Improved artificial potential field method path planning method and system based on memory potential field

Abstract

The invention provides an improved artificial potential field method path planning method and system based on a memory potential field, and solves the problem that a conventional artificial potential field method is liable to fall into a local minimum value by constructing a three-component total potential field model containing a target attraction potential, an obstacle rejection potential and a memory potential. The memory potential field records historical track points through a strategy based on space-time density, is constructed in combination with a weight index attenuation mechanism and a Gaussian kernel superposition method, can dynamically mark an explored area and generate repulsive force, and guides the robot to advance towards an unexplored space. Meanwhile, a fixed-capacity circular buffer area is adopted to manage memory points, so that the algorithm practicability is ensured. On the basis that the advantages of calculation simplicity and reactivity of a traditional artificial potential field method are reserved, the method has limited escapability, asymptotic completeness, local stability and global convergence, it can be ensured that the robot safely and efficiently reaches the target point from the starting point in the complex unknown environment, and the method is suitable for a sensor-driven mobile robot path planning scene.

Description

Technical Field

[0001] This invention relates to the field of mobile robot path planning technology, and more specifically, to an improved artificial potential field method and system for path planning based on a memory potential field. Background Technology

[0002] Path planning for mobile robots is one of the core technologies of autonomous navigation systems. Its goal is to achieve safe and efficient movement from a starting point to a target point in complex environments while avoiding obstacles. The traditional artificial potential field (APF) method is widely used due to its high computational efficiency and strong physical intuitiveness, but it has a fundamental drawback: it easily gets trapped in local minima. In these regions, the attractive and repulsive forces acting on the robot cancel each other out, causing the robot to stagnate and fail to reach the target point.

[0003] Existing solutions mainly fall into three categories: first, random perturbation methods, which introduce randomness to help robots escape local minima, but may lead to path instability and inefficiency; second, virtual target / obstacle methods, which require fine-tuning of parameters and have poor environmental adaptability; and third, hybrid methods, which combine APF with a global planner, but lose the pure reactive advantage of APF. None of these methods fundamentally solve the local minima problem, and they often introduce additional complexity and uncertainty. Therefore, there is an urgent need for a new path planning method that can maintain the computational simplicity and reactive characteristics of APF while effectively avoiding the local minima dilemma. Summary of the Invention

[0004] In view of the above problems, the purpose of this invention is to provide a deterministic APF algorithm with "memory perception" capability. By introducing a memory potential field based on motion history into the traditional potential field, the explored area is dynamically recorded, thereby actively guiding the robot to avoid local minima and move into unexplored space. This method fundamentally solves the local minima problem while retaining the simplicity and responsiveness of APF calculations, and is particularly suitable for sensor-driven unknown environments.

[0005] The first aspect of this invention provides an improved artificial potential field method for path planning based on a memory potential field, comprising the following steps:

[0006] Constructing a target attraction potential Obstacles and repulsion potential and memory potential Three-component potential field model The robot's movement is guided by a three-component potential field model;

[0007] Among them, the three-component potential field model The expression is:

[0008] ;

[0009] in, For time The robot's location;

[0010] Assume the robot is in time The set of memory points in the previously visited historical trajectory is Memory potential Defined as a weighted superposition of Gaussian kernels:

[0011] ;

[0012] in, For memory gain, Representing memory points The weight, The kernel width.

[0013] Furthermore, the memory point set is managed using a fixed-capacity circular storage to prevent unlimited memory growth and ensure the feasibility of the algorithm in a real system.

[0014] Furthermore, the set of memory points is dynamically updated every time the robot completes a time interval. When that happens, a new memory point is added. .

[0015] Furthermore, weight Decays over time, expressed as:

[0016] ;

[0017] in, The preset initial weights, This is the attenuation coefficient.

[0018] Furthermore, the robot's motion is determined by the direction of the negative gradient of the total potential field, that is:

[0019]

[0020] Memory potential The resulting repulsive force causes the robot to move away from the visited area, thus actively exploring new spaces.

[0021] A second aspect of the present invention provides an improved artificial potential field method path planning system based on a memory potential field, comprising a memory and a processor. The memory includes a path planning method program based on a memory potential field, which, when executed by the processor, performs the following steps:

[0022] Constructing a target attraction potential Obstacles and repulsion potential and memory potential Three-component potential field model The robot's movement is guided by a three-component potential field model;

[0023] Among them, the three-component potential field model The expression is:

[0024] ;

[0025] in, For time The robot's location;

[0026] Assume the robot is in time The set of memory points in the previously visited historical trajectory is Memory potential Defined as a weighted superposition of Gaussian kernels:

[0027] ;

[0028] in, For memory gain, Representing memory points The weight, The kernel width.

[0029] A third aspect of the present invention provides a computer-readable storage medium comprising a path planning method program based on an improved artificial potential field method using a memory potential field. When the improved artificial potential field method program is executed by a processor, it implements the steps of the path planning method program based on the improved artificial potential field method using a memory potential field.

[0030] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention provides an improved artificial potential field method and system for path planning based on a memory potential field. By constructing a three-component total potential field model including the target attraction potential, obstacle repulsion potential, and memory potential, it solves the problem of traditional artificial potential field methods easily getting trapped in local minima. The memory potential field records historical trajectory points through a strategy based on spatiotemporal density, and is constructed by combining a weighted exponential decay mechanism and a Gaussian kernel superposition method. It can dynamically mark explored areas and generate repulsive forces, guiding the robot to move into unexplored space. At the same time, a fixed-capacity circular buffer is used to manage memory points, ensuring the practicality of the algorithm. While retaining the advantages of computational simplicity and responsiveness of traditional artificial potential field methods, this invention possesses finite escape, asymptotic completeness, local stability, and global convergence, ensuring that the robot can safely and efficiently reach the target point from the starting point in complex and unknown environments. It is suitable for path planning scenarios of sensor-driven mobile robots. Attached Figure Description

[0031] Figure 1 This is a flowchart of an improved artificial potential field path planning method based on memory potential fields. Detailed Implementation

[0032] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0033] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0034] Example 1

[0035] like Figure 1 As shown, this embodiment discloses an improved artificial potential field method based on a memory potential field for path planning. This embodiment proposes an improved artificial potential field method based on a memory potential field (HM-APF, History-Memory Artificial Potential Field). The memory configuration space... Robot position ,Target Obstacle set , for obstacles minimum external distance In traditional APF, the robot's motion equations are:

[0036] ;

[0037] Where the potential energy function It consists of the attraction potential of the target and the repulsion potential of the obstacle, wherein , , of which each In its sphere of influence The above is Monotonically decreasing and This method is computationally simple and physically intuitive, but it is prone to getting stuck in local minima and stagnating in complex environments. Therefore, this invention introduces an additional potential field term based on historical memory, building upon the classical potential field. Constructing total potential energy:

[0038] ;

[0039] This allows the system to adaptively increase the potential energy in the stagnant region within an analytical framework, forcing the robot to continue moving forward.

[0040] Barrier potential function based on minimum distance: To enable the algorithm to have sensor-driven characteristics, this invention uses the minimum distance to obstacles to represent the environment. For the obstacle set... Define the distance function for each obstacle:

[0041]

[0042] Based on this definition, the barrier repulsion potential is:

[0043]

[0044] in This refers to the radius of effect. This form depends on the distance measured by the sensor in real time. It does not require a prior map and can be used directly in unknown environments.

[0045] Construction of the memory potential field: The core of HM-APF lies in the memory potential term. Assume the robot is in time... The set of previously visited historical trajectory points is Its weight decays over time:

[0046] ;

[0047] The memory potential is defined as a weighted superposition of Gaussian kernels:

[0048]

[0049] in For memory gain, The kernel width.

[0050] Historical trajectory points are continuously recorded during robot operation. To achieve effective global guidance and avoid memory explosion, a spatiotemporal density-based recording strategy is adopted: when the robot traverses a certain time interval... At that time, a new memory point is added at that location. The purpose of this design is, on the one hand, to ensure that the robot stays at a certain point for more than [a certain amount of time]. When a robot stops, a new memory point is inevitably generated. On the other hand, the robot needs the ability to explore, i.e., to be propelled into unknown areas. Therefore, even without stopping, a memory point must be generated to prevent the robot from retracing its path, further enhancing its ability to escape local minima. In short, it is an enhanced representation that incorporates the characteristic of generating new memory points when the robot stops. Simultaneously, this mechanism ensures higher recording density in low-speed or stationary regions, while also increasing the set of memory points. It is managed using fixed-capacity cyclic storage.

[0051] Dynamics and Control Laws: The robot is controlled by the total potential field.

[0052]

[0053] As can be seen from the above equation, the memory potential term exerts an additional repulsive force on the recently visited region, enabling the robot to escape local minima in an analytical sense. Unlike random perturbation or virtual target methods, HM-APF does not introduce randomness or rely on discrete search, thus maintaining analytical solvability and realizability.

[0054] Theoretical Analysis

[0055] The theoretical properties of HM-APF are given below in four aspects: finite escape; asymptotic completeness; local stability; and global convergence.

[0056] Theorem 1: Finite Escape: Suppose the robot is in a continuous potential field

[0057]

[0058] in And memory potential

[0059]

[0060] Set up a core Continuously differentiable and for any radius There exists a constant Make

[0061]

[0062] If the system maintenance strategy satisfies: whenever the robot is in the neighborhood The cumulative stay time inside reached At that time, a historical sample point must be added to that neighborhood. And assign weights And for all Obstacles and target potential gradient upper bound

[0063]

[0064] If the parameters satisfy

[0065]

[0066] Any infinite stagnation of the robot within this neighborhood is impossible; specifically, there exists a finite time upper bound.

[0067]

[0068] Make robots must be Before leaving .

[0069] Proof: Let the current time be... (i.e., the first) (This addition is complete). Time, and neighboring regions The corresponding historical sample weights are

[0070]

[0071]

[0072]

[0073] Therefore, the limit is obtained.

[0074]

[0075] This result indicates that, under the periodic addition / decay mechanism, the local cumulative weight is monotonically increasing and bounded; when hour Linear unbounded growth, which can be viewed as .

[0076] In the neighborhood Inside,

[0077]

[0078] Depend on exist Take the lower bound of the gradient magnitude:

[0079]

[0080] If the radial component of the resultant force is positive (pointing outwards), the robot will move outwards in the next time step.

[0081] Define the lower bound of the radial driving force:

[0082]

[0083] If there exists a smallest integer Make Then in From that moment on, the driving force is strictly positive, and the robot moves outward at a speed, beginning to leave the neighborhood. Because... If a signal is monotonically increasing, it must have a unique minimum value. satisfy:

[0084]

[0085] The solution can be found from (A5). :

[0086]

[0087] Take the logarithm:

[0088]

[0089] Since the right side is positive under assumption (A3), taking the smallest integer upper bound gives:

[0090]

[0091] Therefore, the upper bound of total escape time .

[0092] because denominator And (A3) guarantees that the logarithmic terms within the parentheses are in... Within the range, thus Limited. If Using limit expansion A linear approximation can be obtained:

[0093]

[0094] This indicates that the smaller the memory decay, the shorter the escape time. If Then by Condition (A9) is given Escape time Similarly limited.

[0095] In conclusion, there exist finite integers. Therefore, limited time make .exist At that moment, the direction of the net force points outward from the neighborhood, and the robot leaves the neighborhood at a non-zero velocity, making it impossible for it to remain stationary indefinitely. Q.E.D.

[0096] Theorem 2: Asymptotic Completeness: If the memory mechanism satisfies finite escape (Theorem 1), and the sensor has coverage of all reachable paths in free space within a finite time, that is, for any connected path... ,exist Make Then the HM-APF algorithm has asymptotic completeness; that is, if the target region If it is reachable, then there is a finite time. Make .

[0097] Proof: By Theorem 1, a robot cannot remain stationary indefinitely within any bounded region. Consider starting from the initial point. To the target area any connected path According to the sensor coverage assumption, there exists a finite time... This caused the robot to stop the path. Completely covered by the perceptual range of time, that is:

[0098]

[0099] Memory field The introduction of this feature allows for access to already visited areas. The potential energy is continuously increased, thus generating a tendency in the control law to point towards the unexplored region. The vector field components.

[0100] Due to the path It is connected and subject to finite time. The system is covered by the sensor's field of view, and because it has finite escape properties (Theorem 1) and will not remain stationary indefinitely, its trajectory is guided by both the target's attractive potential and the memory repulsive potential. Able to effectively explore And eventually enter the target area. Therefore, it exists for a finite amount of time. , making .

[0101] Q.E.D.

[0102] Theorem 3 (Locally Asymptotically Stable)

[0103] In the target a certain neighborhood Within this context, if the disturbances in the total potential field (including obstacle repulsion potential and memory potential) are sufficiently small, specifically, if a constant exists... Make

[0104]

[0105] in yes The smallest eigenvalue of the Hessian matrix is ​​the target point. It is a locally asymptotically stable equilibrium point.

[0106] Proof: Selecting Lyapunov function candidates:

[0107]

[0108] Its derivative with respect to time is:

[0109]

[0110] Therefore, in the region Inside, there is According to Lyapunov stability theory, It is locally asymptotically stable.

[0111] Q.E.D.

[0112] Theorem 4: Global Convergence: Under the assumptions of Theorem 1 (Finite Escape), Theorem 2 (Asymptotic Completeness), and Theorem 3 (Local Asymptotic Stability), if the target point... Located in connected free space Within this system, the system controlled by HM-APF is globally convergent. That is, for any initial position... trajectory satisfy:

[0113]

[0114] Proof: According to Theorem 1, a robot cannot remain stationary indefinitely within any bounded region. This means that its trajectory... Either reach the goal within a limited time. Either in free space It moves infinitely and continuously within the system, without converging to any non-target equilibrium point; according to Theorem 2, since the target... If reachable, then for any neighborhood of the target point It exists for a limited time. , making This indicates that the trajectory must enter any small neighborhood of the target point within a finite amount of time. By Theorem 3, there exists a certain... This makes it possible in the neighborhood Inside, target point It is locally asymptotically stable. Combining this with point 2, the trajectory is within a finite time... Enter Subsequently, the local dynamics of the system become dominant, satisfying:

[0115]

[0116] Comprehensive Argument: The above three properties constitute a complete convergence chain: the system will not stagnate permanently at any local minimum (Theorem 1); the system will inevitably explore any small neighborhood of the target point in a finite amount of time (Theorem 2); once it enters the stable attraction region of the target, the system will asymptotically converge to the target (Theorem 3). Therefore, for any initial state... The system trajectory converges globally to .

[0117] Q.E.D.

[0118] HM-APF possesses four key properties in its analytical form:

[0119] 1. Finite escape property: Stasis must be resolved in a finite time, which fundamentally solves the problem of local minima;

[0120] 2. Asymptotic completeness: If the target is reachable, the trajectory will enter the target's neighborhood within a finite amount of time, ensuring reachability;

[0121] 3. Local stability: The target point is an asymptotically stable equilibrium point, ensuring accurate final convergence;

[0122] 4. Global convergence: Combining the above properties, the system can converge to the target from any initial point in free space.

[0123] This theoretical framework demonstrates that HM-APF not only solves the local minima problem of traditional artificial potential field methods but also guarantees the completeness and convergence of the algorithm, providing a solid theoretical foundation for subsequent simulation experiments and practical applications. Implementation considerations: HM-APF parameters. The algorithm needs to be adjusted based on the robot's dynamics and environmental complexity. In practical applications, an upper limit should be set for the number of memory points to avoid memory overload, and sensor noise can be processed through distance filtering. This algorithm is suitable for mobile robot platforms equipped with LiDAR or depth cameras.

[0124] Example 2

[0125] This embodiment, based on Embodiment 1, discloses an improved artificial potential field method path planning system based on a memory potential field, including a memory and a processor. The memory includes a path planning method program based on a memory potential field. When the processor executes the path planning method program based on a memory potential field, it performs the following steps:

[0126] Constructing a target attraction potential Obstacles and repulsion potential and memory potential Three-component potential field model The robot's movement is guided by a three-component potential field model;

[0127] Among them, the three-component potential field model The expression is:

[0128] ;

[0129] in, For time The robot's location;

[0130] Assume the robot is in time The set of memory points in the previously visited historical trajectory is Memory potential Defined as a weighted superposition of Gaussian kernels:

[0131] ;

[0132] in, For memory gain, Representing memory points The weight, The kernel width.

[0133] Example 3

[0134] This embodiment discloses a computer-readable storage medium, which includes a path planning method program based on an improved artificial potential field method using a memory potential field. When the improved artificial potential field method program based on a memory potential field is executed by a processor, it implements the steps of the path planning method based on an improved artificial potential field method using a memory potential field as described in Embodiment 1.

[0135] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0136] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units. They may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0137] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0138] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0139] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

Claims

1. An improved artificial potential field-based path planning method based on memory potential fields, characterized in that, Includes the following steps: Constructing a target attraction potential Obstacles and repulsion potential and memory potential Three-component potential field model The robot's movement is guided by a three-component potential field model; Among them, the three-component potential field model The expression is: ； in, For time The robot's location; Assume the robot is in time The set of memory points in the previously visited historical trajectory is Memory potential Defined as a weighted superposition of Gaussian kernels: ； in, For memory gain, Representing memory points The weight, The kernel width.

2. The improved artificial potential field path planning method based on memory potential field according to claim 1, characterized in that, The set of memory points is managed using a fixed-capacity circular storage to prevent unlimited memory growth and ensure the feasibility of the algorithm in a real system.

3. The improved artificial potential field path planning method based on memory potential field according to claim 1, characterized in that, The set of memory points is dynamically updated every time the robot completes a time interval. When that happens, a new memory point is added. .

4. The improved artificial potential field path planning method based on memory potential field according to claim 1, characterized in that, Weight Decays over time, expressed as: ； in, The preset initial weights, This is the attenuation coefficient.

5. The improved artificial potential field path planning method based on memory potential field according to claim 1, characterized in that, The robot's motion is determined by the direction of the negative gradient of the total potential field, that is: ； Memory potential The resulting repulsive force causes the robot to move away from the visited area, thus actively exploring new spaces.

6. An improved artificial potential field method path planning system based on memory potential fields, characterized in that, The system includes a memory and a processor. The memory contains a program for an improved artificial potential field path planning method based on a memory potential field. When the processor executes the program for the improved artificial potential field path planning method based on a memory potential field, it performs the following steps: Constructing a target attraction potential Obstacles and repulsion potential and memory potential Three-component potential field model The robot's movement is guided by a three-component potential field model; Among them, the three-component potential field model The expression is: ； in, For time The robot's location; Assume the robot is in time The set of memory points in the previously visited historical trajectory is Memory potential Defined as a weighted superposition of Gaussian kernels: ； in, For memory gain, Representing memory points The weight, The kernel width.

7. The improved artificial potential field method path planning system based on memory potential field according to claim 6, characterized in that, The set of memory points is dynamically updated, and the robot updates it every time a time interval occurs. When that happens, a new memory point is added. .

8. The improved artificial potential field method path planning system based on memory potential field according to claim 6, characterized in that, Weight Decays over time, expressed as: ； in, The preset initial weights, This is the attenuation coefficient.

9. The improved artificial potential field method path planning system based on memory potential field according to claim 6, characterized in that, The robot's motion is determined by the direction of the negative gradient of the total potential field, that is: ； Memory potential The resulting repulsive force causes the robot to move away from the visited area, thus actively exploring new spaces.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a path planning method program based on an improved artificial potential field method using a memory potential field. When the improved artificial potential field method program based on a memory potential field is executed by a processor, it implements the steps of a path planning method based on an improved artificial potential field method using a memory potential field as described in any one of claims 1 to 5.

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