintenance and emergency response operations in environments with different radiation levels. The Fukushima Daiichi nuclear power plant disaster and other related incidents highlight the urgent need for robots that can operate in high-radiation environments, as these environments have strict restrictions or are completely prohibited for human entry. In this case, autonomous or semi-autonomous robots can perform basic tasks including visual inspection, radiation mapping, sample collection and object manipulation, thereby minimizing human exposure to harmful radiation. However, traditional mobile robot path planning algorithms usually optimize path length, energy consumption or obstacle avoidance, without considering the unique challenges posed by the radiation field. The radiation spatial distribution in nuclear environments is often complex and non-uniform, with significant differences in radiation intensity in different regions. Therefore, the geometrically shortest path can expose the robot to unnecessary high cumulative radiation dose, potentially damaging electronic components and shortening operational life. Therefore, it is necessary to plan a safe and efficient path for robots working in nuclear radiation environments for this type of robot system.

[0003] Path planning methods are generally divided into graph search-based path planning methods, sampling-based path planning methods and heuristic-based optimization methods. Graph search algorithms represented by A* algorithm need to discretize map information into grids and perform domain search based on grids. The degree of grid division directly affects the accuracy of path planning algorithms, but higher accuracy will significantly increase computational load, thereby reducing planning efficiency. The main advantage of A* algorithm is that it can guarantee to find the globally optimal path, but the generated path may contain more inflection points, affecting the path smoothness in actual applications. Random sampling algorithms represented by RRT algorithm can be used for complex maps and can quickly generate locally optimal solutions. However, due to the randomness of the algorithm, the path generation is unstable and can only obtain a feasible solution, without guaranteeing to obtain an optimal solution. Heuristic algorithms are easy to combine with various algorithms, are not easy to fall into local optimum, and are easy to find a globally optimal path. However, the convergence speed is slow, it is easy to fall into local optimum, and the phenomenon of premature convergence, which is not conducive to finding better solutions.

[0004] The above algorithm has achieved remarkable results in path obstacle avoidance, radiation dose minimization and multi-robot cooperation, greatly improving the safety and intelligence of task execution in high-risk areas. However, it is worth noting that most of these methods are modeled and solved in the framework of Euclidean space. Although Euclidean space has the advantages of simple calculation, intuitive understanding and the like, its expression ability and modeling flexibility are often limited when facing environments with complex terrain constraints, nonlinear radiation distribution or high-dimensional state representation, making it difficult to fully characterize the geometric and physical properties of the actual environment. SUMMARY

[0005] In view of the above problems in the prior art, the path planning method in a radiation environment based on Riemannian manifold provided by the present application effectively realizes efficient and safe path planning of robots in a complex nuclear environment, and solves the problem that the existing method relies on Euclidean distance as a heuristic metric, which cannot truly reflect the influence of environmental factors such as radiation risk on path selection, resulting in unsafe path generation.

[0006] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the present application is as follows: a path planning method in a radiation environment based on Riemannian manifold, comprising the following steps: S1, modeling the environment of robot motion, establishing a Riemannian manifold affected by environmental factors; S2, performing path search on the Riemannian manifold through the RRT* algorithm to generate an initial optimal path; S3, performing path smoothing optimization on the initial optimal path through non-collision constraint and non-decreasing radiation constraint to generate a final smooth path.

[0007] Further, in S1, the method for establishing a Riemannian space affected by environmental factors comprises the following steps: S11, based on the original data of environmental elements in the environmental space of robot motion, converting the original data into a piecewise continuous function in a two-dimensional space through bilinear interpolation and Gaussian filtering to obtain a radiation intensity function and an obstacle function; S12, constructing a potential function according to the radiation intensity function and the obstacle function, mapping and embedding the environmental space into a three-dimensional Euclidean space through the potential function to construct a cost deformation surface; S13, calculating the Riemannian metric according to the inner product matrix of the tangent vector of the cost deformation surface, and constructing the environmental space into a Riemannian manifold according to the Riemannian metric and the cost deformation surface.

[0008] Further, in S11, the original data of environmental elements in the environmental space includes a radiation dose rate array and a binary obstacle mask array, and the expressions of the radiation intensity function and the obstacle function are as follows: Where, is the interpolation function of the radiation dose rate array, is the interpolation function of the binary obstacle mask array, is the standard deviation of the Gaussian kernel used for radiation intensity, is the standard deviation of the Gaussian kernel used to smooth the obstacle mask, x Any point in the environment space q The horizontal axis, y Any point in the environment space q The vertical coordinate, u is the first integration variable, v is the second integral variable, is pi.

[0009] Further: In S12, the potential function The specific expression is: Where, c 1 is the first weighting factor, which is used to adjust the importance of radiation intensity. c 2 is the second weight factor, which is used to adjust the importance of the impact of obstacles.

[0010] Further: In S13, the Riemannian metric The specific expression is: .

[0011] Further: S2 includes the following sub-steps: S21. Get the starting point and end point of the path planning, initialize the tree and the number of iterations; S22. Randomly sample and generate a new extended node in the Riemann manifold, search the tree for the nearest node of the new extended node, and calculate the cost of connecting the nearest node to the new extended node; S23, determine whether the new expansion node meets the barrier-free constraint. If so, add the new expansion node to the tree, update the optimal path from the starting point to the end point in the tree according to the cost between the connected nodes, and enter S24; if not, enter S24; S24. Determine whether the current number of iterations exceeds the iteration threshold. If so, generate an initial optimal path from the starting point to the end point. If not, increase the number of iterations by one and return to S22.

[0012] Further: In S22, the cost is specifically to connect to the nearest node To the new extension node The Riemann path length of the path between , its specific expression is: Where, T is the transpose symbol, is the path connecting the nearest node to the newly expanded node, for The Riemannian metric of is the derivative of the path, t is the path parameter; In S23, the method for determining whether the new extended node meets the accessibility constraint is as follows: Determine whether the new extended node is located in the obstacle area. If so, the new extended node does not meet the barrier-free constraint. If not, the new extended node meets the barrier-free constraint. The method for updating the optimal path from the starting point to the end point is as follows: Search the tree for a path connecting the starting point to the end point, and take the path with the minimum cost connecting the nodes as the optimal path.

[0013] Furthermore, in S3, the method for performing path smoothing optimization on the initial optimal path by using the no-collision constraint and the non-increasing radiation constraint includes the following steps: S31, taking the starting point of the initial optimal path as the starting point of the smoothed path, and taking the starting point of the initial optimal path as the current path point; S32. Starting from the current path point, search for subsequent path points in the initial optimal path, and connect the current path point with the searched subsequent path points to establish a shortcut segment. Determine whether there is a shortcut segment for the subsequent path point that satisfies the no-collision constraint and the non-increasing radiation constraint. If so, proceed to S33; if not, proceed to S34. S33, adding the subsequent path point corresponding to the longest shortcut segment that satisfies the no-collision constraint and the non-increasing radiation constraint to the smooth path, and taking the searched subsequent path point as the current path point, and returning to S32; S34: Add all subsequent path points of the current path point in the initial optimal path to the smooth path to generate a final smooth path.

[0014] Further: In S32, there is no collision constraint The specific expression is: Where, Current path point To the next waypoint The shortcut line segment of is a free space without obstacles, responding to ,but Satisfy the no-collision constraint; respond to ,but Not satisfying the non-collision constraint; The non-increasing radiation constraint is specifically a cumulative radiation dose along The expression is specifically: In the formula, is a unit vector in the direction of the line segment, , is the Euclidean length of the line segment, , is the L2 norm, and it is determined whether it is less than the cumulative radiation dose along the current path point to the subsequent path point in the initial optimal path. If yes, the non-increasing radiation constraint is satisfied; if no, the non-increasing radiation constraint is not satisfied.

[0015] The beneficial effects of the present application are as follows: (1) By introducing Riemannian metrics, the influence of environmental factors such as radiation risk on path selection is more realistically reflected. This enables the robot to avoid high-radiation areas in a nuclear environment, thereby significantly reducing exposure risk.

[0016] (2) The present application introduces a redundant point removal method based on radiation constraints in path optimization. This method optimizes the path through a greedy iterative strategy, so that the generated path not only has a shorter total distance, but also maintains smoothness, reducing unnecessary path turns or turns due to complex terrain and obstacle distribution.

[0017] (3) By introducing a Riemannian metric mechanism that fuses radiation exposure cost, the path planning process is optimized. Compared with traditional RRT-type algorithms, the present application can more effectively avoid high-radiation areas, thereby accelerating the convergence speed of the algorithm, improving the planning efficiency, and adapting to the special needs in a nuclear environment.

[0018] (4) The present application can effectively adapt to environments with uneven radiation intensity and complex obstacle distribution. Using Riemannian metrics for environment modeling, the algorithm has stronger adaptability in practical applications and can handle a variety of complex nuclear environment scenarios.

[0019] (5) By fully considering the influence of radiation distribution and obstacles in path planning, the present application improves the autonomous operation capability of robots in high-radiation environments. The robot can automatically select the safest and most efficient path to perform tasks without human intervention, thereby effectively reducing the risk of manual operation. ​​​

[0020] In summary, the path planning method in a radiation environment based on Riemannian manifold provided by the present application effectively realizes efficient and safe path planning of robots in a complex nuclear environment, and solves the problem that the existing method cannot truly reflect the influence of environmental factors such as radiation risk on path selection, and leads to unsafe path generation, by relying on Euclidean distance as a heuristic metric. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A flowchart of the path planning method in a radiation environment based on Riemannian manifold of the present application. DETAILED DESCRIPTION

[0022] The specific embodiments of the present application are described below to facilitate understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, as long as various changes are within the spirit and scope of the present application defined and determined by the appended claims, these changes are obvious, and all applications utilizing the concept of the present application are within the scope of protection.

[0023] As shown in the drawings, in one embodiment of the present application, a path planning method in a radiation environment based on Riemannian manifold includes the following steps: Figure 1 S1, modeling the environment of robot motion, establishing a Riemannian manifold affected by environmental factors; S2, searching for a path on the Riemannian manifold by RRT* algorithm, generating an initial optimal path; S3, performing path smoothing optimization on the initial optimal path by non-collision constraint and non-decreasing radiation constraint, generating a final smooth path. In this embodiment, the basic idea of the present application is to extend the RRT* algorithm framework and introduce Riemannian manifold theory to adapt to complex environments with different radiation levels and obstacle distributions. By modeling the environment as a Riemannian space affected by environmental factors, the algorithm can use the local geometric changes of the space to guide path search, thereby naturally avoiding high radiation areas or obstacle dense areas and tending to safer and more optimal paths. A redundant point removal method based on radiation constraint is designed, which adopts a greedy iterative "shortcut" strategy to optimize the initial path generated by the algorithm into a smooth path.

[0024] In S1, the method for establishing a Riemannian space affected by environmental factors includes the following steps:

[0025] ​S11, based on the original data of the environmental elements in the environment space of the robot motion, the original data is converted into a piecewise continuous function in two-dimensional space by bilinear interpolation and Gaussian filtering, to obtain the radiation intensity function and the obstacle function; S12, constructing a potential function according to the radiation intensity function and the obstacle function, mapping and embedding the environment space into a three-dimensional Euclidean space through the potential function, and constructing a cost deformation surface; S13, calculating the Riemann metric according to the inner product matrix of the tangent vector of the cost deformation surface, and constructing the environment space into a Riemann manifold according to the Riemann metric and the cost deformation surface.

[0026] In this embodiment, it is assumed that the environment space of the robot motion is , is a matrix, and the environment space contains a radiation field and an obstacle distribution. In order to construct a continuous description of these environmental elements in space, this embodiment takes any point in space as the independent variable, defines the radiation intensity function and the obstacle function . Both functions are generated by bilinear interpolation and Gaussian filtering method from discrete original data, which includes a radiation dose rate array and a binary obstacle mask array; In S11, the discrete data is converted into a piecewise continuous function in two-dimensional space by bilinear interpolation method. For a point , let its grid index be , , is the floor function, and the decimal part is , , then the interpolation function is expressed as follows: In the formula, , , and are the radiation dose rate array, , , and are the binary obstacle mask array; The above interpolation function is respectively subjected to Gaussian smoothing processing to improve the continuity and smoothness of the function, so as to eliminate the sharp change caused by piecewise interpolation, to obtain the radiation intensity function and the obstacle function . The expressions of the radiation intensity function and the obstacle function are as follows: wherein, is an interpolation function of the array of radiation dose rates, is an interpolation function of the array of binary obstacle masks, is a Gaussian kernel standard deviation for radiation intensity, is a Gaussian kernel standard deviation for smoothing obstacle masks, the larger the Gaussian kernel standard deviation, the smoother the function, x is the horizontal coordinate of an arbitrary point in the environment space, q is the vertical coordinate of an arbitrary point in the environment space, y is the horizontal coordinate of an arbitrary point in the environment space, q is the vertical coordinate of an arbitrary point in the environment space, u is a first integral variable, v is a second integral variable, is the ratio of a circle to its diameter.

[0027] In S12, the expression of the potential function is specifically: wherein, c 1 is a first weight factor for adjusting the importance of radiation intensity, c 2 is a second weight factor for adjusting the importance of obstacle influence, .

[0028] In this embodiment, in order to comprehensively consider the influence of radiation intensity and obstacles on robot path planning, the present application introduces a potential function to quantify the cost of the robot passing through different regions. The potential function constitutes a “cost landscape”, the higher the value, the greater the risk or passing cost of the position, which usually occurs in regions with high radiation intensity or close to obstacles.

[0029] The environment space is embedded into a three-dimensional Euclidean space through the potential function , thereby constructing a cost deformation surface . Specifically, the point is mapped to a three-dimensional point . Thus, the original two-dimensional space is embedded into a cost deformation surface defined by the potential function deformation, the height of which reflects the cost required to pass through the corresponding region.

[0030] In S13, the principle of constructing the Riemann metric is specifically: In order to quantitatively measure the path length on the cost morphing surface , the intrinsic Riemannian metric induced by the first fundamental form of the surface needs to be calculated. For a three-dimensional point C , the tangent vector of its parametric representation is: where is the first tangent vector of the three-dimensional point C , is the second tangent vector of the three-dimensional point C , and are the partial derivatives of the potential function with respect to x and y ; According to this, the induced metric tensor, i.e. the local Riemannian metric structure of the point, can be calculated, which is defined as the inner product matrix of the tangent vectors mentioned above, and the specific formula is as follows: where is the identity matrix, is the gradient vector of the potential function, and finally the expression of the Riemannian metric is obtained.

[0031] Under this Riemannian metric , the ambient space is endowed with a new metric structure, thus forming a Riemannian manifold , . On this manifold, the Riemannian path length of the path connecting any two points is defined as: In this Riemannian manifold, the algorithm implementation idea based on RRT* is to use the Riemannian path length as the cost of connecting two points, and to randomly sample in the environment to find a path connecting the starting point to the end point.

[0032] S2 comprises the following steps: S21, obtaining the starting point and the end point of path planning, initializing the tree and the iteration number; S22, randomly sampling to generate a new expansion node in the Riemannian manifold, searching for the nearest node of the new expansion node in the tree, and calculating the cost of connecting the nearest node to the new expansion node; ​S23, judging whether the new extended node meets the no-obstacle constraint, if yes, adding the new extended node to the tree, updating the optimal path from the starting point to the terminal point in the tree according to the cost between the connected nodes, and entering S24; if no, entering S24; S24, judging whether the current iteration number exceeds the iteration threshold, if yes, generating the initial optimal path from the starting point to the terminal point, if no, increasing the iteration number by one and returning to S22.

[0033] In the embodiment, the application performs path searching on the manifold based on the RRT* algorithm framework, and after multiple random sampling and tree expansion, the algorithm obtains an optimal path from the starting point to the terminal point .

[0034] In S22, the cost is specifically the Riemann path length of the path connecting the nearest node to the new extended node . The expression is specifically as follows: In the formula, T is a transpose symbol, is the path connecting the nearest node to the new extended node, is the Riemann metric of , is the derivative of the path, t is the path parameter; In S23, the method for judging whether the new extended node meets the no-obstacle constraint is specifically as follows: judging whether the new extended node is located in the obstacle region, if yes, the new extended node does not meet the no-obstacle constraint, if no, the new extended node meets the no-obstacle constraint; The method for updating the optimal path from the starting point to the terminal point is specifically as follows: searching the path connecting the starting point to the terminal point from the tree, and taking the path with the minimum cost of the connected nodes as the optimal path.

[0035] In the embodiment, the cost of the extended node set by the application adopts the Riemann path length, rather than the Euclidean distance. That is, the Riemann path length of the path connecting the nearest node to the new extended node is taken as the cost.

[0036] In S3, the method for performing path smoothing optimization on the initial optimal path through the no-collision constraint and the non-decreasing radiation constraint includes the following steps: S31, taking the starting point of the initial optimal path as the starting point of the smoothing path, and taking the starting point of the initial optimal path as the current path point; S32, starting from the current path point, searching for a subsequent path point in the initial optimal path, and connecting the current path point and the searched subsequent path point to establish a shortcut line segment, judging whether the shortcut line segment of the subsequent path point meets the non-collision constraint and the non-increasing radiation constraint; if yes, entering S33, and if no, entering S34; S33, adding the longest shortcut line segment meeting the non-collision constraint and the non-increasing radiation constraint to the smoothing path, and taking the searched subsequent path point as the current path point, and returning to S32; S34, adding all subsequent path points of the current path point in the initial optimal path to the smoothing path to generate a final smoothing path.

[0037] In the embodiment, the application introduces a path smoothing post-processing method, aiming to remove redundant path points in the initial optimal path and generate a final smoothing path . Assuming that each of , is a path point in the initial optimal path, n is the total number of path points in the initial optimal path, each of , is a path point in the final smoothing path, m is the total number of path points in the final smoothing path, wherein , , and . Starting from the current path point , the current path point is directly connected with the subsequent path point by a straight line segment to form a shortcut line segment , wherein , the shortcut line segment is considered to be effective and is used to replace the intermediate point in the initial optimal path , and only when the non-collision constraint and the non-increasing radiation constraint are met.

[0038] The path smoothing post-processing method will continuously start from the current path point to find the farthest subsequent path point that can meet the non-collision constraint and the non-increasing radiation constraint. Once such is found, it will become the next point in the smoothing path, and then the algorithm continues from to the next round of iteration. This process continues until the end point is reached.

[0039] In S32, the expression of the non-collision constraint is specifically: Where, Current path point To the next waypoint The shortcut line segment of is a free space without obstacles, responding to ,but Satisfy the no-collision constraint; respond to ,but The no-collision constraint is not satisfied; In this embodiment, the core principle of the no-collision constraint is: Must be completely within the feasible area, i.e. not in contact with any obstacles O A collision occurred.

[0040] The non-increasing radiation constraint is specifically along The cumulative radiation dose , its specific expression is: Where, is the unit vector in the direction of the line segment, , is the Euclidean length of the line segment, , is the L2 norm, judging Is it less than the current path point along the initial optimal path? To the next waypoint The cumulative radiation dose, if so, satisfies the non-increasing radiation constraint; if not, then The non-increasing radiation constraint is not satisfied.

[0041] In this embodiment, the core principle of non-increasing radiation constraint is: The cumulative radiation dose must be less than or equal to along the initial optimal path The cumulative radiation dose , Indicates that along the initial optimal path line segment.

[0042] In the description of the application, it needs to be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the application. In addition, the terms "first", "second", "third" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implying the number of technical features indicated. Therefore, the features defined by "first", "second", "third" can explicitly or implicitly include one or more of the features.

Claims

1. A path planning method in a radiation environment based on Riemannian manifold, characterized in that: The following steps are involved: S1. Model the environment in which the robot moves and establish a Riemannian manifold affected by environmental factors; S2, perform path search on the Riemannian manifold using the RRT* algorithm to generate the initial optimal path; S3. Optimize the initial optimal path through collision-free constraints and non-increasing radiation constraints to generate a final smooth path.

2. The path planning method in a radiation environment based on Riemannian manifold according to claim 1, characterized in that: In S1, the method for establishing the Riemann space affected by environmental factors includes the following steps: S11. Based on the original data of environmental elements in the environment space where the robot moves, the original data is converted into a piecewise continuous function in two-dimensional space through bilinear interpolation and Gaussian filtering to obtain a radiation intensity function and an obstacle function; S12. Constructing a potential function based on the radiation intensity function and the obstacle function, embedding the environment space into the three-dimensional Euclidean space through the potential function mapping, and constructing a cost deformation surface; S13. Calculate the Riemannian metric according to the inner product matrix of the tangent vector of the cost deformation surface, and construct the environment space into a Riemannian manifold according to the Riemannian metric and the cost deformation surface.

3. The path planning method in a radiation environment based on Riemannian manifold according to claim 2, characterized in that: In S11, the original data of environmental elements in the environmental space include radiation dose rate array and binary obstacle mask array, radiation intensity function and obstacle function The specific expression is: Where, is the interpolation function of the radiation dose rate array, is the interpolation function of the binary obstacle mask array, is the standard deviation of the Gaussian kernel used for radiation intensity, is the standard deviation of the Gaussian kernel used to smooth the obstacle mask, x Any point in the environment space q The horizontal axis, y Any point in the environment space q The vertical coordinate, u is the first integration variable, v is the second integral variable, is pi.

4. The path planning method in a radiation environment based on Riemannian manifold according to claim 3, characterized in that: In S12, the potential function The specific expression is: Where, c 1 is the first weighting factor, which is used to adjust the importance of radiation intensity. c 2 is the second weight factor, which is used to adjust the importance of the impact of obstacles.

5. The path planning method in a radiation environment based on Riemannian manifold according to claim 4, characterized in that: In S13, the Riemannian metric The specific expression is: 。 6. The path planning method in a radiation environment based on Riemannian manifold according to claim 5, characterized in that: S2 includes the following sub-steps: S21. Get the starting point and end point of the path planning, initialize the tree and the number of iterations; S22. Randomly sample and generate a new extended node in the Riemann manifold, search the tree for the nearest node of the new extended node, and calculate the cost of connecting the nearest node to the new extended node; S23, determine whether the new expansion node meets the barrier-free constraint. If so, add the new expansion node to the tree, update the optimal path from the starting point to the end point in the tree according to the cost between the connected nodes, and enter S24; if not, enter S24; S24. Determine whether the current number of iterations exceeds the iteration threshold. If so, generate an initial optimal path from the starting point to the end point. If not, increase the number of iterations by one and return to S22.

7. The path planning method in a radiation environment based on Riemannian manifold according to claim 6, characterized in that: In S22, the cost is specifically to connect to the nearest node To the new extension node The Riemann path length of the path between , its specific expression is: Where, T is the transpose symbol, is the path connecting the nearest node to the newly expanded node, for The Riemannian metric of is the derivative of the path, t is the path parameter; In S23, the method for determining whether the new extended node meets the accessibility constraint is as follows: Determine whether the new extended node is located in the obstacle area. If so, the new extended node does not meet the barrier-free constraint. If not, the new extended node meets the barrier-free constraint. The method for updating the optimal path from the starting point to the end point is as follows: Search the tree for a path connecting the starting point to the end point, and take the path with the minimum cost connecting the nodes as the optimal path.

8. The path planning method in a radiation environment based on Riemannian manifold according to claim 6, characterized in that: In S3, the method for smoothing the initial optimal path using the no-collision constraint and the non-increasing radiation constraint includes the following steps: S31, taking the starting point of the initial optimal path as the starting point of the smoothed path, and taking the starting point of the initial optimal path as the current path point; S32. Starting from the current path point, search for subsequent path points in the initial optimal path, and connect the current path point with the searched subsequent path points to establish a shortcut segment. Determine whether there is a shortcut segment for the subsequent path point that satisfies the no-collision constraint and the non-increasing radiation constraint. If so, proceed to S33; if not, proceed to S34. S33, adding the subsequent path point corresponding to the longest shortcut segment that satisfies the no-collision constraint and the non-increasing radiation constraint to the smooth path, and taking the searched subsequent path point as the current path point, and returning to S32; S34: Add all subsequent path points of the current path point in the initial optimal path to the smooth path to generate a final smooth path.

9. The path planning method in a radiation environment based on Riemannian manifold according to claim 8, characterized in that: In S32, there is no collision constraint The specific expression is: Where, Current path point To the next waypoint The shortcut line segment of is a free space without obstacles, responding to ,but Satisfy the no-collision constraint; respond to ,but The no-collision constraint is not satisfied; The non-increasing radiation constraint is specifically along The cumulative radiation dose , its specific expression is: Where, is the unit vector in the direction of the line segment, , is the Euclidean length of the line segment, , is the L2 norm, judging Is it less than the current path point along the initial optimal path? To the next waypoint The cumulative radiation dose, if so, satisfies the non-increasing radiation constraint; if not, then The non-increasing radiation constraint is not satisfied.

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