A robot navigation method suitable for large sparse environments

Abstract

This invention discloses a robot navigation method suitable for large sparse environments, comprising the following steps: Step 1, establishing a system evolution equation based on the robot's state vector and kinematic equations, incorporating an environmental sparsity factor into the system evolution equations, and then introducing trajectory tracking weights and obstacle avoidance weights to construct a dynamic system model; Step 2, determining whether the dynamic system model is in a critical state between stability and chaos by solving the Jacobian matrix and Lyapunov exponent of the dynamic system model. When the maximum Lyapunov exponent is approximately equal to 0, the critical stability condition is reached; Step 3, based on the critical state, designing a path evaluation function to screen stable path points, and dynamically adjusting the obstacle avoidance weights through bifurcation parameter adjustment control equations to achieve adaptive switching between ordered tracking and chaotic obstacle avoidance, thus completing robot navigation in large sparse environments. This invention can ensure that robots can efficiently and stably complete navigation in large sparse environments.

Description

Technical Field

[0001] This invention relates to the field of robot navigation technology, and in particular to a robot navigation method suitable for large sparse environments. Background Technology

[0002] In large, sparse environments such as warehousing and logistics parks, open-pit mines, and large exhibition halls, autonomous robot navigation faces multiple challenges, including complex environmental characteristics, conflicting navigation requirements, and the limitations of traditional methods. These environments are spatially large (typically ≥100m × 100m), with obstacles sparsely distributed (containing 5–10 static obstacles and 2–3 dynamic obstacles), and this sparsity dynamically changes (e.g., temporary stacking of goods in a warehouse leads to increased obstacle density in localized areas). Therefore, robot navigation must simultaneously satisfy the stability of long-distance trajectory tracking (e.g., a warehouse robot following a shelf aisle) and the flexibility of chaotic obstacle avoidance (e.g., avoiding suddenly appearing transport vehicles), with the priorities of these two aspects switching in real-time according to the environment.

[0003] Currently, traditional navigation algorithms can be mainly divided into global planning algorithms based on environment models (such as A*, Dijkstra, and RRT series algorithms) and local obstacle avoidance algorithms based on real-time sensor data (such as Dynamic Window Method (DWA)). However, traditional technologies have significant drawbacks. For example, in terms of planning efficiency, algorithms such as A* and Dijkstra struggle to support real-time navigation due to the large number of node traversals in large scenes. Furthermore, the "tracking weight" and "obstacle avoidance weight" of the Dynamic Window Method (DWA) are mostly fixed values, which cannot match changes in environmental sparsity. This leads to excessively high obstacle avoidance weights in open areas causing trajectory jitter, and excessively high tracking weights in obstacle areas easily causing collisions. In addition, at the state utilization level, traditional methods either forcibly constrain the system to a "stable domain" (obstacle avoidance rigidity) or allow it to enter a "chaotic domain" (trajectory divergence), making it difficult to simultaneously achieve stability under small disturbances and sensitivity under large disturbances.

[0004] In summary, current robot navigation methods cannot achieve an adaptive balance between "tracking stability" and "obstacle avoidance flexibility" in large sparse environments, resulting in navigation efficiency and robustness that are difficult to meet practical needs. Summary of the Invention

[0005] The purpose of this invention is to provide a robot navigation method suitable for large sparse environments. This invention constructs a dynamic system model that incorporates the sparse characteristics of the environment, calculates the path planning and obstacle avoidance control equations under critical states, and achieves adaptive switching between ordered tracking and chaotic obstacle avoidance, ensuring that the robot can efficiently and stably complete navigation in large sparse environments.

[0006] The technical solution provided by this invention is as follows: A robot navigation method suitable for large sparse environments, comprising the following steps:

[0007] Step 1: Establish system evolution equations based on the robot's state vector and kinematic equations. Integrate environmental sparsity factors into the system evolution equations, and then introduce trajectory tracking weights and obstacle avoidance weights to construct a dynamic system model.

[0008] Step 2: By solving the Jacobian matrix and Lyapunov exponent of the dynamic system model, determine whether the dynamic system model is in a critical state between stability and chaos. When the maximum Lyapunov exponent is approximately equal to 0, the critical stability condition is reached.

[0009] Step 3: Based on the critical state, design a path evaluation function to screen stable path points, and dynamically adjust the obstacle avoidance weights by adjusting the control equation through bifurcation parameters to achieve adaptive switching between ordered tracking and chaotic obstacle avoidance, thus completing robot navigation in a large sparse environment.

[0010] In the robot navigation method described above for large sparse environments, step 1, the robot state vector is represented as:

[0011] ;

[0012] In the formula, Indicates the robot's position coordinates. For heading angle, Linear velocity; This is a transpose operation;

[0013] The robot's kinematic equations are as follows:

[0014] ;

[0015] In the formula, and These are the rates of change of position in the x and y directions, respectively; This represents the rate of change of the heading angle; Angular velocity; The rate of change of linear velocity;

[0016] The system evolution equation is expressed as follows:

[0017] ;

[0018] In the formula, To control the input, ; It is a non-linear mapping function.

[0019] The aforementioned robot navigation method applicable to large sparse environments incorporates an environmental sparsity factor in its system evolution equation as follows:

[0020] ;

[0021] in, The environmental sparsity factor is calculated using the following formula:

[0022] ;

[0023] In the formula, The number of obstacles, The average area of ​​a single obstacle. This refers to the total area of ​​the environment.

[0024] The aforementioned robot navigation method applicable to large sparse environments has a dynamic system model represented as follows:

[0025] ;

[0026] In the formula, and These are the introduction of trajectory tracking weights and obstacle avoidance weights. For acceleration control, This is the proportionality coefficient. For trajectory deviation, This is the distance to the nearest obstacle.

[0027] The aforementioned robot navigation method applicable to large sparse environments includes the following iterative calculation steps for the Lyapunov exponent:

[0028] Step 2.1, Select Linearly independent initial perturbation vectors , The dimension is consistent with that of the state vector, and the initial perturbation vector is a unit vector;

[0029] Step 2.2: For each discrete time step Calculate the Jacobian matrix Effect on the perturbation vector:

[0030] ;

[0031] The Jacobian matrix satisfy:

[0032] ;

[0033] In the formula, For simulating step size, The damping coefficient is... For the first Linear velocity of the time step No. The heading angle of the time step;

[0034] Step 2.3: Perform QR orthogonal decomposition on the perturbation vector set:

[0035] ;

[0036] In the formula, It is an orthogonal matrix. It is an upper triangular matrix;

[0037] Step 2.4: Update the perturbation vector And accumulate the upper triangular matrix diagonal elements , ;

[0038] Step 2.5: After N time steps, the first... Estimates of Lyapunov exponents for: ;

[0039] Among them, the largest Lyapunov index The calculation is as follows:

[0040] .

[0041] The aforementioned robot navigation method applicable to large sparse environments includes a path evaluation function as follows:

[0042] ,

[0043] in, For path length, , , These are the weighting coefficients. The maximum Lyapunov exponent; path points are selected using the Routh-Hurwitz criterion, when the first element of the characteristic equation of the dynamic system is... When the value is positive, the corresponding path point is a stable path point and is included in the planned path, where:

[0044] ;

[0045] In the formula: The system damping coefficient is... For environmental sparsity factor, is the linear velocity.

[0046] The aforementioned robot navigation method applicable to large sparse environments, wherein the bifurcation parameter adjustment control equation is:

[0047] ;

[0048] In the formula: and These are the gain adjustment coefficients, This is the critical Lyapunov exponent threshold. The maximum Lyapunov exponent. This represents the rate of change of distance to the obstacle.

[0049] The aforementioned robot navigation method applicable to large sparse environments uses the Euler method to discretize the dynamic system model:

[0050] ,

[0051] in, For simulating step size, For discrete time steps;

[0052] The calculation interval of the Jacobian matrix satisfy:

[0053]

[0054] in, The initial sampling step size and the environmental sparsity factor are given. The larger the value, the longer the calculation interval, in order to reduce computational overhead.

[0055] In the aforementioned robot navigation method applicable to large sparse environments, during the chaotic obstacle avoidance process, when a dynamic obstacle is detected, the distance to the nearest obstacle is obtained in real time through sensors. and the rate of change of obstacle distance And based on the current environmental sparsity factor Adjust obstacle avoidance weights When the environmental sparsity factor When it is large, decrease Prioritize ensuring orderly tracking; when the environmental sparsity factor When it is small, increase To improve obstacle avoidance flexibility and avoid collisions with dynamic obstacles.

[0056] Compared with existing technologies, it has the following beneficial effects:

[0057] 1. This invention quantifies the distribution characteristics of environmental obstacles by defining an environmental sparsity factor and integrates it into a dynamic system model and state equation. This solves the problem of poor adaptability of traditional navigation algorithms in large sparse environments due to the sparseness of environmental features and the high dynamism of obstacles. It can be stably applied to scenarios with large spatial scale and low obstacle density, such as warehousing and logistics parks, open-pit mines, and large exhibition halls. It does not require complex environmental map reconstruction and reduces the dependence on prior environmental information.

[0058] 2. By deriving the path planning and obstacle avoidance control equations under critical conditions, and combining the Lyapunov exponent to determine the "stable-chaotic" critical state of the system, we can achieve adaptive switching between ordered tracking and chaotic obstacle avoidance. For example, in high-sparseness open areas (such as obstacle-free storage channels), we tend to favor the stable state to ensure long-distance tracking accuracy, while in the vicinity of low-sparseness obstacles (such as temporary obstacle areas in mining areas), we tend to favor chaotic characteristics to improve obstacle avoidance flexibility. This avoids the problems of rigid tracking or uncontrolled obstacle avoidance caused by fixed weights in traditional algorithms.

[0059] 3. This invention uses the Euler method to discretize the dynamic system model and dynamically adjusts the Jacobian matrix calculation interval according to the environmental sparsity factor, effectively reducing the unnecessary computational overhead. At the same time, it quickly selects stable path points through the Routh-Hurwitz criterion without the need for complex eigenvalue solutions. Combined with the path evaluation function that integrates critical states, the path planning efficiency is significantly better than traditional algorithms, meeting the real-time requirements of navigation in large sparse environments.

[0060] 4. Based on the bifurcation parameter adjustment control equation, this invention dynamically adjusts the obstacle avoidance weight by combining the obstacle distance change rate and the environmental sparsity factor. It can respond to the motion state of dynamic obstacles (such as a suddenly intruding transport vehicle) in real time and avoid the lag in dynamic obstacle avoidance response. Simulation results show that in a highly dynamic sparse environment (where the dynamic obstacle is located on the only route), the success rate of dynamic obstacle avoidance of this invention is significantly higher than that of traditional algorithms, and the number of collisions is greatly reduced, thus improving navigation safety.

[0061] 5. This invention ensures that the system is in a critical stable state through Lyapunov exponential iterative calculation, combining small disturbance stability (avoiding trajectory divergence) and large disturbance sensitivity (rapid response obstacles); at the same time, it combines the Routh-Hurwitz criterion to screen stable path points, ensuring the stable operation of the robot throughout the entire process from path planning to motion control, and maintaining trajectory smoothness and navigation robustness even in scenarios with dynamically changing environmental sparsity. Attached Figure Description

[0062] Figure 1 This is a simplified structural diagram of the mobile robot of the present invention;

[0063] Figure 2 The trajectory comparison of the three methods is shown in Scenario 1;

[0064] Figure 3 The Lyapunov exponential transformation of the present invention is shown in scenario 1;

[0065] Figure 4 The numerical transformation of obstacle avoidance weights in scenario 1 is demonstrated;

[0066] Figure 5 The multi-target access efficiency of three methods is demonstrated in Scenario 1;

[0067] Figure 6 The total time consumption of the three methods in scenario 1 is compared.

[0068] Figure 7 The total path comparison of the three methods in Scenario 1 is shown;

[0069] Figure 8 Present a comparison of the trajectories of the three methods in scenario 2;

[0070] Figure 9 The Lyapunov exponential transformation of the present invention is shown in scenario 2;

[0071] Figure 10 The numerical transformation of obstacle avoidance weights in scenario 2 is demonstrated;

[0072] Figure 11 The comparison of total obstacle avoidance time in scenario 2 is shown;

[0073] Figure 12 The comparison of the total obstacle avoidance path length under scenario 2 is shown. Detailed Implementation

[0074] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0075] Example: A robot navigation method suitable for large sparse environments, comprising the following steps:

[0076] Step 1: Establish system evolution equations based on the robot's state vector and kinematic equations. Integrate environmental sparsity factors into the system evolution equations, and then introduce trajectory tracking weights and obstacle avoidance weights to construct a dynamic system model.

[0077] In this step, the mobile robot adopts a dual-wheel differential drive structure, which includes two active fixed wheels and one passive omnidirectional wheel (see...). Figure 1 The robot is driven by fixed active wheels and omnidirectional wheels for flexible steering. The robot's state vector is represented as follows:

[0078] ;

[0079] In the formula, Indicates the robot's position coordinates. For heading angle, Linear velocity; This is a transpose operation;

[0080] The robot's kinematic equations are as follows:

[0081] ;

[0082] In the formula, and These are the rates of change of position in the x and y directions, respectively; This represents the rate of change of the heading angle; Angular velocity; The rate of change of linear velocity;

[0083] The system evolution equation is expressed as follows:

[0084] ;

[0085] In the formula, To control the input, ; It is a non-linear mapping function.

[0086] The robot is located in a warehousing and logistics park, which has... There are obstacles, each with an average area of ​​. The total environmental area of ​​the park is The environmental sparsity factor of this warehousing and logistics park is defined as follows: , , A larger value indicates a sparser environment.

[0087] After incorporating the environmental sparsity factor into the system evolution equation, the system evolution equation is updated as follows:

[0088] ;

[0089] Then introduce trajectory tracking weights Obstacle avoidance weights Control input The resulting dynamic system model is represented as follows:

[0090] ;

[0091] In the formula, For acceleration control, This is the proportionality coefficient. For trajectory deviation, This is the distance to the nearest obstacle.

[0092] To enable numerical computation, the dynamic system model is discretized using the Euler method:

[0093] ,

[0094] in, The simulation step size is set to 0.1s. For discrete time steps;

[0095] The discretized function is: .

[0096] Step 2: By solving the Jacobian matrix and Lyapunov exponent of the dynamic system model, determine whether the dynamic system model is in a critical state between stability and chaos. When the maximum Lyapunov exponent is approximately equal to 0, the critical stability condition is reached.

[0097] The critical state of a dynamic system model (referred to as the system) is essentially a marginal balance between "stability" and "chaos": below the critical state, the system is stable, guaranteeing that the target point can be reached, and most path planning methods are carried out under the premise of system stability. However, for large sparse environments, the density of sub-objectives and obstacles (including static and dynamic obstacles) is low, providing limited information. Stable systems lack necessary environmental state information, have sluggish responses to dynamic obstacles, and poor avoidance maneuverability. When the dynamic system is above the critical state, the system enters a chaotic state, which enhances flexibility and innovation, effectively compensating for the aforementioned poor dynamic response of the system. However, chaotic systems are sensitive to initial values ​​and other factors, which can easily lead to system divergence and failure to reach the target point.

[0098] In this step, the core of calculating the Lyapunov exponent is solving the Jacobian matrix for the system's state transitions. The calculation interval is dynamically increased based on the sparsity factor, as shown in the following equation:

[0099] ;

[0100] in, The initial sampling step size is 0.5 seconds; the environmental sparsity factor... The larger the value, the longer the calculation interval, in order to reduce computational overhead.

[0101] Obstacle avoidance weight As a bifurcation parameter, the sigmoid function is chosen as the adjustment function for the sparsity adaptive factor:

[0102] ;

[0103] Design adaptive adjustment to achieve smooth state switching:

[0104] ;

[0105] In the formula, For obstacle avoidance weights in strong obstacle mode, Obstacle avoidance weights for the weak obstacle mode;

[0106] For robot navigation systems in sparse environments, the specific form of the state transition function is as follows:

[0107] ;

[0108] in,

[0109] Taking the partial derivatives with respect to each state variable, we obtain the Jacobian matrix: The Jacobian matrix describes the propagation characteristics of small perturbations in the state space and is the basis for calculating the Lyapunov exponent. It is specifically represented as follows:

[0110] ;

[0111] In the formula, For simulating step size, The damping coefficient is... For the first Linear velocity of the time step No. The heading angle of the time step.

[0112] After obtaining the Jacobian matrix, the Lyapunov exponent is calculated iteratively, as follows:

[0113] Step 2.1, Select Linearly independent initial perturbation vectors , The dimension is consistent with that of the state vector, and the initial perturbation vector is a unit vector;

[0114] Step 2.2: For each discrete time step Calculate the Jacobian matrix Effect on the perturbation vector:

[0115] ;

[0116] Step 2.3: Perform QR orthogonal decomposition on the perturbation vector set:

[0117] ;

[0118] In the formula, It is an orthogonal matrix. It is an upper triangular matrix;

[0119] Step 2.4: Update the perturbation vector And accumulate the upper triangular matrix diagonal elements , ;

[0120] Step 2.5: After N time steps, the first... Estimates of Lyapunov exponents for: ;

[0121] Among them, the largest Lyapunov index The calculation is as follows:

[0122] .

[0123] In sparse environment robot navigation systems, due to the environmental sparsity factor... The statistical stationarity of the system is guaranteed; the critical state control strategy prevents the system from entering a completely chaotic state; the perturbation orthogonalization process (QR decomposition) ensures... The boundedness of the limit value, therefore this limit value It exists and is unique, and satisfies:

[0124] ;

[0125] when When the system reaches the critical stability condition, it is in a critical state on the "edge of chaos", which has the dual advantages of small disturbance stability (ensuring tracking accuracy) and large disturbance sensitivity (improving obstacle avoidance flexibility).

[0126] Furthermore, for the Jacobian matrix, the characteristic equation to be solved is:

[0127] ;

[0128] In the formula, =0.5.

[0129] propose ,get ,for Terms, to obtain characteristic roots For quadratic factors Solving for the given information yields the following results. .

[0130] (1) When When the equation has two distinct real roots:

[0131] ;

[0132] (2) When When: The equation has two distinct real roots:

[0133] ;

[0134] (3) When The equation has two distinct real roots:

[0135] ;

[0136] Analyzing the changes in the roots above, different feature roots correspond to different regions, which in turn correspond to different motion modes of the robot: (1) : Corresponding to the robot's uniform translational motion mode, in an open area without obstacles (high) It dominates, ensuring long-distance navigation efficiency and adapting to long-distance path planning in open environments.

[0137] (2) Conjugate complex roots ( , ): Corresponding to the robot's turning motion pattern, its complex characteristics give the system the flexibility required for obstacle avoidance. Near obstacles (low...) The increase in the imaginary part leads to improved steering flexibility, while the decrease in the absolute value of the real part speeds up the response, thus enabling dynamic obstacle avoidance.

[0138] (3) Through The adaptive adjustment can achieve a dynamic balance between "translational stability and steering flexibility" in sparse environments. For example, in a typical sparse environment, The characteristic roots are The results show that the system exhibits weakly damped oscillation characteristics in a typical sparse environment, maintaining stability over long distances while possessing sufficient obstacle avoidance flexibility, thus meeting the requirements for critical state control.

[0139] Step 3: Based on the critical state, design a path evaluation function to screen stable path points, and dynamically adjust the obstacle avoidance weights by adjusting the control equation through bifurcation parameters to achieve adaptive switching between ordered tracking and chaotic obstacle avoidance, thus completing robot navigation in a large sparse environment.

[0140] In this step, the path evaluation function is:

[0141] ,

[0142] in, For path length, , , These are weighting coefficients, with values ​​of 0.3, 0.5, and 0.2 respectively. The maximum Lyapunov exponent; path points are selected using the Routh-Hurwitz criterion, when the first element of the characteristic equation of the dynamic system is... When the value is positive, the corresponding path point is a stable path point and is included in the planned path, where:

[0143] ;

[0144] In the formula: The system damping coefficient is... For environmental sparsity factor, is the linear velocity.

[0145] The bifurcation parameter adjustment control equation is as follows:

[0146] ;

[0147] In the formula: and These are the gain adjustment coefficients, 0.5 and 0.3 respectively. This is the critical Lyapunov exponent threshold. The maximum Lyapunov exponent. This represents the rate of change of distance to the obstacle.

[0148] During the chaotic obstacle avoidance process, when a dynamic obstacle is detected, the distance to the nearest obstacle is obtained in real time via sensors. and the rate of change of obstacle distance And based on the current environmental sparsity factor Adjust obstacle avoidance weights When the environmental sparsity factor When it is large, decrease Prioritize ensuring orderly tracking; when the environmental sparsity factor When it is small, increase To improve obstacle avoidance flexibility and avoid collisions with dynamic obstacles.

[0149] Furthermore, based on the method described in this embodiment, corresponding simulation calculations are performed, and the steps are as follows:

[0150] Simulation setup: Environment model: 100m×100m sparse space, containing 5-10 static obstacles (radius 1-3m) and 2-3 dynamic obstacles (velocity 1-2m / s, random trajectory); Parameter configuration: robot speed v=1m / s, sensor range 20m, simulation step size 0.1 seconds. Two experimental schemes were designed:

[0151] Scenario 1: Low dynamic sparse environment ( =0.8 (dynamic obstacles are randomly distributed), used to verify the efficiency of path planning;

[0152] Scenario 2: Highly dynamic sparse environment ( =0.8 (with one dynamic obstacle on the only path), used to verify obstacle avoidance performance;

[0153] This invention is compared with the A* algorithm and the RRT algorithm. Figure 2 The trajectories of the three methods are compared in scenario 1. From Figure 1As can be seen, the algorithm of this invention relies on critical state control and dynamic weight switching, ensuring that the overall trajectory closely follows the reference trajectory (deviation ≤0.3m at curves). When facing dynamic obstacles, it only needs to make a small detour before quickly returning to the starting point, perfectly balancing tracking stability and obstacle avoidance flexibility. Traditional algorithms, due to fixed weights, have smooth trajectories in open sections but abrupt changes near obstacles (peak deviation reaching 1.2m), and their response to dynamic obstacles is lagging. Pure chaotic algorithms, on the other hand, completely deviate from the reference trajectory, exhibiting irregular fluctuations. Although they are "flexible" in avoiding static obstacles, the continuous divergence of disturbances exacerbates the fluctuations in dynamic obstacle scenarios, even leading to secondary collisions.

[0154] Figure 3 The Lyapunov exponential transformation of the present invention is demonstrated in scenario 1. Figure 3 The curve shows the dynamic evolution of the maximum Lyapunov exponent, mapping the adaptive switching of the system from "stable" to "critical" to "chaotic": the initial stage From the strongly stable region ( (≈-0.5) Rapidly jumps to 0, initiating critical state control; fluctuation period It oscillates around 0, through the environmental sparsity factor. Adjusting bifurcation parameters to maintain a "stable-chaotic" balance; plateau period Brief negative convergence, relying on the Routh-Hurwitz criterion to deal with static dense obstacles or trajectory correction; peak period Suddenly ascended to the Chaos Domain ( ≈0.2), rapid obstacle avoidance in response to dynamic obstacles; recovery phase By falling back to the critical state and using Lyapunov exponential feedback to rebuild the balance between tracking and obstacle avoidance, and through Jacobi matrix iteration and dynamic weight adjustment throughout the process, a robust breakthrough in navigation in large sparse environments is achieved.

[0155] Figure 4 Obstacle avoidance weights were demonstrated in scenario 1. Numerical transformation. Using a critical weight of 0.42 as the control benchmark: In the initial stage, the system operates in a high-sparseness, open environment (…). (Big) below, Maintain a low level (≈0.405) to prioritize tracking stability; between 20 and 40 seconds, as the static obstacle approaches ( reduce), Gradually ascending, the equations are adjusted through bifurcation parameters to respond to environmental changes; entering a long, open section in 80–110 seconds. It fell back to a low-level platform, relying on critical state control ( ≈0) Weaken obstacle avoidance priority; after 110 seconds, dynamic obstacles rapidly intrude ( <0), The trajectory first drops sharply (with brief trajectory correction) then rises sharply, utilizing chaotic properties to achieve rapid obstacle avoidance, ultimately returning to the vicinity of the critical weight. The entire process utilizes environmental sparsity factors. The Lyapunov exponential feedback and bifurcation parameters work together to achieve a smooth switch between "tracking-dominated" and "obstacle avoidance-enhanced" obstacle avoidance weights, supporting navigation robustness in critical states.

[0156] Figure 5 The multi-target access efficiency of three methods is demonstrated in Scenario 1. It is evident that, relying on critical state control, this invention achieves target breakthrough first in each stage (e.g., the initial target access time is the shortest, and subsequent stair ascents are more agile); the A* algorithm is hampered by redundant calculations of the "globally optimal path," and the RRT algorithm suffers from a persistently lagging target access rhythm due to the blindness of random sampling. The essence lies in this invention's real-time perception of environmental disturbances and dynamic adjustment of obstacle avoidance weights using the Lyapunov exponent and bifurcation parameters, significantly compressing the iteration time of path planning and achieving "efficient multi-target traversal" in stable navigation, directly demonstrating the performance gain of critical state optimization for complex tasks.

[0157] Figure 6 and Figure 7 The total time and total path length of the three methods in Scenario 1 are compared respectively. Compared with the method of this invention, the total time and total path length of the A* algorithm and the RRT algorithm are: Figure 6 In this study, the method of this invention has a significantly shorter time consumption than the A* and RRT algorithms, and the path length is close to that of A* (globally optimal planning), but far superior to RRT (random trees easily generate detours). The two methods work together to verify that critical state optimization compresses planning time through dynamic weight switching and ensures efficient trajectory selection through stable path filtering, achieving a dual breakthrough in "navigation efficiency and path accuracy".

[0158] Figure 8 Presenting a comparison of the trajectories of the three methods in scenario 2, from... Figure 8 As can be seen, this invention smoothly bypasses dense static obstacles. When encountering high-speed dynamic obstacles, it quickly adjusts the obstacle avoidance weights using bifurcation parameters, and the trajectory only changes direction slightly to connect with target G0. Subsequently, it coherently approaches G1 to G3 along the critical stable trajectory, resulting in natural multi-target connection. In contrast, the A* algorithm, due to the rigidity of global grid planning, exhibits abrupt changes in obstacle avoidance trajectory (such as sharp turns before G0 and abrupt turns near G1), and its response to high-speed dynamic obstacles is lagging (the trajectory correction near dynamic obstacles is not timely). The RRT algorithm is constrained by random sampling characteristics, resulting in drastic trajectory fluctuations, high redundancy (exaggerated bypassing behavior before G0, and large path bypass distance after G1), and low efficiency in multi-target connection.

[0159] Figure 9 The Lyapunov exponential transformation of the present invention is demonstrated in scenario 2. In the initial stage, the system starts from a deeper stability region (…). (≈-0.5) Rapid ascent; due to the higher obstacle density in scenario 2, critical state control requires more agile breakthroughs of strong stability constraints; 10–50 seconds. It surged to 0.4 (far exceeding the peak fluctuation of Scenario 1), corresponding to high-speed dynamic obstacles ( (Larger) triggers strong chaotic obstacle avoidance, utilizing the perturbation divergence property to quickly evade obstacles; 60–110 seconds. The value drops back to -0.1 and remains on the platform. At this point, the system enters a static obstacle cluster area. The system enhances stability using the Routh-Hurwitz criterion, suppressing chaos to ensure trajectory continuity for multiple targets. After 110 seconds... The second fluctuation to 0.3 corresponds to a second obstacle disturbance (such as another dynamic obstacle entering). The system reactivates the chaotic response, avoids the obstacle, falls back to the weakly stable region, and continues to converge toward the target.

[0160] Figure 10 Obstacle avoidance weights were demonstrated in scenario 2. The numerical transformation. In the initial stage, due to the higher basic obstacle density in Scene 2 ( (lower) The starting point (≈0.405) already implicitly adapts to the rule that "obstacle avoidance has a higher priority than scenario 1"; 20–40 seconds, high-speed dynamic obstacles ( Rapid intrusion (speed exceeding 2m / s) triggers bifurcation parameter adjustment equations. Rapid ascent and oscillation, leveraging chaotic characteristics to enhance obstacle avoidance response (corresponding to the strong chaotic phase where the Lyapunov exponent surges to 0.4); 60–110 seconds, entering the transition phase between static obstacle clusters and multiple targets (G0–G3). The trajectory returns to a low platform (slightly higher than Scenario 1, due to the still dense static obstacles), and with the negative convergence of the Lyapunov exponent (strong stable state), stable path points are selected through the Routh-Hurwitz criterion to ensure the trajectory is coherent and connected to the target; after 110 seconds, a second dynamic obstacle interference occurs (such as another obstacle cutting in). First, it drops sharply (a short-term trajectory correction strategy to avoid excessive obstacle avoidance that could disrupt multi-target connectivity), then it rises sharply to break through the critical weight of 0.42, activating chaotic obstacle avoidance for rapid response, and then falls back to the vicinity of the critical point to continue adapting to the environment.

[0161] Figure 11 and Figure 12 The comparison of total obstacle avoidance time and total obstacle avoidance path length in Scenario 2 is presented respectively. Figure 11In the scenario 2, the A* algorithm, due to the rigid recalculation characteristic of global grid planning, requires repeated path corrections under dense dynamic interference, resulting in a time consumption of nearly 1000 seconds. Although the RRT algorithm is flexible in random obstacle avoidance, it still consumes more than 150 seconds due to blind sampling when connecting multiple targets. The critical state control of this invention avoids global replanning redundancy and consumes only about 150 seconds, improving efficiency by several times. Figure 12 In the past, the A* algorithm's global optimal planning resulted in the shortest path (≈55 meters), but the time cost was significantly higher. The random tree characteristics of the RRT algorithm led to severe detours, with a path length of ≈175 meters. This invention achieves a balanced optimization of obstacle avoidance efficiency (time consumption) and trajectory economy (path) by smoothly switching obstacle avoidance weights in critical states. This avoids the rigid detours of A* and suppresses the random redundancy of the RRT algorithm, with a path length of ≈155 meters.

[0162] In summary, this invention constructs a dynamic system model that incorporates the sparse characteristics of the environment, calculates the path planning and obstacle avoidance control equations under critical states, and achieves adaptive switching between ordered tracking and chaotic obstacle avoidance, ensuring that the robot can complete navigation and walking efficiently and stably in large sparse environments.

Claims

1. A method for robot navigation suitable for large sparse environments, characterized by: The method comprises the following steps: Step 1, establishing a system evolution equation based on a state vector of the robot and a kinematics equation, fusing an environment sparsity factor in the system evolution equation, and introducing a trajectory tracking weight and an obstacle avoidance weight to construct a dynamic system model; The environment sparsity factor fused in the system evolution equation is expressed as follows: ； wherein, is a robot state vector; is a control input, , is a linear velocity, is an angular velocity; is a nonlinear mapping function; is an environmental sparsity factor, calculated by the following equation: ； wherein is the number of obstacles, is the average area of a single obstacle, is the total area of the environment; Step 2, judging whether the dynamic system model is in a critical state at the edge of stability and chaos by solving a Jacobian matrix and a Lyapunov exponent of the dynamic system model, and reaching a critical stable condition when the maximum Lyapunov exponent is approximately equal to 0; Step 3, designing a path evaluation function based on the critical state to screen stable path points, and dynamically adjusting the obstacle avoidance weight by a bifurcation parameter adjustment control equation to realize adaptive switching of orderly tracking and chaotic obstacle avoidance, and completing robot navigation in a large sparse environment.

2. The method for robot navigation suitable for large sparse environments of claim 1, wherein: In step 1, the state vector of the robot is expressed as: ； wherein represents the robot position coordinates, is the heading angle, is the linear velocity; is the transpose operation; The kinematics equation of the robot is shown as follows: ； wherein and are the position change rates in the x and y directions, respectively; is the heading angle change rate; is the angular velocity; is the linear velocity change rate; The system evolution equation is expressed as follows: ； In the formula, is a control input, ; is a nonlinear mapping function.

3. The method for robot navigation suitable for large sparse environments of claim 1, wherein: The dynamic system model is expressed as follows: ； wherein, and are the introduced trajectory tracking weight and obstacle avoidance weight, respectively, is the acceleration control amount, is the proportional coefficient, is the trajectory deviation, is the distance to the nearest obstacle.

4. The method for robot navigation suitable for large sparse environments of claim 3, wherein: The iterative calculation steps of the Lyapunov exponent include: Step 2.1, selecting a linearly independent initial perturbation vector , consistent with the dimension of the state vector, and the initial perturbation vector is a unit vector; Step 2.2, for each discrete time step , compute Jacobian matrix Effect on perturbation vector: ； the Jacobian matrix satisfies: ； wherein is the simulation step size, is the damping coefficient, is the first linear velocity at the time step, heading angle at the first time step; Step 2.3, QR orthogonal decomposition is performed on the perturbation vector set: ； wherein is an orthogonal matrix, is an upper triangular matrix; Step 2.

4. Update the perturbation vector and accumulate the diagonal elements of the upper triangular matrix , ;​ Step 2.

5. After N time steps, the estimate of the first Lyapunov exponent is ;​​ where the largest Lyapunov exponent is calculated as follows: 。 5. The method for robot navigation suitable for large sparse environments of claim 1, wherein: The path evaluation function is: ， wherein, is the path length, , , is the weight coefficient, is the maximum Lyapunov exponent; the path points are screened by Routh-Hurwitz criterion, when the first column elements of the dynamic system model are positive values, the corresponding path points are stable path points, which are included in the planning path. ； where: is the system damping coefficient, is the environmental sparsity factor, is the linear velocity.

6. The method for robot navigation suitable for large sparse environments of claim 1, wherein: The bifurcation parameter adjustment control equation is: ； In the formula: and are gain adjustment coefficients, respectively, is a critical Lyapunov exponent threshold value, is a maximum Lyapunov exponent, is an obstacle distance change rate.

7. The method for robot navigation suitable for large sparse environments of claim 4, wherein: The dynamic system model is discretized by using the Euler method: ， wherein, is the simulation step size, is the discrete time step; The computation interval of the Jacobian matrix satisfies: wherein, is the initial sampling step size, the environmental sparsity factor The larger the environmental sparsity factor, the longer the computation interval to reduce the computation overhead.

8. The method for robot navigation suitable for large sparse environments of claim 3, wherein, During the chaotic obstacle avoidance process, when a dynamic obstacle is detected, the distance to the nearest obstacle is obtained in real time through sensors. and the rate of change of obstacle distance And based on the current environmental sparsity factor Adjust obstacle avoidance weights When the environmental sparsity factor When it is large, decrease Prioritize ensuring orderly tracking; when the environmental sparsity factor When it is small, increase To improve obstacle avoidance flexibility and avoid collisions with dynamic obstacles.

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