Sensor deployment replanning method based on field verification and staged recovery

Abstract

The application relates to a sensor deployment replanning method based on field verification and hierarchical recovery, and belongs to the technical field of robot autonomous deployment wireless sensor network. On the basis of generating a global candidate point ranking table, the reachability of a robot field execution stage, wireless link connectivity and execution stage update information value are verified in the field; when the verification fails, local fine-tuning and local replanning processing are sequentially performed; if the local replanning still fails to pass the verification, or the unified cumulative score evaluation of the accumulated deviation of multiple local recoveries exceeds the preset threshold, then the remaining candidate points are globally and consistently replanned with the deployed points as anchor points. Through the closed-loop structure of the combination of the global candidate point ranking table and the field three-element verification, hierarchical processing according to the recovery space range from small to large, and the gating recognition mechanism of the unified cumulative deviation score to the local deviation, the completion rate is maintained, the recovery calculation cost is reduced, and the cumulative degradation of the network performance is inhibited.

Description

Technical Field

[0001] This invention relates to the field of autonomous robot deployment and wireless sensor network architecture, and particularly to a sensor deployment replanning method based on field verification and hierarchical recovery. It can be used by legged robots such as robot dogs to autonomously deploy temperature sensor nodes, build low-power wide-area wireless (LoRa) sensor networks, and reconstruct regional temperature fields in natural environments with uncertainties, such as forests. It can also be used for other mobile robot platforms in similar uncertain environments for autonomous sensor deployment tasks. Background Technology

[0002] Temperature monitoring in natural environments such as forests is of great significance for early warning of forest fires and ecological environment research. Compared with manually deploying observation nodes, using legged robots such as robotic dogs equipped with temperature sensors to autonomously deploy observation nodes can significantly reduce labor costs, improve deployment efficiency, and reduce the safety risks of personnel entering complex terrain.

[0003] Existing autonomous sensor deployment methods generally adopt the technical route of offline global optimal planning: based on prior maps and terrain information obtained by simultaneous localization and mapping (SLAM) or remote sensing, a global candidate point ranking table is generated in one go by algorithms such as greedy selection, which takes into account the value of observation information, robot accessibility and wireless network connectivity. Then the robot goes to each point according to the table and completes the deployment.

[0004] However, existing technologies generally have the following shortcomings in actual field implementation:

[0005] First, the prior maps and terrain information that the offline global optimal deployment scheme relies on during the generation phase cannot cover uncertainties on site such as newly added obstacles, local ground loosening, terrain prior errors, and wireless link obstruction. This may cause the robot to fail to complete the deployment as originally planned during the actual execution phase because a certain planned deployment point is physically inaccessible, the wireless link is unavailable, or the actual observation information is far less valuable than expected.

[0006] Second, if global planning is re-executed for the entire candidate point pool every time the above failure occurs, although the current global optimal deployment scheme can be obtained, the calculation scope covers all candidate points, the calculation cost is high, and the deployment plan that has not yet been executed will be changed repeatedly, increasing the uncertainty of the deployment process, which is difficult to meet the real-time operation requirements of airborne embedded platforms.

[0007] Third, if only one replacement point is selected near the failure point whenever a failure occurs, although the computational cost is low, the replacement point may not be able to retain the information value contribution of the original planned point to the reconstruction of the target physical field, nor may it be able to maintain the connectivity structure of the original wireless network. Especially when the failure point plays the role of relay in the original network topology, the local cost of multiple replacements will gradually accumulate, causing the overall performance of the observed network to have an imperceptible systematic shift relative to the global optimal solution.

[0008] Fourth, existing technologies typically set independent thresholds for indicators such as coverage, connectivity, and observation effectiveness when determining whether a global replanning is needed, and then use the worst value within the statistical window for judgment. This approach fails to distinguish between the "normal cost of a reasonable large-scale local restoration" and the "systematic cumulative deviation caused by multiple local restorations." It is easy to misjudge the former as the latter and trigger global replanning prematurely, or conversely, fail to detect the real cumulative deviation in time. In addition, existing technologies use the conventional method of explicit inversion of the relevant covariance matrix in ill-conditioned situations such as the approximate collinearity of candidate point sets. This can easily lead to the systematic amplification of numerical errors, affecting the accuracy of physical field reconstruction.

[0009] In summary, existing technologies urgently need an autonomous deployment method that can continuously verify the effectiveness of deployment schemes during the field execution phase, and adaptively select local fine-tuning, local on-demand replanning, or third-level global consistency recovery based on the impact scale of failures. This would maintain the deployment task completion rate while controlling computational costs, avoiding cumulative degradation of observation network performance, and taking into account numerical stability. Summary of the Invention

[0010] The purpose of this invention is to provide a sensor deployment replanning method based on field verification and hierarchical recovery, which solves the problems in the existing technology that offline global deployment schemes cannot cope with field uncertainties, the cost of global recalculation for each failure is too high, the value of observation information and network structure is lost due to nearby replacement, and the global replanning trigger judgment cannot distinguish between normal local costs and systemic cumulative deviations.

[0011] The above-mentioned objective of the present invention is achieved through the following technical solution:

[0012] The sensor deployment replanning method based on field validation and hierarchical recovery includes the following steps:

[0013] Step 1: Global Candidate Point Ranking Generation: Based on the information value, reachability, and wireless multi-hop connectivity of candidate points, select the best one point at a time to generate a global candidate point ranking table.

[0014] Step 2, On-site verification: Go to each planned deployment point in the order of the global candidate point sorting table, and conduct on-site verification of reachability, wireless link connectivity and the value of execution phase update information. The verification is considered successful when all of them pass.

[0015] Step 3, Tiered Recovery: If the verification fails, perform the following three recovery levels in ascending order of the recovery space range:

[0016] Step 3.1, First-level local fine-tuning: Search for candidate landing points within the first preset radius of the planned deployment point's neighborhood and re-verify them;

[0017] Step 3.2, Second-level local replanning: If step 3.1 fails, determine the local search range based on the parameters obtained on site, reselect candidate landing points according to step 1, and re-verify;

[0018] Step 3.3, Third-level Global Consistency Restoration: Based on the proportion of points within the window that have been restored in Step 3.1 or Step 3.2, the local deviation terms consisting of the information value loss ratio, the wireless hop count inflation ratio, and the point offset are gated. Combined with the degree of uncertainty deficiency and the degree of anomaly in the covariance matrix condition number, the unified cumulative deviation score is calculated using the following formula:

[0019]

[0020] In the formula, The percentage of points that have been restored. , , These are the proportion of information value loss, the proportion of wireless hop expansion, and the location offset. The degree of uncertainty, The degree of abnormality of the condition number. , , , , , Preset weights; Step 3.2 Failure or Unified Cumulative Deviation Score If the threshold is exceeded, step 3.3 is triggered, using the verified actual deployment point as the anchor point, and the remaining candidate points are reselected and sorted according to step 1;

[0021] Step 4: Repeat steps 2 and 3 until the actual number of deployment points reaches the predetermined number or the preset task termination condition is met.

[0022] The information value mentioned in step 1 is calculated using the variance reduction of a non-stationary Gaussian process, where the correlation length l(x) of the non-stationary Gaussian process is adaptively determined according to the local terrain complexity ρ(x) of the candidate point's location; the larger ρ(x) is, the shorter l(x) is. The reachability is determined by calculating the reachability domain on the obstacle grid map and combining it with A* path search. The wireless multi-hop connectivity is achieved by using a preset gateway node and selected deployment points as nodes, with a preset communication radius. An undirected graph is constructed based on the edge pre-screening criteria, and the shortest path hop count (hop) from the candidate point to the preset gateway node is calculated after the candidate point is added to the undirected graph. The selection of candidate points also satisfies the requirement that the distance between the candidate points and the set of already selected deployment points is not less than the preset minimum distance. Constraints.

[0023] The accessibility verification in step 2 is performed by executing a path search algorithm on the obstacle map obtained by the robot in real time to determine whether there is a feasible path to the planned deployment point. The wireless link connectivity verification is performed by sending a preset number of probe data packets to a preset gateway node and / or the actual deployment point, obtaining at least one measured link quality indicator among the received signal strength indication, signal-to-noise ratio, or data packet reception success rate, and determining whether it reaches a preset link quality threshold. The distance is used as a pre-screening condition before sending probe data packets, and whether it is within a preset communication radius. The verification of the updated information value in the execution phase is performed by re-estimating at least one of the kernel parameters, local correlation length, observation noise variance, or covariance of the non-stationary Gaussian process using the observation data of the actual deployed sensors. Based on the updated parameters, the ratio of the reduction in the updated variance of the current planned deployment point to the expected information value recorded in the global candidate point ranking table of the current planned deployment point is calculated, and it is determined whether the ratio is not lower than the preset information value ratio threshold η.

[0024] The first preset radius mentioned in step 3.1 is preset based on the robot's mobility and the robotic arm's placement capability. It is used to characterize the maximum range within which the robot can complete a small-scale adjustment of its landing point without needing to perform the local replanning in step 3.2.

[0025] Step 3.2 describes a method for determining the local search range, which includes the following two switchable implementation methods:

[0026] Method 1: Based on the failure reasons of the planned deployment points, the complexity of the local terrain, and the distance to the nearest actual deployment point, output the local search radius at once, and perform a candidate landing point search only within this radius;

[0027] Method 2: Starting from the local search radius determined by the parameters in Method 1, if no verified candidate landing point is found within the current search radius, the search radius is gradually expanded by a preset expansion coefficient β, and the search is restarted. The search continues until the expanded search radius exceeds the preset maximum allowable radius. At that time, the search radius was determined to be... And perform a final search; the operation of determining the local search range is performed by the search range determination module, which adopts preset deterministic rules, including the failure cause of the planned deployment point, the local terrain complexity, the distance to the nearest actually deployed point, and including a first preset radius and a preset maximum allowable radius. Taking a reference boundary, including a preset communication radius, as input, the output suggests a search radius, and limits the local search radius to a first preset radius and a preset maximum allowable radius. Within the defined interval.

[0028] The search range determination module can also employ a learning model or intelligent agent, taking the failure cause of the current planned deployment point, the local terrain complexity, the distance to the nearest actually deployed point, and the reference boundary as input, and outputting the local search radius and confidence level or estimated uncertainty. When the confidence level is not lower than a preset confidence threshold or the estimated uncertainty is not higher than a preset uncertainty threshold, method one is used; otherwise, method two is used. When the currently available computing resources are lower than a preset resource threshold or the task real-time requirements are higher than a preset real-time level, method one is used.

[0029] The unified cumulative deviation score mentioned in step 3.3 is calculated as follows: using the on-site verification and recovery records since the last triggering of step 3.3 as the statistical window, the percentage of points within the window that were recovered in step 3.1 or step 3.2 is calculated. Average information value loss ratio within the window Average wireless hop count inflation rate within the window The normalized value of the average point offset within the window relative to the preset maximum allowable radius. ,Will , , After weighted summation, multiply by The first part is obtained; the degree of deficiency in the reconstruction uncertainty of the physical field independent of the statistical window relative to the expected improvement progress is calculated. And the degree of anomaly in the condition number of the covariance matrix corresponding to the deployment point set. The two weighted values ​​are then added to the first part to obtain a unified cumulative deviation score. After each trigger of step 3.3, the statistics window is reset starting from the current set of fixed anchor points. The remaining candidate point pool selected in step 3.3 excludes actual deployment points that have been used as anchor points, candidate points that have been actually visited by the robot, candidate points that are still within the fault area that the robot can actually perceive, and candidate points within the preset exclusion radius around candidate points that have failed on-site verification due to failure of wireless link connectivity verification or failure of execution phase update information value verification.

[0030] It also includes a tail re-optimization step: after the predetermined number of sensors have been physically deployed, a unified cumulative deviation score is calculated based on the final deployment point set composed of all actual deployment points; if the unified cumulative deviation score exceeds a preset threshold, a predetermined number of end deployment points that have been physically deployed are determined from the final deployment point set, and the robot retrieves the sensors already placed at the end deployment points and removes them from the actual deployment point set and re-includes them in the scope to be replanned; using the remaining actual deployment points that have not been retrieved as fixed anchor points, the same number of alternative deployment points as the preset number are reselected from the remaining candidate point pool, and the robot replaces the retrieved sensors at the alternative deployment points; after the predetermined number of deployment points is reached again, the unified cumulative deviation score is calculated again.

[0031] A preset upper limit is set for the number of times step 3.3 can be triggered in a single deployment task. If the planned deployment point still fails the on-site verification after reaching the preset upper limit, step 3.3 will not be triggered again. Instead, among the candidate points that meet the reachability verification and wireless link connectivity verification, the one with the highest value of the currently searched execution phase update information will be accepted as the final result of the planned deployment point. If there is no candidate point that meets both of the above verifications, the planned deployment point will be marked as a deployment failure and the preset task termination condition will be met. The numerical robust solution step is as follows: In the process of solving the covariance matrix involved in calculating the information value or the unified cumulative deviation score, if the condition number of the covariance matrix is ​​lower than the preset condition number threshold, the linear equation will be used to solve it directly. If it is not lower than the threshold, the covariance matrix will be eigenvalued, and the eigenvalues ​​smaller than the preset proportion of its maximum eigenvalue will be clamped to the lower limit corresponding to the proportion before the inverse operation is performed.

[0032] The robot is a legged robot, wheeled robot, tracked robot, or wheel-leg hybrid robot equipped with at least one target physical quantity sensor and sensor placement mechanism; the target physical quantity field includes the temperature field of the forest environment.

[0033] The beneficial effects of this invention are as follows: the closed-loop structure that combines a global candidate point ranking table with on-site three-element verification and processes the recovery space range in ascending order (corresponding to the first point below), and the gating recognition mechanism for local deviations based on the unified cumulative deviation score (corresponding to the second point below), are the core features that distinguish this invention from the prior art and solve the on-site replanning problem described in the background art.

[0034] First, by combining a global candidate point ranking table with on-site verification using three key factors, the system retains the advantages of globally optimal planning to the greatest extent while also possessing the ability to cope with on-site uncertainties. Simulation results show that, compared to a fixed scheme without any on-site recovery mechanism (average completion rate 73.43%, root mean square error 1.3907±1.4647), introducing only the first-level local fine-tuning can increase the average completion rate of deployment tasks to 96.95%, and adding the second-level local replanning achieves a completion rate of 100%.

[0035] Second, the third-level global consistency recovery uses a unified cumulative deviation score instead of setting independent thresholds for coverage, connectivity, and observation effectiveness and taking the worst value. This can distinguish between a reasonable large-scale local recovery and the systematic bias caused by the superposition of multiple local recovery processes. Simulation results show that after adding the third-level global consistency recovery, the mean and standard deviation of the root mean square error of the temperature field reconstruction are narrowed to 0.8367 and 0.1255, respectively, which are significantly better than 1.8519 and 5.6047 when only the first two levels of recovery are used.

[0036] Third, the second-level local replanning adopts a method where the search range is determined by the search range determination module according to the on-site context. It defaults to using deterministic doubling and upper limit clamping rules, and can optionally employ a learning model or an intelligent agent, avoiding the need to pre-calculate complete backup solutions for all candidate points. The main simulation experiment in this embodiment uses the aforementioned deterministic rules. Statistics show that the global candidate point pool contains an average of approximately 997 candidate points, while the second-level local replanning actually only evaluates an average of approximately 218.1 candidate points on-site, which is about 21.87% of the global candidate size. This significantly reduces computational resource consumption while maintaining the completion rate.

[0037] Fourth, the second-level local replanning provides two switchable implementation methods: one-time bounding and starting point expansion, covering application scenarios where deterministic rules, learning models, or agents determine the search range individually or in combination. Simulation results show that when the scope of the fault impact expands, the starting point expansion method is less likely to prematurely transfer the problem to the third-level global consistency recovery process compared to the one-time bounding method, providing a more robust and configurable solution for actual deployment.

[0038] Fifth, the third-level global consistency recovery uses the deployed points as fixed anchor points during the deployment task execution process, and usually only replans the remaining candidate points that have not yet been deployed; when it is found that the final cumulative deviation exceeds the preset threshold after all sensors have been physically deployed, the tail re-optimization is used to retrieve and redeploy a preset number of end sensors, without redeploying all sensors, thereby limiting the rework scope to the tail of the deployment sequence.

[0039] Sixth, by introducing the anomaly of the covariance matrix condition number as an independent component of the unified cumulative bias score, and replacing explicit matrix inversion with a robust solution method using eigenvalue clamping when the condition number exceeds a preset threshold, the numerical error amplification caused by ill-conditioned scenarios such as near-collinear deployment points is effectively avoided. Simulation examples show that in ill-conditioned scenarios where deployment points are near-collinear, the reconstruction error can converge from tens or even higher orders of magnitude to an order of magnitude comparable to that in normal scenarios.

[0040] Seventh, in stress test scenarios where multiple known physical obstruction faults exist simultaneously in the same deployment task, the third-level global consistency recovery usually only needs to be triggered once to avoid all known physical obstruction areas during the candidate point selection stage, achieving a completion rate of 100%. This indicates that the mechanism has strong structural resistance to cascading failures caused by physical obstruction. Further verification for cascading failure scenarios caused by non-physical soft faults such as progressive degradation of wireless links shows that the trigger limit protection mechanism is more likely to be fully utilized in practice under these scenarios. In some random environments, the completion rate may be lower than 100%. After introducing the candidate point exclusion method, the completion rate recovers to 100%, and the standard deviation of the reconstruction root mean square error narrows simultaneously. For detailed data, please refer to the effect experiment data section. Attached Figure Description

[0041] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate the invention and are used to explain it, but do not constitute an undue limitation of the invention.

[0042] Figure 1 The diagram shows the overall system architecture and hierarchical dynamic replanning closed loop of the present invention, illustrating the data flow relationship between the global coarse planning module, robot on-site execution and three-element verification, hierarchical recovery module (first level / second level / third level) and target physical field reconstruction;

[0043] Figure 2 The flowchart of the hierarchical recovery decision-making process of this invention shows the judgment logic of step-by-step upgrade from the failure of on-site verification at the planned deployment point to the first level of local fine-tuning, the second level of local replanning (including two switchable implementation methods: one-time delimitation and starting point expansion), and the third level of global consistency recovery.

[0044] Figure 3This is a comparison chart of the average completion rate of the present invention under four combinations of recovery levels;

[0045] Figure 4 This is a comparison chart of the mean and standard deviation of the root mean square error of the target physical quantity field reconstruction under four combinations of recovery levels in this invention (logarithmic coordinates on the vertical axis).

[0046] Figure 5 This is a comparison chart (vertical axis is logarithmic) of the root mean square error of the target physical quantity field reconstruction before and after introducing numerical robust solution in ill-conditioned scenarios such as near collinearity of deployment point locations. Detailed Implementation

[0047] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] See Figures 1 to 5 As shown, the sensor deployment replanning method based on field verification and hierarchical recovery of this invention addresses the problems of offline global deployment schemes being unable to cope with field obstacles, terrain errors, and wireless link changes, while successive global recalculation is costly and successive local replacement erodes information value and network structure. This invention, based on generating a global candidate point ranking table, performs field verification on the reachability, wireless link connectivity, and updated information value of the robot during the execution phase. If verification fails, local fine-tuning and local replanning are performed sequentially. If local replanning still fails verification, or if the cumulative deviation of multiple local recovery attempts exceeds a preset threshold after unified cumulative score evaluation, then global consistency replanning is performed on the remaining candidate points using the deployed points as anchors. This invention maintains the completion rate while reducing recovery calculation costs and suppressing cumulative network performance degradation, and can be used for robots such as robot dogs to autonomously deploy sensors in uncertain environments such as forests. The method of this invention includes the following steps:

[0049] Step 1: Global candidate point sorting and generation:

[0050] In the global candidate deployment point pool, the information value of each candidate point for the reconstruction of the target physical field, the robot's accessibility to the candidate point, and the wireless multi-hop networking connectivity of the candidate point relative to the set of selected deployment points are considered. The best candidate points are selected one by one according to the predetermined number of deployment points to generate a global candidate point ranking table.

[0051] The non-stationary Gaussian process uses the following non-stationary covariance kernel function:

[0052]

[0053] In the formula, x and x′ represent any two spatial locations within the region. For signal variance, The relevant length at location x is determined by the local terrain complexity ρ(x) at that location: The maximum relevance length is preset, and γ is the preset complexity sensitivity coefficient. The larger ρ(x) is (the more complex the terrain), the shorter l(x) will be.

[0054] Given a set of selected deployment points and observation noise variance Candidate points The posterior variance of a nonstationary Gaussian process under set S is:

[0055]

[0056] In the formula, Let S be the n×n covariance matrix calculated pairwise using the kernel function described above. Candidate points The covariance vector between points in S and the covariance vector between them. Candidate points. The informational value of reconstructing the target physical field is defined as the value of the data at the set of actually deployed points. Under the condition that candidate points bring about the integrated reduction in the observation variance of each point in the evaluation grid ( For the global evaluation of the grid point set, Evaluation point under this condition With candidate points The difference between the covariance of the candidate points themselves and the variance of the observation noise, rather than the difference between the posterior variance of the candidate points themselves and the variance of the observation noise.

[0057]

[0058] The global coarse planning module selects the candidate point with the highest information value among those that satisfy the minimum spacing constraint and the wireless multi-hop connectivity constraint at each step.

[0059]

[0060] in, To preset the minimum spacing, hop( ), The definition is given in the formulas related to wireless multi-hop connectivity below.

[0061] Reachability is determined using a graph search method: the obstacle grid map is modeled as a graph G = (V, E), where nodes are unobstructed grids, and adjacent unobstructed grids are connected by edges; the reachability indicator function for candidate point x is: If a path exists in G from the robot's current position x0 to x; otherwise

[0062] The path search uses the A* algorithm, whose evaluation function is:

[0063]

[0064] In the formula, g(n) is the known actual cost from the starting point x0 to node n, and h(n) is the heuristically estimated cost from node n to the target point x. The A* algorithm expands along the node with the smallest f(n) until the target point is reached (reachable) or the search space is exhausted and the target point is not reached (unreachable).

[0065] Wireless multi-hop network connectivity is determined using graph theory methods: based on the current set of deployment points. With preset gateway node Let be nodes, any two nodes , Between if and only if When there are connected edges (with a preset communication radius), an undirected graph is formed. Candidate points join in Then to the preset gateway node The shortest path hop count is:

[0066]

[0067] The path with the fewest edges can be found using breadth-first search (BFS). To preset the maximum allowed number of jumps, hop( ) ≤ And hop ( When ) is a finite value, candidate points are determined. Satisfy wireless multi-hop connectivity constraints.

[0068] Step 2: On-site verification:

[0069] The robot proceeds to each planned deployment point in turn according to the deployment order of the candidate point ranking list, and verifies the accessibility, wireless link connectivity and the value of the update information during the execution phase on-site.

[0070] The three on-site verifications are determined according to the following formulas. The calculation methods for reachability and hop count are the same as in step one above, except that the prior map and candidate point ranking table are replaced with the actual obstacle map and the set of actually deployed points obtained by the robot in real time: If and only if in the actual obstacle map corresponding to the map There exists a feasible path from the robot's current position to x (determined by the A* algorithm).

[0071] In wireless link connectivity verification, a robot or the node to be deployed sends a preset number of probe data packets to a preset gateway node and / or an already deployed point; when the received signal strength indication, signal-to-noise ratio, or data packet reception success rate of at least one link reaches the corresponding preset link quality threshold, the connection is established. ,otherwise Distance not exceeding a preset communication radius is used as a pre-screening condition before link detection; when connected, the distance is calculated according to the hop(·) formula. .

[0072] The value of updated information during the execution phase is verified by calculating the ratio of the reduction in update variance to the expected value of the information.

[0073]

[0074] In the formula, This is the set of points that have been actually deployed. The posterior variance is calculated according to the formula described in step one; during the execution phase, at least one of the kernel parameters, local correlation length, observation noise variance, or covariance of the non-stationary Gaussian process is re-estimated using the observation data of the actually deployed sensors, and the posterior variance and the reduction in updated variance are calculated with the updated parameters. This represents the estimated information value recorded for that point in the candidate point ranking table. When , ,and ( When the preset information value ratio threshold is met simultaneously, it is determined that all three on-site verifications at the deployment point of the plan have passed.

[0075] Step 3: Graded Recovery

[0076] If the verification fails, multiple recovery levels are executed sequentially in ascending order of the recovery space range. This implementation method includes the following three levels:

[0077] Level 1 local fine-tuning: absorbs point failures at low cost within the first preset radius of the planned point's neighborhood;

[0078] The second-level local replanning: The search range determination module determines the local search range based on the cause of failure, the complexity of the local terrain, and the distance to the nearest deployed points. The module can use deterministic rules by default (including two switchable implementation methods: one-time boundary and starting point expansion), and can optionally use a learning model or an intelligent agent, and re-execute point selection optimization as needed within this range;

[0079] Level 3 Global Consistency Recovery: When candidate points fail to pass verification in Level 2 local replanning, or when the unified cumulative deviation score exceeds the preset threshold, the remaining candidate points are replanned globally with the deployed points as anchor points.

[0080] In Method 2, the radius used in the k-th search is determined step by step using the following formula:

[0081] = Suggested search radius output by the search range determination module; = min(β · , k = 0, 1, 2, …

[0082] In the formula, β is the preset expansion coefficient. The preset maximum allowable radius; when Obtained from clamp If no verified candidate landing point is found within this radius, the recovery at this level is deemed unsuccessful.

[0083] When using a learning model or agent, the uncertainty of its output proposed radius estimate can be converted into a confidence level using the following formula:

[0084]

[0085] In the formula, û0 is a preset normalization constant. The larger û is, the lower the conf. Method 1 is used when conf is not lower than the preset confidence threshold; otherwise, Method 2 is preferred. This calculation relationship is optional and does not restrict the use of other monotonically reflecting confidence definitions of estimation uncertainty.

[0086]

[0087] In the formula, The percentage of points within the window that have been restored by the first or second level; This represents the average percentage of information value lost within the window. The inflation rate of the average number of wireless hops within the window; This is the normalized value of the average point offset within the window; This refers to the degree of lack of improvement in the uncertainty of physical field reconstruction relative to the expected progress under the current deployment point set; The degree of anomaly in the condition number of the covariance matrix; , , , , , These are preset weights. It can be seen that... , , The contributions of the three factors to the cumulative bias are Gating – If the proportion of recent recovery points is very low, even if the cost of a single recovery is high, it will not affect the recovery rate. This significantly increases the risk of misjudging a "reasonable large-scale local recovery" as a systematic bias; and and Unaffected Gating, because both characterize whether the global state itself is abnormal, regardless of the number of recovery attempts.

[0088] The specific calculation formulas for each of the above components are as follows: Let This is the set of planned deployment points processed since the last triggering of Level 3 global consistency recovery. For the set of points that have been recovered by the first or second level:

[0089]

[0090] right Let the final information value, hop count, and landing point offset after processing be recorded as follows: , Δ(w), the corresponding original planned value is , :

[0091]

[0092]

[0093]

[0094] (The Σ in the above three formulas are all correct) (Summation) The degree of deficiency in the physical field reconstruction uncertainty relative to the expected improvement progress under the current deployment point set and the degree of anomaly in the condition number are independent of the statistical window and can be calculated at any time: Let the global evaluation grid point set be... , For deployment point set Evaluation grid under conditions The mean of the posterior variance of a nonstationary Gaussian process; The global candidate point ranking generation steps sequentially select the top... The mean value corresponding to each candidate point is pre-calculated in this step and constitutes the expected variance improvement trajectory. After each trigger of the third-level global consistency recovery, the expected variance improvement trajectory is recalculated and reset based on the remaining candidate points after reselection and sorting, starting from the current fixed anchor point set. The mean posterior variance of the corresponding trajectory starting point; The number of planned deployment points processed since the last triggering of Level 3 global consistency recovery:

[0095]

[0096] set up Let S be the noisy covariance matrix corresponding to the currently deployed point set S. The noisy covariance matrix is ​​obtained by adding the kernel covariance matrix to the diagonal terms of the observation noise variance. ) is its condition number; Here, s represents the preset health condition reference value, and s is the preset logarithmic scaling factor. The upper limit of the number of preset conditions is given; in the following formula, log represents the logarithm to the base 10:

[0097]

[0098]

[0099] Regarding the weights of each item in the unified cumulative deviation score ( , , , , , The determination of the trigger threshold: A set of weights can be pre-set based on the dimensions, value ranges, and impact on deployment performance of each deviation component. Then, two types of test scenarios with opposite trigger semantics are selected as threshold calibration scenarios—the first type is a scenario where a reasonable large-scale local recovery occurs, which should not trigger a third-level global consistency recovery in principle; the second type is a scenario where multiple local recovery events overlap and form a systematic deviation, which should trigger a third-level global consistency recovery in principle. The unified cumulative deviation scores corresponding to the two types of test scenarios are obtained under multiple random environments, and candidate trigger thresholds are scanned. Based on the false positive rate, true positive rate, and Youden index corresponding to the candidate thresholds, the trigger threshold is determined according to the principle of a larger Youden index and a lower false positive rate. The specific values ​​of the above weights and trigger thresholds are illustrated in the exemplary settings in the detailed implementation section below, and do not constitute a limitation on the scope of protection of this invention. In other robot platforms, wireless communication conditions, or field environments, the same threshold scanning method can be used to redetermine the trigger threshold, and the weights can be further adjusted through grid search, random search, Bayesian optimization, or on-site calibration.

[0100] The method also includes a numerically robust solution step: in the process of solving the covariance matrix involved in the calculation of information value and unified cumulative deviation score, when the condition number is lower than the preset threshold, the linear equation is directly solved; when the condition number is not lower than the preset threshold, the robust solution method of eigenvalue clamping and then inversion is used to avoid the numerical error being systematically amplified due to ill-conditioned matrix solution.

[0101] The specific formulas for the two solution methods mentioned above are as follows: When the condition number is lower than a preset threshold, a linear equation is used for direct solution; for a symmetric positive definite covariance matrix, Cholesky decomposition can be used.

[0102]

[0103] Solve in sequence and ,get The inverse of the matrix is ​​not explicitly calculated throughout the process; when the condition number is not lower than a preset threshold, eigenvalue decomposition of the covariance matrix is ​​performed.

[0104]

[0105] Clamp eigenvalues ​​smaller than a preset proportion of the maximum eigenvalue:

[0106]

[0107] Construct a robust inverse matrix using the clamped eigenvalues, and solve for it:

[0108]

[0109] Example:

[0110] Overall process of autonomous deployment of forest ambient temperature sensors:

[0111] This embodiment uses a quadruped robot dog autonomously deploying 15 temperature sensor nodes in a forest environment of approximately 50 meters × 50 meters with a grid resolution of 0.5 meters as an example, combined with... Figure 1 , Figure 2 The specific implementation of each step of the present invention is explained.

[0112] Step 1: Global candidate point sorting and generation:

[0113] The robot obtains an obstacle grid map of the forest area beforehand using SLAM or remote sensing priors, and calculates its reachability domain based on this map. Simultaneously, it calculates the spatial variation of terrain complexity based on the local density of obstacle distribution, mapping it to the correlation length of a non-stationary Gaussian process—the more complex the terrain and the denser the obstacles, the shorter the correlation length, indicating a smaller spatial correlation range for observing target physical quantities within that area. The obstacle grid is sampled at a fixed step size, and grid points that are obstacle-free and reachable by the robot are retained to form a global candidate point pool (approximately 997 candidate points in this embodiment).

[0114] The statistical method for determining the size of the candidate point pool is as follows: In 20 random forest environments (different random seeds correspond to different obstacle distributions and terrain complexities) consistent with the experimental data, a 50m × 50m area is sampled at a grid resolution of 0.5m, and grid points that simultaneously satisfy the constraints of unobstructed occupancy and robot reachability are retained. The number of candidate points in each random environment is obtained and then averaged, which is the statistical result of approximately 997 candidate points in this embodiment. The specific size of the candidate point pool varies with the distribution of environmental obstacles, the area of ​​the region, and the grid resolution. 997 is only an exemplary statistical value under the simulation settings of this embodiment and is not intended to limit the scope of protection of this invention.

[0115] The global coarse planning module greedily selects the best candidate point from the pool: at each step, among the candidate points that satisfy the minimum distance constraint with the selected deployment points (3 meters in this embodiment) and the wireless multi-hop connectivity with the set of selected deployment points that satisfies the preset communication radius (10 meters in this embodiment), the module selects the candidate point that maximizes the reduction of the posterior variance of the non-stationary Gaussian process, until the predetermined number of deployment points (15 in this embodiment) is selected, and a global candidate point ranking table containing the deployment order, expected information value and expected number of wireless hops is obtained.

[0116] For the specific calculation formulas of information value, accessibility and wireless multi-hop connectivity in step one, please refer to the previous technical solution section; the preset minimum spacing is 3 meters in this embodiment, and the cost h(n) estimated by the A* algorithm is Euclidean distance in this embodiment.

[0117] Step 2: On-site verification:

[0118] The robot plans its path on the real-time obstacle map obtained by its real-time perception according to the candidate point ranking list and proceeds to each planned deployment point. Before and / or during the movement, it determines whether it can reach the preset deployment operation area of ​​the planned deployment point based on the real-time obstacle map obtained by its real-time perception, and obtains the accessibility verification result. Upon reaching the pre-deployment area, the following verifications are performed sequentially: (i) Wireless link connectivity—The robot or the node to be deployed sends a pre-set number of probe data packets to the pre-set gateway node and / or the already deployed point to obtain at least one measured link quality indicator among Received Signal Strength Indicator (RSSI), Signal-to-Noise Ratio (SNR), or Data Packet Reception Success Rate, and determines whether the indicator reaches the pre-set link quality threshold; the distance criterion is only used as a pre-screening condition before sending probe data packets, and the shortest path hop count from the point to the pre-set gateway node is further calculated when connectivity is achieved; (ii) Execution phase update information value—At least one of the kernel parameters, local correlation length, observation noise variance, or covariance of the non-stationary Gaussian process is re-estimated using the observation data of the already deployed sensors, and the update variance reduction of the point is calculated based on the updated parameters, and compared with the expected information value recorded in the candidate point ranking table to determine whether the ratio is not lower than the pre-set information value ratio threshold (0.5 in this embodiment). When all three verifications are passed, the planned deployment point is determined to have passed verification and confirmed for deployment; otherwise, it enters the hierarchical recovery in order of increasing recovery space range.

[0119] The specific calculation formulas for the three on-site verifications are as follows:

[0120] The specific calculation formulas for the above three on-site verifications are described in the previous technical solution section; the preset information value ratio threshold η is set to 0.5 in this embodiment.

[0121] Step 3: Graded Recovery

[0122] (a) First-level local fine-tuning:

[0123] When a planned deployment point fails verification due to point-like reasons such as loose gravel or local slope, the robot searches for candidate landing points that meet the constraints of accessibility, wireless connectivity, and information value within the first preset radius of the neighborhood of that point (3 meters in this embodiment; this value can be determined based on the mobility of the specific robot platform and the calibration of the robotic arm placement operation parameters, and is not intended to limit the scope of protection of this invention). The robot then searches for candidate landing points that meet the constraints of accessibility, wireless connectivity, and information value, and re-performs on-site verification for the searched candidate points.

[0124] (ii) Second-level local replanning:

[0125] When the first-level local fine-tuning fails to obtain a verified candidate point (e.g., a regional failure caused by fallen trees, terrain collapse, etc., whose impact range exceeds the first preset radius), the failure reason of the planned deployment point, the local terrain complexity of the point (expressed as the correlation length of a non-stationary Gaussian process), and the distance between the point and the nearest actually deployed point are obtained. These three factors, along with the first preset radius, the preset maximum allowable radius (in this embodiment, 1.5 times the preset communication radius, i.e., 15 meters), and the preset communication radius, are input into the search range determination module. In this embodiment, the search range determination module outputs a suggested search radius using preset deterministic rules and limits this suggested search radius to the interval formed by the first preset radius and the preset maximum allowable radius; the learning model or agent is only an optional enhancement implementation method described later.

[0126] As an optional enhanced implementation, the search range determination module can also employ a learning model or intelligent agent, taking the failure reasons of the planned deployment points, local terrain complexity, distance to the nearest actually deployed point, and reference boundary as inputs, and outputting a suggested search radius, and can also output confidence or estimated uncertainty; when the model is unavailable, the call times out, or the output parsing fails, it falls back to the aforementioned deterministic rules. The suggested search radius can be used in the following two ways:

[0127] Method 1 (One-time Boundary): The suggested radius output by the search range determination module is directly used as the final search radius. Within this radius, a candidate point search is performed and the on-site verification is re-executed. If a point is found, the deployment is confirmed. If no point is found, it is determined that the second-level local replanning has failed to restore the planned deployment point.

[0128] Method 2 (Starting Point Expansion): The suggested radius output by the search range determination module is used as the initial search radius. If no verified candidate point is found within this radius, the search radius is expanded step by step according to the preset expansion coefficient (2 times in this embodiment) and the search is repeated. When the expanded radius exceeds the preset maximum allowable radius, the current search radius is clamped to the preset maximum allowable radius and a final search is performed. If no point is found, the recovery at this level is deemed unsuccessful.

[0129] The formula for determining the k-th search radius in Method 2 is described in the previous section on technical solutions; the preset expansion coefficient β is set to 2 in this embodiment.

[0130] The two methods can be flexibly switched according to specific application scenarios: Method 1 has a shorter computation path and is suitable for scenarios where computational overhead is prioritized; Method 2, even when the initial radius given by the search range determination module is too small, still has room to continue expanding the search range, making it more robust and suitable as a safe redundancy mode for the suggested search radius. The two methods are not mutually exclusive within the scope of this invention and can be selected or combined according to the different emphases on computational overhead and recovery success rate based on the deployment task.

[0131] Selection criteria and their experimental verification:

[0132] When the learning model or agent outputs confidence or estimation uncertainty, either method one or method two can be selected accordingly: method one is used when the confidence is not lower than the preset threshold or the estimation uncertainty is not higher than the preset threshold; otherwise, method two is preferred. When computing resources are insufficient or real-time requirements are high, method one is preferred.

[0133] Stress tests were conducted to address the scenario where the suggested search radius is too small. In a 7-meter fault radius scenario, Method 2 triggered the third-level global consistency recovery an average of 0.8333 times, while Method 1 triggered it 1.000 times. In the 10-meter and 13-meter scenarios, the average for both methods was 1.0, but Method 2 was still able to evaluate more local candidate points through extended search. The results indicate that extended search from the starting point can provide redundancy for a small search radius estimate, while one-time bounding has lower deterministic computational overhead.

[0134] (iii) Higher recovery level – Level 3 global consistency recovery in this implementation:

[0135] The system continuously collects statistics on the following data recorded during on-site verification and the aforementioned two-level recovery processes for each planned deployment point since the last triggering of the third-level global consistency recovery: the percentage of recovered points, the average information value loss ratio, the average wireless hop count inflation ratio, the average point offset (normalized relative to the preset maximum allowable radius), and the degree of deficiency in the physical field reconstruction uncertainty relative to the expected improvement progress under the current deployment point set, which can be calculated at any time without relying on the above statistical windows, and the degree of anomaly in the condition number of the covariance matrix corresponding to the actual deployment point set. A unified cumulative deviation score is calculated using the following formula:

[0136] The unified cumulative deviation score calculation formula defined in the aforementioned technical solution section (including) , , , , , and weight , , , , , (Definition), in this embodiment, based on the dimensions, value range, and degree of impact on deployment performance of each deviation component, a set of exemplary weights are pre-set, and... =1.0、 =1.0、 =1.0、 =0.6、 =1.0、 =1.0; According to the aforementioned threshold scanning method, in the two test scenarios selected under this weight, the trigger threshold determined in this embodiment is 0.035. At this time, the false positive rate of the first test scenario (reasonable large-scale local recovery) is 10%, and the true positive rate of the second test scenario (systematic cumulative deviation) is 100%. The above weights and thresholds are exemplary settings in the simulation environment of this embodiment and do not constitute a limitation on the scope of protection of this invention. The preset health condition reference value mentioned in the formula... In this embodiment, the value is 2200; the preset logarithmic scaling factor s is 1.55 in this embodiment; and the preset upper limit of the number of conditional terms is... In this embodiment, 3.0 is used.

[0137] Regarding the boundary cases in the calculation of the unified cumulative deviation score, the following stipulations are made: When the number of planned deployment points processed since the last triggering of the third-level global consistency recovery is less than the preset minimum sample size (3 in this embodiment), the proportion of recovered points, the proportion of average information value loss within the window, the proportion of average wireless hops expansion within the window, and the normalized point offset are all taken as 0. At this time, the unified cumulative deviation score is contributed by the component of the lack of physical quantity field reconstruction uncertainty relative to the expected improvement progress and the component of the abnormality of condition number; when no planned deployment points have been processed since the last trigger, i.e., the statistical window is empty, the proportion of recovered points and the above three window items are all taken as 0. The average quantity within the mouth is also set to 0; when calculating the inflation ratio of the average wireless hop count within the window, the denominator (original planned hop count) is set to be no less than 1 to avoid division by zero caused by the original planned hop count being 0; when calculating the degree of deficiency of the physical field reconstruction uncertainty under the current deployment point set relative to the expected improvement progress, if the improvement amount of the expected variance improvement trajectory in the corresponding interval is not greater than the preset threshold, then this item is set to 0; when calculating the degree of anomaly of the covariance matrix condition number, if the number of actually deployed points is less than 3, then this item is set to 0; if the number of actually deployed points is not less than 3, but the covariance matrix condition number cannot be calculated, is not positive, or is a non-finite value, then this item is set to the preset upper limit value.

[0138] When the second-level local replanning fails to validate the candidate landing points, or When the threshold is exceeded (in this embodiment, the threshold is determined to be 0.035 by scanning two types of test scenarios with opposite semantics), the third level of global consistency recovery is triggered: taking the current set of actually deployed points as fixed anchor points, the actual deployed points that have been used as anchor points, the points that the robot has actually visited, and the candidate points that are still in the fault area actually perceived by the robot are excluded from the remaining candidate point pool (optionally, candidate points within a preset exclusion radius around candidate points that have recently failed verification due to failure of wireless link connectivity verification or failure of verification of value of update information during execution phase are also excluded). The remaining candidate points that have not yet been deployed are reselected and sorted using the same method as the global candidate point sorting generation steps.

[0139] Furthermore, if all sensors at the predetermined deployment points have been physically deployed, but the unified cumulative deviation score calculated based on the final deployment point set still exceeds a preset threshold, it indicates that the cumulative deviation or the ill-conditioned state of the deployment point set may only become fully apparent after all deployments are completed. At this point, since there are no longer any unexecuted planned deployment points, the system initiates tail re-optimization. The robot retrieves the predetermined number of sensors that have been physically deployed and removes their corresponding deployment points from the actual deployment point set, re-forming the same number of deployment slots. Subsequently, using the remaining actual deployment points that were not retrieved as fixed anchor points, alternative deployment points are re-selected from the remaining candidate point pool, and the retrieved sensors are re-placed at these alternative deployment points. In this embodiment, the preset retrieval number is 2, meaning the first 13 actual deployment points are retained as fixed anchor points, and the last 2 deployment points are re-selected and re-placed. After reaching 15 actual deployment points again, the unified cumulative deviation score is calculated again. The system determines whether the final set of deployment points after tail re-optimization meets the preset requirements. The preset number of sensors to be retrieved can be determined based on the robot's ability to recover the placed sensors, the allowable increase in travel distance, and the real-time requirements of the task, and is not limited to two. By retrieving only the preset number of end sensors without redeploying all deployed sensors, the rework scope can be limited to the tail of the deployment sequence.

[0140] In addition, a preset upper limit is set for the number of times the third-level global consistency recovery is triggered in a single deployment task (4 times in this embodiment). If the planned deployment point still fails the on-site verification after reaching the upper limit, no new global consistency recovery will be triggered. Instead, only candidate points that simultaneously meet the reachability verification and wireless link connectivity verification will be selected from the currently searched candidate points, and the one with the highest value of the execution phase update information will be accepted as the final result of the planned deployment point. If there are no candidate points that simultaneously meet the reachability verification and wireless link connectivity verification, the planned deployment point will be marked as a deployment failure and it will be determined that the preset task termination condition is met, so as to ensure that the deployment task is terminated within a limited time.

[0141] Step 4: Numerically Robust Solution

[0142] In the process of calculating information value and solving the covariance matrix involved in unifying the cumulative deviation score, if the matrix condition number is lower than the preset condition number threshold (taken in this embodiment), The linear equation is used to solve the problem directly. If the condition number is not lower than the threshold, the covariance matrix is ​​decomposed into eigenvalues, and the values ​​smaller than the maximum eigenvalue are determined by a preset proportion (in this embodiment, the proportion is taken as...). The eigenvalues ​​of the covariance matrix are clamped to the lower bound corresponding to the ratio before inversion. Compared with the conventional approach of directly inverting the covariance matrix and then multiplying, this method can effectively avoid the systematic amplification of floating-point errors caused by ill-conditioned matrix solutions.

[0143] Repeat steps two through four until the number of actual deployment points reaches the predetermined number of deployment points, or the preset task termination condition is met; when the predetermined number of deployment points is reached, the target physical field of the entire region is reconstructed based on the field observations of all actual deployment points using a non-stationary Gaussian process.

[0144] Explanation of numerical parameters in the embodiments:

[0145] In this embodiment, the minimum spacing (3 meters), preset communication radius (10 meters), number of predetermined deployment points (15), preset information value ratio threshold (0.5), first preset radius (3 meters), preset maximum allowable radius (in this embodiment, it is 1.5 times the preset communication radius, i.e., 15 meters), preset expansion coefficient (2 times), and covariance matrix condition number threshold (…) are mentioned. ), Eigenvalue clamping ratio ( The specific values, such as the upper limit of the number of triggers for the third-level global consistency recovery (4 times) and the number of tail re-optimization points (2), are exemplary settings used to verify the effectiveness of the method of the present invention in the aforementioned simulation environment (approximately 50m × 50m forest area, grid resolution 0.5m), and do not constitute a limitation on the scope of protection of the present invention. In actual engineering deployment, the above values ​​should be recalibrated and determined through field testing or engineering experience based on the specific robot platform (e.g., robotic arm reach, body size and mobility), the measured communication range of the wireless communication module used, the received signal strength indication (RSSI) and packet loss rate, the sensor measurement noise level, and the specific requirements of the on-site task for completion rate and computational overhead; the preset communication radius should not exceed the reliable communication distance of the wireless module under the constraint of the target packet loss rate, the preset maximum allowable radius can be taken as about 1 to 2 times the preset communication radius to balance recovery capability and network connectivity, and the first preset radius should not exceed the maximum working range that the robot body can reach by small-range adjustments in place or the robotic arm end effector. The calibration method for each weight and trigger threshold in the unified cumulative deviation score is described in the corresponding paragraph above, and its values ​​are not intended to limit the scope of protection of this invention.

[0146] Effect experimental data:

[0147] To verify the effectiveness of the method of this invention, 20 random forest environments were used, and 7 types of on-site fault scenarios with clear physical meaning were set in each random forest environment, including point obstacles, regional obstacles, continuous small map errors, key relay point blockage, sudden drop in information value, regional faults within the applicable range of the second-level recovery, and cumulative drift caused by continuous local offsets. Simulations were performed for the combined activation modes of the 4 different levels of recovery mechanisms, and a total of 20×7×4=560 independent deployment task simulations were completed. For each system version in Table 1, the average completion rate and the mean and standard deviation of the root mean square error of reconstruction were calculated based on the results of 140 independent tasks formed by 20 random environments × 7 types of fault scenarios; the typical scenario data in Table 2 were calculated based on the repeated experimental results of 20 random environments under the corresponding scenarios.

[0148] Among them, the root mean square error of reconstruction is calculated according to (k = 1, 2, ..., N) Calculation: N is the total number of grid sampling points in the region used for evaluation, and T is the true value (x k ) represents the true value of the target physical quantity at the k-th evaluation grid point, and T is the reconstructed value of (x). k The RMSE value is the estimated value of the point obtained by reconstructing it using a non-stationary Gaussian process based on the field observations of all actual deployment points. The mean and standard deviation reported in Tables 1, 2 and later are the statistical results of the RMSE index in the corresponding randomized repeated experiments (20, 6 or 4, depending on the specific experimental setup).

[0149]

[0150] As shown in the table above, introducing only the first-level local fine-tuning can improve the completion rate from 73.43% to 96.95%, but due to the lack of mid-to-long-range recovery capability and cumulative bias correction capability, the standard deviation of the reconstruction error is relatively large. After adding the second-level local reprogramming, the completion rate reaches 100%, but outliers still exist due to cumulative bias and numerical ill-conditioned results. After adding the third-level global consistency recovery, the completion rate remains at 100%, while the mean and standard deviation of the root mean square error of reconstruction narrow to 0.8367 and 0.1255, respectively. The comparison of the average completion rate and root mean square error of reconstruction under the above four recovery level combinations can be found in [reference]. Figure 3 and Figure 4 .

[0151] In terms of on-demand computation, the global candidate pool contains an average of about 997 candidate points. When the second-level local replanning is actually triggered, only about 218.1 candidate points are evaluated on-site on average, which is about 21.87% of the global candidate scale. This indicates that the present invention does not require pre-calculating complete backup schemes for all candidate points, but only performs local calculations when there is a real need on-site, which significantly reduces the computational resource overhead.

[0152] Further verification results for typical scenarios are shown in Table 2: In scenarios where the regional fault radius (6 meters) exceeds the first preset radius (3 meters), the completion rate is 87.00% when only the first-level local fine-tuning is used. After adding the second-level local replanning, the completion rate increases to 100%, verifying the necessity of the second-level local replanning for faults beyond the local fine-tuning range. In scenarios where five consecutive local small-range offsets form cumulative drift, the completion rate can reach 100% when only the first-level and second-level recovery are used, but the root mean square error of reconstruction is 0.9194±0.3546. After adding the third-level global consistency recovery, the root mean square error of reconstruction is further reduced to 0.8008±0.0806, verifying the ability of the unified cumulative deviation score to identify and correct cumulative drift.

[0153]

[0154] In the ill-conditioned case of the covariance matrix (where some deployment points in a random forest environment are approximately collinear), without the introduction of the covariance matrix conditional number component, numerical robustness, and tail re-optimization mechanism, the root mean square error (RMSE) of reconstruction reached 45.42 in some scenarios. After introducing the corresponding mechanisms, it narrowed to 0.66. In another test scenario in the same environment, the RMSE of reconstruction narrowed from 17.99 to 0.65, verifying the effectiveness of the numerical robustness and conditional number component in the unified cumulative bias score in step four of this invention. For a comparison of the RMSE of reconstruction before and after introducing numerical robustness in the above ill-conditioned scenarios, see [link to relevant documentation]. Figure 5 .

[0155] In a stress test where six known physical obstruction faults (each with a radius of 3.5 meters, significantly exceeding the maximum number of triggers for Level 3 global consistency recovery in a single deployment task) were injected simultaneously, regardless of whether the Level 2 local replanning used a one-time delimitation method or a starting point expansion method, Level 3 global consistency recovery only required one trigger to complete the deployment task, achieving a 100% completion rate and not triggering the preset trigger limit protection mechanism. This result demonstrates that Level 3 global consistency recovery can simultaneously avoid all known physical obstruction areas in the same replanning process when reselecting candidate points, exhibiting strong structural resistance to cascading failures caused by physical obstruction. This verification currently primarily targets physical obstruction faults. Further verification is provided for cascading failure scenarios caused by non-physical soft faults such as progressive degradation of the wireless link, as follows.

[0156] In a stress test scenario where 16 existing observation sources unknown during the planning phase are scattered throughout the region, potentially causing the update information value to fall short of the standard for almost every planned deployment point (repeated independently in 6 random environments), without enabling the candidate point exclusion method, the trigger limit protection mechanism for the third-level global consistency recovery was fully triggered (4 times) in all 6 random environments, with an average completion rate of 97.78% and a reconstruction root mean square error mean ± standard deviation of 2.6886 ± 3.6306. In one random environment, the completion rate dropped to 86.7% and the reconstruction root mean square error reached 10.06. After introducing the candidate point exclusion method described in claim 7 (excluding candidate points within a preset exclusion radius around candidate points that recently failed verification due to soft reasons), the completion rate of all 6 random environments recovered to 100%, the reconstruction root mean square error mean ± standard deviation narrowed to 1.1447 ± 0.3775, and the average number of times the trigger limit protection mechanism was actually suppressed decreased from 10.5 times to 4.0 times. The above results accurately demonstrate that in soft fault scenarios, the third-level global consistency recovery is more likely to be repeatedly triggered, thus exhausting the preset upper limit. The candidate point exclusion method described in claim 7 can effectively alleviate this problem in most random environments (4 directions are consistent in 6 environments), but it is not consistently effective for every random environment. In one environment, the root mean square error of reconstruction actually increased from 1.189 to 1.348 after enabling the candidate point exclusion method, indicating that a reduction in the number of triggers is not necessarily equivalent to a better final point distribution.

[0157] The method described in this invention is also applicable to other mobile robot platforms equipped with target physical quantity sensors and sensor placement mechanisms, such as bipedal humanoid robots, wheeled robots, tracked robots, and hybrid wheel-leg robots. For different robot platforms, parameters such as the first preset radius and the preset maximum allowable radius can be adjusted to adapt to differences in their mobility and operational capabilities without modifying the logical structure of the graded recovery method itself.

[0158] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. For example, the non-stationary Gaussian process can be replaced with other interpolation or regression models that can characterize spatial correlation; the greedy optimization algorithm used for global candidate point ranking can be replaced with other combined optimization algorithms that satisfy the joint constraints of information value, accessibility, and wireless connectivity; the search range determination module can employ preset deterministic rules, learning models, intelligent agents, or combinations thereof. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sensor deployment replanning method based on field verification and hierarchical recovery, characterized in that: Includes the following steps: Step 1: Global Candidate Point Ranking Generation: Based on the information value, reachability, and wireless multi-hop connectivity of candidate points, select the best one point at a time to generate a global candidate point ranking table. Step 2, On-site verification: Go to each planned deployment point in the order of the global candidate point sorting table, and conduct on-site verification of reachability, wireless link connectivity and the value of execution phase update information. The verification is considered successful when all of them pass. Step 3, Tiered Recovery: If the verification fails, perform the following three recovery levels in ascending order of the recovery space range: Step 3.1, First-level local fine-tuning: Search for candidate landing points within the first preset radius of the planned deployment point's neighborhood and re-verify them; Step 3.2, Second-level local replanning: If step 3.1 fails, determine the local search range based on the parameters obtained on site, reselect candidate landing points according to step 1, and re-verify; Step 3.3, Third-level Global Consistency Restoration: Based on the proportion of points within the window that have been restored in Step 3.1 or Step 3.2, the local deviation terms consisting of the information value loss ratio, the wireless hop count inflation ratio, and the point offset are gated. Combined with the degree of uncertainty deficiency and the degree of anomaly in the covariance matrix condition number, the unified cumulative deviation score is calculated using the following formula: ； In the formula, The percentage of points that have been restored. , , These are the proportion of information value loss, the proportion of wireless hop expansion, and the location offset. The degree of uncertainty, The degree of abnormality of the condition number. , , , , , Preset weights; Step 3.2 Failure or Unified Cumulative Deviation Score If the threshold is exceeded, step 3.3 is triggered, using the verified actual deployment point as the anchor point, and the remaining candidate points are reselected and sorted according to step 1; Step 4: Repeat steps 2 and 3 until the actual number of deployment points reaches the predetermined number or the preset task termination condition is met.

2. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1, characterized in that: The information value mentioned in step 1 is calculated using the variance reduction of a non-stationary Gaussian process, where the correlation length l(x) of the non-stationary Gaussian process is adaptively determined according to the local terrain complexity ρ(x) of the candidate point's location; the larger ρ(x) is, the shorter l(x) is. The reachability is determined by calculating the reachability domain on the obstacle grid map and combining it with A* path search. The wireless multi-hop connectivity is achieved by using a preset gateway node and selected deployment points as nodes, with a preset communication radius. An undirected graph is constructed based on the edge pre-screening criteria, and the shortest path hop count (hop) from the candidate point to the preset gateway node is calculated after the candidate point is added to the undirected graph. The selection of candidate points also satisfies the requirement that the distance between the candidate points and the set of already selected deployment points is not less than the preset minimum distance. Constraints.

3. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1, characterized in that: The accessibility verification in step 2 is performed by executing a path search algorithm on the obstacle map obtained by the robot in real time to determine whether there is a feasible path to the planned deployment point. The wireless link connectivity verification is performed by sending a preset number of probe data packets to a preset gateway node and / or the actual deployment point, obtaining at least one measured link quality indicator among the received signal strength indication, signal-to-noise ratio, or data packet reception success rate, and determining whether it reaches a preset link quality threshold. The distance is used as a pre-screening condition before sending probe data packets, and whether it is within a preset communication radius. The verification of the updated information value in the execution phase is performed by re-estimating at least one of the kernel parameters, local correlation length, observation noise variance, or covariance of the non-stationary Gaussian process using the observation data of the actual deployed sensors. Based on the updated parameters, the ratio of the reduction in the updated variance of the current planned deployment point to the expected information value recorded in the global candidate point ranking table of the current planned deployment point is calculated, and it is determined whether the ratio is not lower than the preset information value ratio threshold η.

4. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1, characterized in that: The first preset radius mentioned in step 3.1 is preset based on the robot's mobility and the robotic arm's placement capability. It is used to characterize the maximum range within which the robot can complete a small-scale adjustment of its landing point without needing to perform the local replanning in step 3.

2.

5. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1, characterized in that: Step 3.2 describes a method for determining the local search range, which includes the following two switchable implementation methods: Method 1: Based on the failure reasons of the planned deployment points, the complexity of the local terrain, and the distance to the nearest actual deployment point, output the local search radius at once, and perform a candidate landing point search only within this radius; Method 2: Starting from the local search radius determined by the parameters in Method 1, if no verified candidate landing point is found within the current search radius, the search radius is gradually expanded by a preset expansion coefficient β, and the search is restarted. The search continues until the expanded search radius exceeds the preset maximum allowable radius. At that time, the search radius was determined to be... And perform a final search; the operation of determining the local search range is performed by the search range determination module, which adopts preset deterministic rules, including the failure cause of the planned deployment point, the local terrain complexity, the distance to the nearest actually deployed point, and including a first preset radius and a preset maximum allowable radius. Taking a reference boundary, including a preset communication radius, as input, the output suggests a search radius, and limits the local search radius to a first preset radius and a preset maximum allowable radius. Within the defined interval.

6. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 5, characterized in that: The search range determination module can also employ a learning model or intelligent agent, taking the failure cause of the current planned deployment point, the local terrain complexity, the distance to the nearest actually deployed point, and the reference boundary as input, and outputting the local search radius and confidence level or estimated uncertainty. When the confidence level is not lower than a preset confidence threshold or the estimated uncertainty is not higher than a preset uncertainty threshold, method one is used; otherwise, method two is used. When the currently available computing resources are lower than a preset resource threshold or the task real-time requirements are higher than a preset real-time level, method one is used.

7. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1, characterized in that: The unified cumulative deviation score mentioned in step 3.3 is calculated as follows: Using the on-site verification and recovery records since the last triggering of step 3.3 as a statistical window, calculate the percentage of points within the window that were recovered by step 3.1 or step 3.

2. Average information value loss ratio within the window Average wireless hop count inflation rate within the window The normalized value of the average point offset within the window relative to the preset maximum allowable radius. ,Will , , After weighted summation, multiply by The first part is obtained; the degree of deficiency in the reconstruction uncertainty of the physical field independent of the statistical window relative to the expected improvement progress is calculated. And the degree of anomaly in the condition number of the covariance matrix corresponding to the deployment point set. The two weighted values ​​are then added to the first part to obtain a unified cumulative deviation score. ; After each trigger of step 3.3, the statistics window is reset with the current set of fixed anchor points as the starting point. The remaining candidate point pool selected in step 3.3 excludes actual deployment points that have been used as anchor points, candidate points that have been actually visited by the robot, candidate points that are still in the fault area that the robot can actually perceive, and candidate points within the preset exclusion radius around candidate points that have failed on-site verification due to failure of wireless link connectivity verification or failure of execution phase update information value verification.

8. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1, characterized in that: It also includes a tail re-optimization step: after the predetermined number of sensors have been physically deployed, a unified cumulative deviation score is calculated based on the final deployment point set composed of all actual deployment points; if the unified cumulative deviation score exceeds a preset threshold, a preset number of end deployment points that have been physically deployed are determined from the final deployment point set, and the robot retrieves the sensors that have been placed at the end deployment points and removes them from the actual deployment point set and re-includes them in the scope to be replanned; Using the remaining actual deployment points that were not retrieved as fixed anchor points, alternative deployment points of the same number as the preset number are selected from the remaining candidate point pool, and the robot repositions the retrieved sensors at the alternative deployment points; after the preset number of deployment points is reached again, the unified cumulative deviation score is calculated again.

9. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 1 or 7, characterized in that: A preset upper limit is set for the number of times step 3.3 can be triggered in a single deployment task. If the planned deployment point still fails the on-site verification after the preset upper limit is reached, step 3.3 will not be triggered again. Instead, the candidate point that meets the reachability verification and wireless link connectivity verification will be selected as the final result of the planned deployment point, based on the highest value of the currently searched execution phase update information. If there is no candidate point that meets both of the above verifications, the planned deployment point will be marked as a deployment failure and the preset task termination condition will be met. And the numerically robust solution steps: In the process of solving the covariance matrix involved in calculating information value or unified cumulative deviation score, if the condition number of the covariance matrix is ​​lower than the preset condition number threshold, the linear equation is used to solve it directly. If it is not lower than the threshold, the covariance matrix is ​​subjected to eigenvalue decomposition, and the eigenvalues ​​smaller than the preset proportion of its largest eigenvalue are clamped to the lower limit corresponding to the proportion before the inverse operation is performed.

10. The sensor deployment replanning method based on field verification and hierarchical recovery according to claim 3, 4, 7, or 8, characterized in that: The robot is a legged robot, wheeled robot, tracked robot, or wheel-leg hybrid robot equipped with at least one target physical quantity sensor and sensor placement mechanism; the target physical quantity field includes the temperature field of the forest environment.

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