Dynamic trajectory planning method for mobile robot under constraint of elastic band

Abstract

The invention belongs to the technical field of artificial intelligence, and relates to a mobile robot dynamic trajectory planning method under elastic band constraint, comprising: initializing a robot kinetic equation, and using a cost function to represent an optimal motion planning problem; a random tree data set is constructed, a rewiring operation is executed in combination with the variable sampling region, and a random tree structure is optimized; adjusting a limited sampling area by using a target bias method; a layered collision detection method is adopted for obstacles, and rough collision detection and fine detection are carried out to eliminate invalid paths; calculating collision risk probabilities, and eliminating nodes with the collision risk probabilities exceeding a threshold value; the dynamic trajectory of the robot is optimized by applying an elastic band method, and the dynamic trajectory planning of the mobile robot is realized. According to the method, the state and collision risk of each node are detected in the trajectory optimization process, and the robustness and adaptability of the system are remarkably improved. The robot can adjust the track in a self-adaptive mode in a complex environment, and the obstacle avoidance requirement is met.

Description

Technical Field

[0001] The invention relates to the field of artificial intelligence technology, and in particular to a dynamic trajectory planning method for a mobile robot under elastic band constraints. Background Art

[0002] With the continuous maturity and enrichment of robotics technology, robots are increasingly used in industrial production, medical services, logistics and transportation, and other fields, greatly improving efficiency and convenience. Robot systems are usually composed of environmental perception, decision-making, control and communication modules, among which the decision-making module is the core, responsible for intelligent decision-making and task judgment. In today's robotics field, path planning research occupies a core position. Path planning refers to finding an effective path from the initial position to the target position in the configuration space, while avoiding various obstacles and meeting certain specific optimization criteria. In the application of actual scenarios, the robot needs to follow the trajectory generated by the algorithm to reach the target point from the starting point without collision. Sometimes it is necessary to consider the mutual constraints of multiple target tasks and optimize multiple process parameters, such as shortening the arrival time, reducing resource consumption, and improving safety and robustness. It can be foreseen that trajectory planning technology will face more and more severe challenges in future applications, and urgently needs the support of innovative algorithms.

[0003] At present, the common path planning algorithms are algorithm, Algorithm, genetic algorithm, particle swarm algorithm, etc. These traditional methods have been widely used, but they still show their limitations when facing different problems. The algorithm requires a large number of samples and has many useless nodes, which is inefficient. Genetic algorithms require a lot of computing power for multiple iterations to converge to the optimal solution. Particle swarm algorithms tend to fall into local optimal solutions too early when facing high-dimensional problems. Compared with the above traditional methods, the rapid random exploration tree (RRT) algorithm has attracted widespread attention due to its low complexity, strong adaptability, and no need for pre-modeling of the environment. However, the RRT algorithm does not contain heuristic information, the exploration space is random, and the path found is not the optimal solution. To solve this problem, An algorithm was proposed, which not only maintains probabilistic completeness but also achieves asymptotic optimality. However, this continuous path optimization process requires a large number of iterations, which leads to The algorithm is relatively slow in converging to the optimal solution. The sampling method is optimized and bias points are used for intelligent sampling, but this method is more dependent on the quality of the initial path. The algorithm uses the triangle inequality principle to provide a better method for reselecting parent nodes and rerouting routes, but since the range of parent nodes becomes wider, the search time will be extended.

[0004] Some improved algorithms of RRT are also applied to the motion planning problem in a dynamic environment. These algorithms can be divided into two categories: reactive algorithms and proactive algorithms. Reactive algorithms calculate only one next action at each moment according to the current conditions. When the environment changes, path replanning is required. This type of algorithm can handle highly dynamic and unpredictable environments, but it also requires a continuous high refresh rate. Its variants focus on improving the rapidity of replanning. Proactive algorithms, on the other hand, need to predict the trajectories of moving obstacles, delete the paths that may collide, and then actively avoid obstacles. RiskRRT is a time-based RRT algorithm that proposes a probabilistic collision risk function to guide the planning and pathfinding method, but it does not consider optimizing the path.

[0005] The Elastic Band (EB) method can be used to optimize and adjust the current trajectory in a dynamic environment. It is heuristically guided by physical characteristics and can avoid obstacles while optimizing the path. The EB method requires the construction of an initial trajectory and a configuration space. In a dynamic environment, the path planner needs to generate a feasible trajectory as soon as possible. When the working scenario is quite large, such as an airport, constructing the configuration space will consume a large amount of computing resources, and it is difficult to quickly generate a feasible initial trajectory.

[0006] Although both reactive and proactive algorithms have been widely used in the field of robot motion planning, their focuses are different. Many methods have solved part of the trajectory planning problem to a certain extent, but they still face many challenges. Therefore, how to efficiently generate an initial trajectory in a dynamic environment, maintain the safety of the trajectory throughout the process, improve the speed of optimizing the trajectory as much as possible, reduce the consumption of computing resources as much as possible, and ensure the real-time effectiveness of the trajectory is still the core problem that urgently needs to be solved in the field of robot control. Summary of the Invention

[0007] In view of the above-mentioned technical problems, a dynamic trajectory planning method for a mobile robot under elastic band constraint is provided. The present invention mainly uses an improved fast method, and uses a target biasing sampling method with a variable sampling region to quickly obtain an initial feasible path with better quality. By combining the Elastic Band (EB) method with a time-based RRT algorithm, the trajectory is dynamically optimized to achieve real-time motion planning for the robot.

[0008] The technical means adopted by the present invention are as follows: A dynamic trajectory planning method for a mobile robot under elastic band constraint, comprising: Initializing the robot dynamics equation and representing the optimal motion planning problem using a cost function; Constructing a random tree data set, combining a variable sampling region, performing a rewiring operation, and optimizing the random tree structure; The target bias method is used to adjust the restricted sampling area; A hierarchical collision detection method is used for obstacles, and rough collision detection and fine detection are performed to eliminate invalid paths; Calculate the collision risk probability and remove nodes whose collision risk probability exceeds the threshold; The elastic band method is used to optimize the dynamic trajectory of the robot and realize the dynamic trajectory planning of the mobile robot.

[0009] Furthermore, the initialization of the robot dynamics equation specifically includes: Assume the state space is , collision space , free space , yes A proper subset of ; In a dynamic environment, the state space is time-varying, and the collision space is recorded as , the free space is denoted as ; Let the starting position be and the target location is , the target region is defined as , represents the radius of the target area, and the control space of the robot is , , the dynamics of the robot are expressed as follows:

[0010] in, represents the state of the robot at timestamp t, Represents the dynamic function of the robot, through the state and control Derived Status .

[0011] Furthermore, the optimal motion planning problem is expressed using a cost function, specifically including: The set of all feasible trajectories is represented as , construct the cost function as follows:

[0012]

[0013] in, is a constant, is the robot linear speed; and is the position information of the robot's front and back states, Timestamp The linear velocity of the robot at this time; the optimal motion planning problem is expressed as:

[0014] in, Represents the feasible path with the minimum cost.

[0015] Furthermore, the construction of the random tree data set, combining the variable sampling area, performing a rewiring operation, and optimizing the random tree structure specifically includes: Constructing the Random Trees Dataset , represents a set of vertices in a tree, Representing the connection relationship of each vertex in the group, determining the positions of the starting point and the target point, and constructing an environment map containing obstacles; before each iteration of the sampling process, first determining whether the initial path has been determined; if the initial path has not been determined, using the variable sampling area to optimize the sampling effect; Generate sampling points , traverse the existing random trees and find The closest node ,from Towards The direction is extended by a step length to form a new node ;if and If the connected path is not blocked by obstacles, the new node Reselect the parent node through the adaptively adjusted reconnection radius and perform the rewiring operation to optimize the random tree structure; and If the connected paths are blocked by obstacles, the sampling strategy is reselected and the algorithm continues until the set maximum number of iterations is reached and the task ends.

[0016] Furthermore, the method of adjusting the restricted sampling area by using the target bias method specifically includes: For complex or special environments, the target bias method is used to adjust the restricted sampling area to generate the initial path:

[0017] in, are random sampling points, is a uniformly distributed random number generated in the range (0,1). Indicates that sampling points are randomly selected in free space; is the target deviation threshold, is the target point. When the path is not blocked by an obstacle, sample at the target point and expand toward the target point until an obstacle blocks the path.

[0018] Furthermore, the rough collision detection uses the bounding volume technology to calculate the center position and the radius of the bounding circle of each polygonal obstacle to obtain the obstacle center Minimum distance to path segment , obstacle center The coordinates of , the two endpoints of the path segment and The coordinates of and , let the vector is the path segment direction vector, For endpoint arrive The vector of , is:

[0019]

[0020] Use parameters express In line segment The projection position on is calculated by the inner product:

[0021]

[0022] Will Restricted to Make sure the projected point is on the actual path rather than an extension of the path:

[0023] According to the parameters , the projection point coordinates It is expressed as:

[0024] The minimum distance The center point of the obstacle The distance to the projection point is expressed as:

[0025] If the minimum distance If it is larger than the radius of the enclosing circle, it is considered that there is no collision and the rough detection is completed.

[0026] Furthermore, the fine detection generates interpolation points on the path using a linear interpolation method, and traverses each point to detect whether a collision occurs; Assume that the starting point and the end point of the path are and , through the parameters Perform linear interpolation to generate any point for:

[0027] During the detection process, the step size is set Generate an interpolation point sequence to detect the upper, lower, left, and right boundaries of the obstacle in a given coordinate system, i.e., width and height. It is expressed as:

[0028] in, is the upper boundary position parameter of the obstacle, is the lower boundary position parameter of the obstacle, is the left boundary position parameter of the obstacle, is the right boundary position parameter of the obstacle, is the lateral length parameter of the obstacle, is the longitudinal length parameter of the obstacle; and is the coordinate of the obstacle center. If the interpolation point Requirements: , a collision is considered to have occurred, the algorithm terminates and marks the path invalid.

[0029] Furthermore, the calculation of the collision risk probability and elimination of nodes whose collision risk probability exceeds a threshold value specifically includes: The robot's state is represented as , is the parent node and child node of the node, is the tree depth, Timestamp , the timestamp of the root node is , the time increment between two nodes is ; is the control input, To control the output, for The probability collision risk when , is expressed as:

[0030]

[0031] in, represents the collision probability due to static obstacles, Indicates that due to the timestamp The collision probability of the moving obstacle at Indicates that due to the timestamp Moving obstacles The collision probability of the planned trajectory is calculated during the optimization process. If the collision probability is greater than the threshold, the corresponding node is not added to the optimized trajectory.

[0032] Furthermore, the application of the elastic band method to optimize the dynamic trajectory of the robot specifically includes: The internal contraction force The definition is as follows:

[0033] The node position is updated according to the following equation:

[0034] in, and are two positive proportional factors, the elastic band method optimization process will end when the following conditions are met: when , is the number of nodes on the trajectory, indicating the contraction force Less than the set force is the optimal trajectory; when the dynamic and kinematic constraints that the robot needs to satisfy make the optimization process unable to proceed further, the optimization process ends; when the collision probability of the new node exceeds the threshold, that is, , then the new node Invalidation.

[0035] Compared with the prior art, the present invention has the following advantages: The method for dynamic trajectory planning of a mobile robot under elastic band constraints provided by the present invention improves computational efficiency and real-time performance. The present invention uses a target bias sampling method with a variable sampling area, which improves sampling efficiency compared to random sampling of the entire map, and improves the speed and quality of generating the initial trajectory. After quickly generating the initial trajectory, the position of each node is optimized using an elastic band-based method, and on this basis, the structure of the original time base tree generated initially is not changed, there is no waste on branches, and additional calculations are avoided to modify the node information on the time base tree.

[0036] The method for dynamic trajectory planning of a mobile robot under elastic band constraints provided by the present invention ensures safety in a dynamic environment. The present invention uses a probabilistic collision risk function as an external repulsive force of the trajectory, so that nodes on the trajectory can avoid places where motion obstacles may reach, ensuring the feasibility and safety of trajectory planning.

[0037] The dynamic trajectory planning method of a mobile robot under elastic band constraints provided by the present invention improves robustness and adaptability. Through the time-based RRT algorithm, the present invention realizes the detection of each node state and collision risk during the trajectory optimization process, significantly improving the robustness and adaptability of the system. The robot can adaptively adjust the trajectory in a complex environment to meet the needs of obstacle avoidance.

[0038] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0040] Figure 1 This is a flow chart of the dynamic trajectory planning method of a mobile robot under elastic band constraints of the present invention.

[0041] Figure 2 This is the working framework of the global planner and the dynamic replanner in the embodiment of the present invention.

[0042] Figure 3 This is a flow chart of target bias sampling of variable sampling area of ​​the present invention.

[0043] Figure 4 This is the trajectory optimization process under obstacle constraints in the present invention. DETAILED DESCRIPTION

[0044] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0045] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0047] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, the numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be clear that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The technology, methods and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, methods and equipment should be regarded as part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0048] like Figure 1 As shown, the present invention provides a method for dynamic trajectory planning of a mobile robot under elastic band constraints, comprising: Initialize the robot dynamics equations and use the cost function to express the optimal motion planning problem.

[0049] In specific implementation, as a preferred embodiment of the present invention, the initialization robot dynamics equation specifically includes: Assume the state space is , collision space , free space , yes A proper subset of ; In a dynamic environment, the state space is time-varying, and the collision space is recorded as , the free space is denoted as ; Let the starting position be and the target location is , the target region is defined as , represents the radius of the target area, and the control space of the robot is , , the dynamics of the robot are expressed as follows:

[0050] in, represents the state of the robot at timestamp t, and are two adjacent states. Represents the dynamic function of the robot, which can be expressed by the state and control Derived Status .

[0051] In specific implementation, as a preferred embodiment of the present invention, the use of a cost function to represent the optimal motion planning problem specifically includes: The set of all feasible trajectories is represented as , construct the cost function as follows:

[0052]

[0053] in, is a constant, is the robot linear velocity, and is the position information of the robot's front and back states, Timestamp The linear velocity of the robot at time . The optimal motion planning problem is expressed as:

[0054] in, Represents the feasible path with the minimum cost.

[0055] like Figure 3 As shown, a random tree dataset is constructed, variable sampling regions are combined, a rewiring operation is performed, and the random tree structure is optimized.

[0056] In specific implementation, as a preferred embodiment of the present invention, the construction of a random tree data set, combining a variable sampling area, performing a rewiring operation, and optimizing a random tree structure specifically include: Constructing the Random Trees Dataset , represents a set of vertices in a tree, The connection relationship between the vertices in the group is represented, the positions of the starting point and the target point are determined, and an environment map containing obstacles is constructed; before each sampling process iteration, it is first determined whether the initial path has been determined; if the initial path has not been determined, the variable sampling area is used to optimize the sampling effect.

[0057] Generate sampling points , traverse the existing random trees and find The closest node ,from Towards The direction is extended by a step length to form a new node ;if and If the connected path is not blocked by obstacles, the new node Reselect the parent node through the adaptively adjusted reconnection radius and perform the rewiring operation to optimize the random tree structure; and If the connected paths are blocked by obstacles, the sampling strategy is reselected and the algorithm continues until the set maximum number of iterations is reached and the task ends.

[0058] The target bias method is used to adjust the restricted sampling area.

[0059] In specific implementation, as a preferred embodiment of the present invention, the method of adjusting the restricted sampling area by using the target offset method specifically includes: For complex or special environments, the target bias method is used to adjust the restricted sampling area to generate the initial path:

[0060] in, are random sampling points, is a uniformly distributed random number generated in the range (0,1). Indicates that sampling points are randomly selected in free space; is the target deviation threshold, is the target point. When the path is not blocked by an obstacle, sample at the target point and expand toward the target point until an obstacle blocks the path.

[0061] In implementation, when sampling of a new node fails due to obstacles, the algorithm focuses the sampling range on the local area centered on the new node, rather than blindly sampling the entire global environment, thereby increasing the probability of placing the new node in a local narrow channel, enabling it to quickly bypass obstacles and reducing the initial path calculation time. If local expansion fails multiple times in a row, it jumps out of the vicinity of the local minimum point and performs more extensive random sampling, thereby preventing the algorithm from falling into the local optimum and maintaining probabilistic completeness.

[0062] A hierarchical collision detection method is used for obstacles, and rough collision detection and fine detection are performed to eliminate invalid paths. Studies have shown that collision detection is an important factor affecting the convergence speed of trajectory planning algorithms. Therefore, the present invention proposes a hierarchical detection method that combines rough detection with fine detection to improve detection efficiency.

[0063] In specific implementation, as a preferred embodiment of the present invention, the rough collision detection adopts the bounding volume technology. For each polygonal obstacle, its center position and the radius of the bounding circle are calculated to obtain the obstacle center. Minimum distance to path segment , obstacle center The coordinates of , the two endpoints of the path segment and The coordinates of and , let the vector is the path segment direction vector, For endpoint arrive The vector of , is:

[0064]

[0065] Use parameters express In line segment The projection position on is calculated by the inner product:

[0066]

[0067] Will Restricted to Make sure the projected point is on the actual path rather than an extension of the path:

[0068] According to the parameters , the projection point coordinates It is expressed as:

[0069] The minimum distance The center point of the obstacle The distance to the projection point is expressed as:

[0070] If the minimum distance If it is larger than the radius of the enclosing circle, it is considered that there is no collision and the rough detection is completed.

[0071] In specific implementation, as a preferred embodiment of the present invention, the fine detection uses a linear interpolation method to generate interpolation points on the path, and traverses each point to detect whether a collision occurs.

[0072] Assume that the starting point and the end point of the path are and , through the parameters Perform linear interpolation to generate any point for:

[0073] During the detection process, the step size is set Generate an interpolation point sequence to detect the upper, lower, left, and right boundaries of the obstacle in a given coordinate system, i.e., width and height. It is expressed as:

[0074] in, is the upper boundary position parameter of the obstacle, is the lower boundary position parameter of the obstacle, is the left boundary position parameter of the obstacle, is the right boundary position parameter of the obstacle, is the lateral length parameter of the obstacle, is the longitudinal length parameter of the obstacle. and are the coordinates of the obstacle center.

[0075] If the interpolation point Requirements: , it is considered that a collision occurs, the algorithm terminates and marks the path invalid. The optimization process is as follows Figure 4 shown.

[0076] Calculate the collision risk probability and remove nodes whose collision risk probability exceeds the threshold.

[0077] In specific implementation, as a preferred embodiment of the present invention, the calculation of the collision risk probability and the removal of nodes whose collision risk probability exceeds a threshold value specifically include: The robot's state is represented as , is the parent node and child node of the node, is the tree depth, Timestamp , the timestamp of the root node is , the time increment between two nodes is ; is the control input, To control the output, for The probability collision risk when , is expressed as:

[0078]

[0079] in, represents the collision probability due to static obstacles, Indicates that due to the timestamp The collision probability of the moving obstacle at , the trajectory of the moving obstacle is represented by a Gaussian process, Indicates that due to the timestamp Moving obstacles The collision probability of the planned trajectory is calculated during the optimization process. If the collision probability is greater than the threshold, the corresponding node is not added to the optimized trajectory.

[0080] The elastic band method is applied to optimize the dynamic trajectory of the robot and realize the dynamic trajectory planning of the mobile robot. The invention applies an internal contraction force to the nodes on the heuristic trajectory so that the nodes continue to deform until they are balanced.

[0081] In specific implementation, as a preferred embodiment of the present invention, the elastic band method is used to optimize the dynamic trajectory of the robot, specifically including: The internal contraction force The definition is as follows:

[0082] The node position is updated according to the following equation:

[0083] in, and are two positive proportional factors, the elastic band method optimization process will end when the following conditions are met: when , is the number of nodes on the trajectory, indicating the contraction force Less than the set force is the optimal trajectory; when the dynamic and kinematic constraints that the robot needs to satisfy make the optimization process unable to proceed further, the optimization process ends; when the collision probability of the new node exceeds the threshold, that is, , then the new node Invalidation.

[0084] During the optimization process, the structure of the original time-base tree does not change, there is no branch waste, and no additional calculation is required to modify the node information on the tree. The optimized trajectory is recorded as The optimization process is attached. Figure 4 shown.

[0085] Example like Figure 2 As shown in FIG. 1 , the method of the present invention constructs a global planner and a dynamic replanner to plan the trajectory of the robot. The global planner is based on an improved fast The method first uses the target bias sampling method of the variable sampling area to quickly obtain an initial feasible path with better quality during the iteration process; then, the time-based RRT algorithm dynamic replanner combined with the elastic band method is used to dynamically optimize the trajectory (the contraction force inside the trajectory, the repulsion force of external obstacles) during the environmental changes, ensuring the safety, probabilistic completeness and homotopic optimality of the trajectory generated in real time.

[0086] Based on the technical solution of the present invention, numerical simulation, semi-physical simulation and physical experiment are carried out to verify the effectiveness and practicality of the method. Numerical simulation is carried out through tools such as MATLAB and Python to verify the accuracy of the trajectory planning model. Semi-physical simulation is carried out based on the ROS platform to verify the robustness of the method. Experiments are carried out on the actual physical platform to further debug and optimize the model to ensure that the robot can efficiently and safely complete the trajectory planning task in a real environment.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for dynamic trajectory planning of a mobile robot under elastic band constraints, characterized in that: include: Initialize the robot dynamics equation and use the cost function to express the optimal motion planning problem; Construct a random tree dataset, combine variable sampling regions, perform rewiring operations, and optimize the random tree structure; The target bias method is used to adjust the restricted sampling area; A hierarchical collision detection method is used for obstacles, and rough collision detection and fine detection are performed to eliminate invalid paths; Calculate the collision risk probability and remove nodes whose collision risk probability exceeds the threshold; The elastic band method is used to optimize the dynamic trajectory of the robot and realize the dynamic trajectory planning of the mobile robot.

2. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The initialization of the robot dynamics equation specifically includes: Assume the state space is , collision space , free space , yes A proper subset of ; In a dynamic environment, the state space is time-varying, and the collision space is recorded as , the free space is denoted as ; Let the starting position be and the target location is , the target region is defined as , represents the radius of the target area, and the control space of the robot is , , the dynamics of the robot are expressed as follows: in, represents the state of the robot at timestamp t, Represents the dynamic function of the robot, through the state and control Derived Status .

3. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The use of a cost function to represent the optimal motion planning problem specifically includes: The set of all feasible trajectories is represented as , construct the cost function as follows: in, is a constant, is the robot linear velocity, and is the position information of the robot's front and back states, Timestamp The linear velocity of the robot at this time; the optimal motion planning problem is expressed as: in, Represents the feasible path with the minimum cost.

4. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The random tree data set is constructed, and a rewiring operation is performed in combination with a variable sampling region to optimize the random tree structure, specifically including: Constructing the Random Trees Dataset , represents a set of vertices in a tree, Representing the connection relationship of each vertex in the group, determining the positions of the starting point and the target point, and constructing an environment map containing obstacles; before each iteration of the sampling process, first determining whether the initial path has been determined; if the initial path has not been determined, using the variable sampling area to optimize the sampling effect; Generate sampling points , traverse the existing random trees and find The closest node ,from Towards The direction is extended by a step length to form a new node ;if and If the connected path is not blocked by obstacles, the new node Reselect the parent node through the adaptively adjusted reconnection radius and perform the rewiring operation to optimize the random tree structure; and If the connected paths are blocked by obstacles, the sampling strategy is reselected and the algorithm continues until the set maximum number of iterations is reached and the task ends.

5. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The method of adjusting the restricted sampling area by using the target bias method specifically includes: For complex or special environments, the target bias method is used to adjust the restricted sampling area to generate the initial path: in, are random sampling points, is a uniformly distributed random number generated in the range (0,1). Indicates that sampling points are randomly selected in free space; is the target deviation threshold, is the target point. When the path is not blocked by an obstacle, sample at the target point and expand toward the target point until an obstacle blocks the path.

6. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The rough collision detection adopts the bounding volume technology. For each polygonal obstacle, its center position and the radius of the bounding circle are calculated to obtain the obstacle center Minimum distance to path segment , obstacle center The coordinates of , the two endpoints of the path segment and The coordinates of and , let the vector is the path segment direction vector, For endpoint arrive The vector of , is: Use parameters express In line segment The projection position on is calculated by the inner product: Will Restricted to Make sure the projected point is on the actual path rather than an extension of the path: According to the parameters , the projection point coordinates It is expressed as: The minimum distance The center point of the obstacle The distance to the projection point is expressed as: If the minimum distance If it is larger than the radius of the enclosing circle, it is considered that there is no collision and the rough detection is completed.

7. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The fine detection generates interpolation points on the path using a linear interpolation method, and traverses each point to detect whether a collision occurs; Assume that the starting point and the end point of the path are and , through the parameters Perform linear interpolation to generate any point for: During the detection process, the step size is set Generate an interpolation point sequence to detect the upper, lower, left, and right boundaries of the obstacle in a given coordinate system, i.e., width and height. It is expressed as: in, is the upper boundary position parameter of the obstacle, is the lower boundary position parameter of the obstacle, is the left boundary position parameter of the obstacle, is the right boundary position parameter of the obstacle, is the lateral length parameter of the obstacle, is the longitudinal length parameter of the obstacle; and is the coordinate of the obstacle center; if the interpolation point Requirements: , a collision is considered to have occurred, the algorithm terminates and marks the path invalid.

8. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The calculation of the collision risk probability and the removal of nodes whose collision risk probability exceeds a threshold value specifically include: The robot's state is represented as , is the parent node and child node of the node, is the tree depth, For timestamp , the timestamp of the root node is , the time increment between two nodes is ; is the control input, To control the output, for The probability collision risk when , is expressed as: in, represents the collision probability due to static obstacles, Indicates that due to the timestamp The collision probability of the moving obstacle at Indicates that due to the timestamp Moving obstacles The collision probability of the planned trajectory is calculated during the optimization process. If the collision probability is greater than the threshold, the corresponding node is not added to the optimized trajectory.

9. The method for dynamic trajectory planning of a mobile robot under elastic band constraints according to claim 1, characterized in that: The application of the elastic band method to optimize the dynamic trajectory of the robot specifically includes: The internal contraction force The definition is as follows: The node position is updated according to the following equation: in, and are two positive proportional factors, the elastic band method optimization process will end when the following conditions are met: when , is the number of nodes on the trajectory, indicating the contraction force Less than the set force is the optimal trajectory; when the dynamic and kinematic constraints that the robot needs to satisfy make the optimization process unable to proceed further, the optimization process ends; when the collision probability of the new node exceeds the threshold, that is, , then the new node Invalidation.

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