Local region path planning algorithm based on state tree structure and electronic equipment
By employing a local region path planning algorithm based on a state tree structure, redundant states are removed and alternative states are merged, thus solving the state explosion problem of automata in large-scale complex systems and achieving efficient and accurate path planning.
Patent Information
- Application Number
- CN202511609928.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-05
- Publication Date
- 2026-02-17
AI Technical Summary
Automata suffer from state explosion, lack of hierarchical description, and insufficient state pruning ability in large-scale complex systems, resulting in high modeling and computational complexity and difficulty in effectively planning paths.
A local area path planning algorithm based on a state tree structure is adopted. By deleting and merging redundant state nodes, the path search is simplified and the path planning process is optimized.
It improves the processing efficiency and accuracy of path planning, reduces computational complexity and storage space, and enhances the efficiency and accuracy of path planning.
Smart Images
Figure CN121543850A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of optimal path algorithms, and more specifically, to a local region path planning algorithm and electronic device based on a state tree structure. Background Technology
[0002] Currently, automata are the primary tool for modeling and controlling discrete event systems. Automata describe the behavioral constraints of a system using formal languages, effectively characterizing state transition rules. In automata-based modeling methods, when the initial or target node of the system changes, only the set of labeled states needs to be adjusted, without rebuilding the entire model, thus offering good flexibility and effectiveness.
[0003] However, automata suffer from the following shortcomings in large-scale complex systems: State explosion problem: As the system size increases, the number of states grows exponentially, leading to a sharp increase in modeling and computational complexity. Lack of hierarchical description: Automata models are typically flat structures, unsuitable for hierarchically representing complex systems. Insufficient state pruning capability: While the model can be reused after the initial or target state changes, it often leaves behind a large number of unreachable or redundant states, affecting data processing efficiency. Therefore, a new modeling method is urgently needed to overcome the limitations of automata in large-scale complex systems. Summary of the Invention
[0004] The purpose of this invention is to provide a local region path planning algorithm based on a state tree structure. This algorithm simplifies the path by deleting redundant state nodes, thereby improving the processing efficiency of the local region path planning algorithm based on a state tree structure.
[0005] To achieve the above objectives, this invention provides a local region path planning algorithm based on a state tree structure, comprising the following steps: S1: Obtain the topological information of the area to be planned, and model the area based on the state tree structure model to obtain the initial state tree model; S2: Perform a redundant state deletion operation on the initial state tree model to obtain a simplified state tree model; S3: On the simplified state tree model, run the path search algorithm to calculate the optimal path from the starting point to the ending point.
[0006] Preferably, the state tree structure model is a six-tuple structure, including: a state tree ST, a set of state diagrams H, an event set E, a transition function δ, an initial sub-state tree ST0, and a set of labeled sub-state trees ST. m .
[0007] Preferably, in step S1, modeling the region based on the state tree structure model includes: S11: Perform rasterization processing on the area to be planned; S21: Map each feasible grid to a state node in the sub-state tree; Based on the topology information, establish the event and transition relationships between the state nodes.
[0008] Preferably, the redundant state deletion operation performed on the initial state tree model in step S2 includes: Invalid state deletion, the invalid state deletion includes: S21: Traverse the sub-state trees in the initial state tree model. If a sub-state tree cannot be reached from the initial state or the target state cannot be reached from the sub-state tree, then it is determined to be an invalid sub-state tree. S22: Delete the invalid sub-state tree and the edges and subtrees associated with the invalid sub-state tree from the model.
[0009] Preferably, the redundant state deletion operation performed on the initial state tree model in step S2 further includes: Replaceable sub-state tree merging, wherein the replaceable sub-state tree merging includes: S23: Traverse the sub-state trees in the initial state tree model. If two sub-state trees in the state tree model have the same set of paths to the target state, then they are determined to be replaceable sub-state trees. S24: Then retain one of the alternative sub-state trees and delete the other alternative sub-state tree.
[0010] Preferably, the redundant state deletion operation performed on the initial state tree model in step S2 specifically involves iteratively executing the invalid state deletion and the merging of the replaceable sub-state trees until there are no more redundant states in the state tree model.
[0011] Preferably, in step S3, model optimization is further included before running the path search algorithm, and the model optimization includes: S31: Identify the key nodes in the simplified state tree model, wherein the key nodes include at least the start point, the end point, and all branch nodes; S32: If there is a unique connected path between any two adjacent key nodes, then compress that path into a direct connection with path weights.
[0012] Preferably, the path weight is the number of state nodes contained in the compressed path, or the actual cost of the path.
[0013] Preferably, the path search algorithm described in step S3 is Dijkstra's algorithm or A* algorithm.
[0014] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of a local region path planning algorithm based on a state tree structure.
[0015] Based on the above technical solution, the traditional Dijkstra's algorithm uses directed graphs for modeling. Directed graphs contain limited data and lack flexibility in data processing. Therefore, by introducing a state tree structure model before the traditional Dijkstra's algorithm for data processing, the efficiency of Dijkstra's algorithm in planning paths at high resolutions can be optimized, and the accuracy of local path planning can be improved.
[0016] When modeling a local area of an urban road network, everything in that local area except for paths can be considered an obstacle. The local area is divided into grids, and after the division, the entire local area is composed of grids. Modeling under the grid using a state tree structure would result in an excessively large state set and overly complex calculations if all grids were modeled. Therefore, modeling is only performed on feasible blocks, i.e., feasible paths, within the grid. Feasible blocks are no longer in a flat state but are organized into sub-state tree nodes of the state tree. Each leaf node represents a specific feasible block, and each internal OR node represents a hierarchical set of feasible blocks. The movement between feasible blocks is given by the transition function, rather than global event migration. In hierarchical solution, for local modules, the solution is performed in the local OR subtree, and the local path optimum is calculated first. Globally, the transitions between subtrees are synthesized to obtain the global path. In this way, the path visualization is not a single automaton graph, but a tree structure + nested local graphs, which directly shows the hierarchical relationship between local and global regions.
[0017] Traditional path planning solutions typically involve sequentially searching each feasible block. In the paths formed by these feasible blocks, some routes require retracing to a feasible block within the initial block for further searching. This results in partially overlapping paths, excessively long paths, and non-optimal paths. Therefore, it's necessary to remove redundant feasible blocks and optimize feasible paths. Removing feasible blocks corresponds to removing state nodes. By deleting these state nodes, the path can be simplified, thereby improving the processing efficiency of local region path planning algorithms based on state tree structures.
[0018] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description
[0019] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the following detailed description to explain the invention, but do not constitute a limitation thereof. In the drawings: Figure 1 It is a schematic diagram of an actual local area; Figure 2 It is a local sub-state tree model; Figure 3 It is a local sub-state tree model after invalid states have been removed; Figure 4 It is a local sub-state tree model after merging sub-state trees that can be replaced; Figure 5 It is a local sub-state tree model after iterative deletion; Figure 6 This is a MATLAB simulation graph after the invalid state has been deleted; Figure 7 It is a MATLAB simulation graph after the replacement state is deleted; Figure 8 It is a MATLAB simulation graph after iterative state deletion; Figure 9 This is a schematic diagram of array storage for model optimization; Figure 10 It is the final local sub-state tree structure model. Detailed Implementation
[0020] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.
[0021] In this invention, unless otherwise stated, directional terms such as "one end," "the other end," "outer surface," "axis," "conical," and "near" in the terminology represent only the orientation of the term in its conventional use or are common terms understood by those skilled in the art, and should not be regarded as limitations on the term.
[0022] A local region path planning algorithm based on a state tree structure includes the following steps: S1: Obtain the topological information of the area to be planned, and model the area based on the state tree structure model to obtain the initial state tree model; S2: Perform redundant state deletion operation on the initial state tree model to obtain a simplified state tree model; S3: On the simplified state tree model, run the path search algorithm to calculate the optimal path from the starting point to the ending point.
[0023] When using the above technical solutions, the traditional Dijkstra's algorithm uses directed graphs for modeling. Directed graphs contain limited data and lack flexibility in data processing. Therefore, by introducing a state tree structure model before the traditional Dijkstra's algorithm for data processing, the efficiency of Dijkstra's algorithm in planning paths at high resolutions can be optimized, and the accuracy of local path planning can be improved.
[0024] In one implementation, local areas of the urban road network are modeled. Everything in the local area except paths can be considered an obstacle. The local area is divided into grids, and after division, the entire local area is composed of grid cells. Modeling under the grid using a state tree structure would result in an excessively large state set and overly complex calculations if all grid cells were modeled. Therefore, modeling is only performed on feasible blocks, i.e., feasible paths, within the grid cells. Feasible blocks are no longer in a flat state but are organized into sub-state tree nodes of the state tree. Each leaf node represents a specific feasible block, and each internal OR node represents a hierarchical set of feasible blocks. Movement between feasible blocks is determined by a transition function. Instead of global event migration, hierarchical solution provides a solution for local modules, solving in the local OR subtree and calculating the optimal local path first; then, globally, the transitions between subtrees are synthesized to obtain the global path. In this way, path visualization is not a single automaton graph, but a tree structure + nested local graphs, directly showing the hierarchical relationship between local and global regions.
[0025] Traditional path planning solutions typically involve sequentially searching each feasible block. In paths composed of these feasible blocks, some routes require retracing to a previous feasible block within the initial block for further searching. This results in partially overlapping paths, excessively long paths, and non-optimal paths. Therefore, it's necessary to remove redundant feasible blocks and optimize feasible paths. Removing feasible blocks corresponds to removing state nodes; by deleting these state nodes, the path can be simplified.
[0026] Finally, a six-tuple automaton is used to model the actual region. The entrance and exit points of the actual region are determined and set as the initial and flag states. The remaining feasible blocks are numbered sequentially from left to right and top to bottom as 1, 2, 3…, and each block is represented by states y1, y2, y3… The states and events have the following relationship: ,like and For adjacent states, add an event and a weight between the two states. The event is represented by... Indicates the weight =1. State set event collection , This is the initial state. The state is terminated.
[0027] Therefore, the state tree structure model can be used to divide the local area of the urban road network into layers. After deleting some invalid nodes, the state tree structure model becomes more concise. Finally, the optimal path can be obtained in the local area of the urban road network by using the automaton model in the concise state tree model.
[0028] The time complexity of the traditional Dijkstra algorithm is The time complexity of the optimization algorithm is equal to the time complexity of the simplified model. and the complexity of simplified nodes The sum of The simplification involves omitting most nodes, leaving only a small number for shortest path calculation. According to the formula... Furthermore, as the grid size increases, the time complexity of the simplified model increases. If the efficiency can be ignored, the efficiency of the optimization algorithm is significantly improved compared to the traditional algorithm.
[0029] In this embodiment, preferably, the state tree structure model is a six-tuple structure, including: a state tree ST, a set of state diagrams H, an event set E, a transition function δ, an initial sub-state tree ST0, and a set of labeled sub-state trees ST. m .
[0030] In this embodiment, preferably, step S1, modeling the region based on the state tree structure model, includes: S11: Grid-process the area to be planned; S21: Map each feasible grid cell to a state node in a sub-state tree; Based on the topology information, establish the event and transition relationships between state nodes.
[0031] When modeling local areas of an urban road network, everything in the local area except paths can be considered as obstacles. The local area is divided into grids, and the entire local area is composed of grids after the division. Modeling under the grid using a state tree structure would result in an excessively large state set and overly complex calculations if all grids were modeled. Therefore, modeling is only performed on feasible blocks and feasible paths within the grid.
[0032] The state tree structure model is a six-tuple structure, and the state tree structure of this six-tuple... ; It is a state tree; It is the set of state diagrams for all OR superstates assigned to the state tree, where aIt is an OR superstate. Is with a The matching state diagram describes a Local dynamic information between components; It includes H The event set of all events that appear in the text. represent The internal event set; It is the transfer function, where Represents the substate tree of ST; This is the initial sub-state tree; This is a set of labeled sub-state trees.
[0033] Feasible blocks are no longer in a flat state but are organized into sub-state tree nodes of the state tree. Each leaf node represents a specific feasible block, and each internal OR node represents a hierarchical set of feasible blocks. Movement between feasible blocks is determined by a transition function. Instead of global event migration, hierarchical solution provides a solution for local modules, solving in the local OR subtree and calculating the optimal local path first; then, globally, the transitions between subtrees are synthesized to obtain the global path. In this way, path visualization is not a single automaton graph but a tree structure + nested local graphs, which can directly show the hierarchical relationship between local and global regions.
[0034] Therefore, when using a state tree structure for modeling, it's necessary to visualize the distances when calculating the length of the optimal path in a local region. Thus, a weight w is introduced into the automaton model, and the local subtree is an automaton consisting of 6 tuples. This indicates that w is additive. This represents the cost required to drive a state transition. (Used...) The weight of a certain path segment is defined as follows:
[0035] Therefore, when using a local region path planning algorithm based on a state tree structure, the actual local region is first processed using a six-tuple automaton. Modeling. Determine the entrance and exit points of the local region and set them as the initial state. and identifier status The remaining feasible blocks are numbered 1, 2, 3... from left to right and top to bottom, and each block is assigned a state. , , ...indicates that states and events have the following relationship. ,like and For adjacent states, add an event and a weight between the two states. The event is represented by... Indicates the weight =1. State set event collection , This is the initial state. The state is terminated.
[0036] In this embodiment, preferably, step S2 involves performing a redundant state deletion operation on the initial state tree model, including: Deletion of invalid states, including: S21: Traverse the sub-state trees in the initial state tree model. If a sub-state tree cannot be reached from the initial state or the target state cannot be reached from the sub-state tree, then it is determined to be an invalid sub-state tree. S22: Remove invalid substate trees and the edges and subtrees associated with invalid substate trees from the model.
[0037] In this embodiment, preferably, the redundant state deletion operation performed on the initial state tree model in step S2 further includes: Replaceable sub-state tree merging includes: S23: Traverse the sub-state trees in the initial state tree model. If two sub-state trees in the state tree model have the same set of paths to the target state, then they are determined to be replaceable sub-state trees. S24: Then keep one of the alternative sub-state trees and delete the other alternative sub-state tree.
[0038] In this embodiment, preferably, in step S2, a redundant state deletion operation is performed on the initial state tree model, specifically by iteratively performing invalid state deletion and merging of replaceable sub-state trees until there are no redundant states in the state tree model.
[0039] Traditional path planning solutions typically involve sequentially searching each feasible block. In the paths formed by these feasible blocks, some routes, after entering, need to backtrack to a feasible block within the original block for further searching. This results in partially overlapping paths, excessively long paths, and non-optimal paths. Therefore, it is necessary to delete redundant feasible blocks and optimize feasible paths. Deleting feasible blocks corresponds to deleting state nodes.
[0040] Definition 1: For ,inevitable ,make ,like ,make ,but This is called a valid state. If it does not meet the requirements, it is an invalid state.
[0041] Valid states form a valid path, while invalid states are like dead ends; entering an invalid state requires backtracking and re-searching. Invalid states cause partial path overlap, wasting path storage space and pathfinding time. The destination can still be reached by omitting the invalid state, so deleting invalid states simplifies the path.
[0042] The deletion of invalid states is shown in Algorithm 1:
[0043] The invalid state removal algorithm is iterative. After deleting an invalid state, the valid states adjacent to the current invalid state may become invalid. Therefore, the algorithm searches for and judges the states adjacent to the invalid state until all invalid states in the path have been deleted.
[0044] After the invalid state is deleted, the remaining paths are valid paths, and these paths are better. After the invalid state deletion operation, the duplication rate decreases, and the smaller the value, the less storage space and pathfinding time are required.
[0045] Based on the removal of invalid states, a type of branching state is found, which can be searched in two directions. After each search passes through a different state, it can reach the same state. The two paths formed have the same starting state, merging state, and path length. Therefore, the two paths are duplicate paths. The less flexible path can be deleted without affecting the solution of the optimal path.
[0046] Definition 2: If make , make and Then it is called This is a replaceable state.
[0047] Form a path To form another path, the starting point, ending point, and... They are identical. Therefore, these two paths are duplicate paths, but they pass through the same intermediate states. If they are different, then the intermediate state is called a replaceable state. Deleting one of the replaceable states will delete the duplicate path containing that replaceable state.
[0048] The conditions for deletion are , making , , making , The set retains the majority of elements and deletes the minority ones, offering greater flexibility in the remaining paths.
[0049] Alternative sub-state tree merging is shown in Algorithm 2:
[0050] Delete the replaceable sub-state tree in the duplicate path. Deleting the sub-state tree has no effect on the path length. The value remains unchanged. After deleting the replaceable sub-state tree, the number of redundant points in the multiple paths to the destination is reduced accordingly.
[0051] Duplicate paths lead to data redundancy and high memory overhead. Therefore, removing duplicate paths reduces redundancy and consequently reduces memory consumption.
[0052] The replacement substate tree merging operation is an iterative algorithm.
[0053] When merging substate trees with alternatives, invalid states may appear; when deleting invalid states, alternative states may appear. Therefore, iterative processing using both algorithms is required until all redundant points are removed. After deleting invalid states, the path becomes a valid path; the deletion of alternative states does not affect the path finding. Therefore, the iteration of the two algorithms will not affect the finding of the optimal path.
[0054] Iterative deletion is shown in Algorithm 3:
[0055] Algorithms 1, 2, and 3 were used to remove redundant points, which reduced the search range and memory overhead when finding the optimal path, thus improving search efficiency.
[0056] The above algorithm removes redundant points on the path, making the path between any two nodes the shortest and the weight the smallest. Thus, the simplified sub-state tree model is globally optimal.
[0057] In this embodiment, preferably, step S3 further includes model optimization before running the path search algorithm. The model optimization includes: S31: Identify the key nodes in the simplified state tree model. The key nodes include at least the start point, the end point, and all branch nodes. S32: If there is a unique connected path between any two adjacent key nodes, then compress that path into a direct connection with path weights.
[0058] In this embodiment, preferably, the path weight is the number of state nodes contained in the compressed path, or the actual cost of the path.
[0059] In this embodiment, preferably, the path search algorithm in step S3 is Dijkstra's algorithm or A* algorithm.
[0060] The traditional Dijkstra's algorithm calculates the shortest path between all nodes. When used for practical local path planning, high accuracy is often required. However, Dijkstra's algorithm is imprecise because it only calculates up to each fork in the path. Calculating the path on a segmented grid requires storing information for each node, leading to excessive data storage. Similarly, each node needs to be traversed and calculated during path calculation, resulting in a time complexity of O(log n). As the number of nodes increases, the computation time grows exponentially. Efficiency is significantly reduced when high precision is required in localized areas.
[0061] Local area path planning is often used for short-distance navigation, therefore the planned path needs to closely approximate the actual path. To ensure high accuracy, the resolution of the local area is maximized when dividing it into grids to reflect actual road conditions and meet the traveler's requirements. However, high accuracy often means a larger number of grids, increasing the number of nodes during modeling and the amount of data to be stored, which reduces efficiency in path calculation.
[0062] After iterative deletion, redundant points in the model have been removed. However, the problem of too many states and events still exists when the local region is large. Therefore, further optimization of the model is necessary. The remaining paths are feasible paths, and the weights are adjusted along these paths. and weight Optimizing states and events can improve computational efficiency and save storage space.
[0063] array This stores the state nodes on one of the paths after a node is deleted; 0 represents the initial state. m indicates the status. The remaining values represent channel states. (Array) It stores the initial state, branch state, and flag state.
[0064] array The weights between branch state nodes are stored in the middle, with an initial value of 0.
[0065] In array Search array The number of channel state nodes between states is determined by the unique movement path of each channel state node; therefore, weights are introduced for optimization. This process is repeated to find the weights between all branch states.
[0066] By omitting the remaining paths and introducing weights, the optimal path can be found using an automaton.
[0067] Example 1 First, a local area of the urban road network is modeled. Everything in this local area except paths can be considered an obstacle. This local area is divided into grids, and the entire local area is composed of these grids. A state tree structure is used to model the grid. However, modeling all grids would result in an excessively large state set and overly complex calculations; therefore, modeling is only performed on feasible blocks and feasible paths within the grid.
[0068] exist Figure 1 The actual local region shown is represented by a six-tuple automaton. Modeling. Determine the entrance and exit points of the local region and set them as the initial state. and identifier status The remaining feasible blocks are numbered 1, 2, 3... from left to right and top to bottom, and each block is assigned a state. , , ...indicates that states and events have the following relationship. ,like and For adjacent states, add an event and a weight between the two states. The event is represented by... Indicates the weight =1. State set event collection , This is the initial state. The state is terminated.
[0069] The constructed local sub-state tree model is as follows: Figure 2 As shown.
[0070] After the invalid state deletion operation, the local sub-state tree model is as follows: Figure 3 As shown.
[0071] According to Algorithm 2 Figure 3 Merge the substate trees of replaceable substates.
[0072] state After the incident Arrival Status Then from state After the incident Transition to state It can also be done through events. Reaching the intermediate state Then from state After the incident Arrival Status The initial state of both paths is... The convergence status is The replaceable state is , The event set connected in the middle , . Therefore, the state is preserved. Deleted status And related events.
[0073] After the alternative substate tree merging operation, the local substate tree model is as follows: Figure 4 As shown.
[0074] After iterative deletion operations, the local sub-state tree model is as follows: Figure 5 As shown.
[0075] Based on the model constructed using the state tree structure and the algorithm steps, a program was written in MATLAB to verify the algorithm and display it using a GUI interface. The simulated graphs were compared with the theoretically expected results.
[0076] Figure 6 This is a MATLAB simulation graph after the invalid state has been removed. Figure 6 Model with local sub-state trees Figure 3 Comparative analysis shows the following correspondence between the deletion status and the fill coordinates: , , , , , , , The state corresponds to the coordinate, thus proving the effectiveness of the invalid state deletion algorithm.
[0077] Figure 7 This is a MATLAB simulation graph after the removal of replaceable states. Figure 7 With automata model Figure 4 Comparative analysis shows the following correspondence between the deletion status and the fill coordinates: , , The deletion state corresponds to the filling coordinate, thus proving the effectiveness of the replaceable state deletion algorithm.
[0078] Figure 8 This is a MATLAB simulation graph after the iterative states have been removed. Figure 8 and Figure 5 Comparative analysis shows the following correspondence between the deletion status and the fill coordinates: , The deletion state corresponds one-to-one with the filling coordinate, thus proving the effectiveness of the iterative deletion algorithm.
[0079] Depend on Figure 8As we can see, the local region after iterative deletion consists of all paths from the starting point to the ending point, and all paths are now valid. Removing redundant points reduces the number of states, resulting in less data to store paths and saving memory. It also eliminates some interference for subsequent shortest path calculations, reducing computation time and improving efficiency.
[0080] For the iterative local sub-state tree model Figure 5 Perform model optimization.
[0081] First, put all the state nodes of a path into an array. ; set the initial state node Branch status nodes , , and identifier status nodes Put into array Secondly, adjacent branch nodes are selected and weighted to simplify the process, such as in the route. → → → → → → → → , Arrived after 8 states ,but arrive Weight The weight is 8, so put the weights into the array. In the middle. Optimized array storage as follows: Figure 9 As shown.
[0082] By filtering nodes in feasible paths, unnecessary nodes are omitted, leaving only key nodes for storage. This significant reduction in the number of nodes also greatly reduces computer memory consumption.
[0083] After state deletion and optimization, the number of states and events in the automata model is greatly reduced. The number of states is reduced from 43 to 6, and the number of events is reduced from 96 to 14. The final local sub-state tree structure model is as follows: Figure 10 As shown. Through the above node deletion and optimization, not only is the computer's storage requirement reduced, but the efficiency of path solving is also improved.
[0084] Model optimization is performed based on a local sub-state tree model. This optimization can be divided into two parts: node deletion and node optimization. Node deletion removes redundant points from the path, while node optimization filters and saves key nodes of feasible paths, thus reducing memory overhead. Therefore, the shortest path is calculated using the traditional Dijkstra algorithm on the simplified sub-state tree model, as shown in Table 1.
[0085]
[0086] As shown in Table 1, the shortest distance from the initial state to the marked state is 14. Two shortest paths were found. → → → → or → → → → This method can not only find multiple shortest paths, but also provide detailed information on the distance and route of each path.
[0087] If yes Figure 2 The state tree structure in the table is solved using the traditional Dijkstra algorithm, as shown in Table 2, with a time complexity of O(n log n). .
[0088] Table 1 is obtained by using node deletion and model optimization followed by Dijkstra's algorithm, with a time complexity of O(n log n). .
[0089] Solve using MATLAB simulation When solving mazes, the traditional Dijkstra's algorithm takes 36 milliseconds, while the optimized algorithm takes 0.8 milliseconds, showing a significant difference in time complexity. As the scale of the problem increases, the time complexity difference between the traditional Dijkstra's algorithm and the local region path planning algorithm based on the state tree structure proposed in this application will become even greater.
[0090] Traditional Dijkstra's algorithm calculates the distances of multiple dead-end paths, adding unnecessary workload. The optimized algorithm, however, removes dead-end paths at the outset, retaining only the shortest distance to the target point.
[0091] Furthermore, while the traditional Dijkstra's algorithm uses weights, all weights are set to 1 when solving local regions of a raster map, rendering them almost useless for subsequent solutions. The optimized algorithm omits unnecessary nodes, and these omitted nodes are represented using weights, thus leveraging the role of the weights.
[0092] Traditional Dijkstra's algorithm can usually only find a single shortest path, while this paper uses an improved algorithm on a simplified automata model to find multiple shortest paths.
[0093] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a method for a local region path planning algorithm based on a state tree structure.
[0094] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.
[0095] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.
[0096] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.
Claims
1. A local region path planning algorithm based on a state tree structure, characterized in that, Includes the following steps: S1: Obtain the topological information of the area to be planned, and model the area based on the state tree structure model to obtain the initial state tree model; S2: Perform a redundant state deletion operation on the initial state tree model to obtain a simplified state tree model; S3: On the simplified state tree model, run the path search algorithm to calculate the optimal path from the starting point to the ending point.
2. The local region path planning method of claim 1, wherein, The state tree structure model is a six-tuple structure, comprising: a state tree ST, a state graph set H, an event set E, a transition function δ, an initial sub-state tree ST0, and a marked sub-state tree set ST m .
3. The local area path planning method according to claim 2, characterized in that, In step S1, modeling the region based on the state tree structure model includes: S11: Perform rasterization processing on the area to be planned; S21: Map each feasible grid to a state node in the sub-state tree; Based on the topology information, establish the event and transition relationships between the state nodes.
4. The local area path planning method according to claim 3, characterized in that, The redundant state deletion operation performed on the initial state tree model in step S2 includes: Invalid state deletion, the invalid state deletion includes: S21: Traverse the sub-state trees in the initial state tree model. If a sub-state tree cannot be reached from the initial state or the target state cannot be reached from the sub-state tree, then it is determined to be an invalid sub-state tree. S22: Delete the invalid sub-state tree and the edges and subtrees associated with the invalid sub-state tree from the model.
5. The local area path planning method according to claim 4, characterized in that, The redundant state deletion operation performed on the initial state tree model in step S2 further includes: Replaceable sub-state tree merging, wherein the replaceable sub-state tree merging includes: S23: Traverse the sub-state trees in the initial state tree model. If two sub-state trees in the state tree model have the same set of paths to the target state, then they are determined to be replaceable sub-state trees. S24: Then retain one of the alternative sub-state trees and delete the other alternative sub-state tree.
6. The local area path planning method according to claim 4, characterized in that, The redundant state deletion operation performed on the initial state tree model in step S2 specifically involves iteratively executing the invalid state deletion and the merging of the replaceable sub-state trees until there are no more redundant states in the state tree model.
7. The local area path planning method according to any one of claims 1 to 6, characterized in that, In step S3, model optimization is further included before running the path search algorithm. The model optimization includes: S31: Identify the key nodes in the simplified state tree model, wherein the key nodes include at least the start point, the end point, and all branch nodes; S32: If there is a unique connected path between any two adjacent key nodes, then compress that path into a direct connection with path weights.
8. The local area path planning method according to claim 7, characterized in that, The path weight is the number of state nodes contained in the compressed path, or the actual cost of the path.
9. The local area path planning method according to claim 1, characterized in that, The path search algorithm described in step S3 is either Dijkstra's algorithm or A* algorithm.
10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 9.