An online flow field estimation path planning method based on bayesian inference

Abstract

This invention discloses an online flow field estimation path planning method based on Bayesian inference, aiming to solve the problem of efficient detection and estimation of unknown flow fields by mobile robots. The method first discretizes the two-dimensional flow field region into a grid and constructs a probabilistic roadmap. In each planning round, a weighted maximum a posteriori (MAP) estimation problem is constructed based on the residuals of velocity measurements and fluid equations to solve for the flow field state and calculate the posterior accuracy matrix. Candidate paths are generated through bundle search and then prospectively expanded using subsequent information gain. After mapping path nodes to a set of proposed measurements, a joint prediction covariance matrix is ​​calculated. Based on a task weight matrix dynamically weighted according to velocity magnitude, a task-weighted posterior uncertainty reduction score is calculated for the candidate paths. The path with the highest score is selected for execution, and new measurements are collected. This process is repeated until a preset termination condition is met. This method integrates physical constraints and prospective search, guiding priority exploration of high-velocity regions and significantly improving the efficiency of online robot perception.

Description

Technical Field

[0001] This invention relates to the fields of robot environmental perception, flow field estimation, and information path planning, specifically to an online flow field estimation and path planning method based on Bayesian inference. Background Technology

[0002] In applications such as indoor ventilation monitoring, pollutant diffusion assessment, wind field monitoring, and ocean current field observation, mobile robots need to collect local velocity measurements under motion budget constraints and estimate the flow field distribution within the area. To improve robot perception efficiency, existing technologies typically combine robot path planning with environmental uncertainty assessment, enabling the robot to prioritize locations with higher information value for measurement.

[0003] Existing robot path planning methods often employ metrics such as Gaussian processes, Bayesian optimization, map entropy, mutual information, or local posterior variance to evaluate candidate measurement locations. While these methods are suitable for general environmental monitoring tasks, in flow field estimation tasks constrained by fluid control equations, local velocity measurements can influence the estimation results of distant nodes through fluid equations, boundary conditions, and regularization terms. Selecting a path solely based on local uncertainties at a single point fails to reflect this physical coupling.

[0004] Furthermore, the ideas of posterior uncertainty reduction in Bayesian inverse problems and optimal experimental design are usually geared towards offline measurement design or sensor placement problems, without considering the feasible paths of mobile robots, online replanning, and task weights of the velocity field. Therefore, a path planning method for online flow field estimation of mobile robots is needed, which can use the posterior accuracy matrix formed by the current Bayesian flow field estimation to comprehensively evaluate candidate paths containing multiple measurement points, and continuously update the estimation and planning results after obtaining new velocity measurements. Summary of the Invention

[0005] The purpose of this invention is to provide an overall score for candidate paths containing multiple measurement points based on the posterior uncertainty obtained from the current Bayesian flow field estimation during the process of mobile robots collecting velocity measurements and estimating the flow field online, so that path selection can simultaneously consider fluid physics coupling and reduce the posterior uncertainty of the task-related velocity field.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A Bayesian inference-based online flow field estimation path planning method is used for mobile robots to collect velocity measurements and select subsequent motion paths within a two-dimensional flow field region. The method includes the following steps:

[0008] S1. The two-dimensional flow field region to be measured is discretized using a mesh generation method to generate a region containing... The physical computational grid of discrete nodes in the flow field; nodes are randomly selected from the discrete nodes in the flow field as the set of road map nodes. And establish a set of connecting edges based on the drivability between the nodes in the road map. Constructing a probabilistic road map ;

[0009] S2, Initialize planning rounds And the initial position of the robot, to obtain the first Speed ​​measurement sets collected before wheel planning , among which when hour, For the initial velocity measurement set;

[0010] S3. Express the state of the flow field to be estimated as follows: ,in, and The respective Two velocity components at discrete nodes in the flow field For the Pressure at discrete nodes in the flow field; based on the velocity measurement set A measurement residual term is constructed, and based on the fluid control equation residual term, boundary condition residual term, and regularization residual term obtained by Picard linearization of the two-dimensional Navier-Stokes equations, a weighted maximum a posteriori estimation problem for the current round is constructed. Using preset residual weight matrices, the weighted measurement residual term, fluid control equation residual term, boundary condition residual term, and regularization residual term are stacked into a linearized residual matrix. and corresponding vector Solving the weighted maximum a posteriori estimation problem yields the current flow field estimate to reflect the actual distribution of the physical flow field, and the linearized residual matrix is ​​used to obtain the estimate. Forming the posterior accuracy matrix ;

[0011] S4, in the probability roadmap In, from the current position node of the mobile robot A candidate path set is generated using beam search. The candidate path set Each candidate path in is denoted as And the total length of each candidate path does not exceed the maximum expansion depth in the beam search. For each of the candidate paths , and include Each path node is mapped to its corresponding discrete flow field node to form a set of pseudo-measurements for evaluating information gain. ;

[0012] S5. For each of the candidate paths... Based on the set of measurements to be measured Construct the observation matrix and positive definite measurement noise covariance matrix And based on the posterior accuracy matrix Calculate the covariance column matrix and joint prediction covariance matrix ;

[0013] S6: Construct the task weight matrix The first two weights correspond to two velocity components, while the weight corresponding to pressure is zero; for each candidate path... According to the formula Calculate the candidate path The task-weighted posterior uncertainty reduction score is used to quantitatively assess the degree of uncertainty reduction in the mobile robot's perception of the global physical flow field after moving along the candidate path.

[0014] S7, in the candidate path set The candidate path with the largest weighted posterior uncertainty reduction score for the task is selected as the chosen candidate path. Execute the selected candidate path The former Step and collect new velocity measurements, among which, To preset the number of execution steps; add the new speed measurement to the speed measurement set. This will form the speed measurement set for the next round of planning. Determine if the preset termination condition is met. If it is, end the path planning and output the final flow field estimation result; otherwise, set... Then, return to step S2 to proceed to the next round of planning. The termination conditions include: the number of planning rounds reaches the preset maximum total number of rounds, or the global uncertainty of the current flow field estimation is lower than a preset threshold.

[0015] Further, in step S5, for each of the candidate paths... The set of measurements to be measured Includes non-repeating Discrete nodes in the flow field:

[0016] The observation matrix According to the corresponding description Two velocity component selection operators for each node The result of vertical stacking is represented as:

[0017]

[0018] The measurement noise covariance matrix The noise covariance matrix corresponding to the two velocity component observations of each node. The resulting block diagonal matrix is ​​represented as:

[0019]

[0020] in, .

[0021] Further, in step S6, the task weight matrix In Based on the current flow field estimate at the... Two velocity components at a discrete node in the flow field and speed magnitude Normalized generation.

[0022] Further, in step S4, the current position node of the mobile robot... A candidate path set is generated using beam search. Specifically, it includes:

[0023] Set beam width parameters Initialize the expansion depth The set of times ;

[0024] At each extended depth For the current set of retention Each candidate path prefix in The adjacent nodes are expanded to generate the extended prefix set for the next depth;

[0025] For each candidate path prefix in the extended prefix set Calculate the corresponding task-weighted posterior uncertainty reduction score. ;

[0026] Combined with subsequent information gain estimation Calculate the candidate path prefix Overall priority score ,in, The subsequent information gain estimation uses preset weighting coefficients. This is the upper bound of the information gain within the remaining extended depth, calculated based on single-point independent observation evaluation.

[0027] Based on the comprehensive priority score Sort the extended prefix set in descending order and retain the first few prefixes. The candidate path prefixes constitute the reserved set for the next depth. ;

[0028] The expansion and retention process described above is executed iteratively until the maximum expansion depth is reached. The paths generated during the search process are included in the candidate path set. .

[0029] Beneficial effects

[0030] This invention uses candidate path scoring directly based on the posterior accuracy matrix formed by the current Bayesian flow field estimation, thus reflecting the physical coupling relationship between velocity measurement, fluid control equations, boundary conditions, and regularization terms.

[0031] This invention employs a task weight matrix that assigns weights to velocity components, thus enabling path scoring to correspond to the reduction of posterior uncertainty in the task-related velocity field, rather than merely the uncertainty of local measurement points.

[0032] This invention employs a rolling execution method, which acquires new velocity measurements and re-estimates the flow field and replans the path after executing a portion of the selected path. Therefore, it enables the mobile robot to continuously adjust subsequent paths using the latest measurement information during online measurement. Attached Figure Description

[0033] Figure 1 This is the overall flowchart of the present invention;

[0034] Figure 2 This is a schematic diagram of path planning for online flow field estimation; Detailed Implementation

[0035] To provide a better understanding of the structural features and effects achieved by the present invention, a detailed description is provided with reference to the accompanying drawings, as follows:

[0036] This embodiment provides an online flow field estimation and path planning method based on Bayesian inference, including the following steps:

[0037] In step S1, the two-dimensional flow field region to be measured is discretized using a mesh generation method to generate a region containing... A physical computational grid of discrete nodes in the flow field. These discrete nodes represent the discrete locations of the flow field state variables; each node corresponds to two velocity components and pressure components to be estimated. A subset of nodes is randomly selected from these discrete nodes to form a roadmap node set. For two roadmap nodes, if the mobile robot can move from one roadmap node to the other without violating motion constraints and environmental drivability constraints, then a connecting edge is established between them, thus forming a set of connecting edges. Constructing a probabilistic road map The probabilistic roadmap is used to limit the feasible range of motion for subsequent candidate paths of the mobile robot.

[0038] In step S2, the planning rounds are initialized. And determine the initial position of the mobile robot. Map the initial position of the mobile robot to the current position node in the probability road graph. Obtain the first... Speed ​​measurement sets collected before wheel planning The velocity measurement set includes the index of the discrete nodes of the measured flow field, and the measured values ​​of the two velocity components at the corresponding locations.

[0039] In step S3, the flow field state to be estimated is represented as:

[0040]

[0041] in, and Each represents the Two velocity components at discrete nodes in the flow field Indicates the Pressure at discrete nodes in the flow field. Based on the first... Speed ​​measurement set before wheel planning The measurement residual term is constructed. For the measured discrete nodes of the flow field, the measurement residual term is used to constrain the state vector. The difference between the two velocity components of the corresponding node and the actual velocity measurement value. The fluid control equation residuals are constructed based on the two-dimensional Navier-Stokes equations, which include momentum equations and continuity constraints. To form a solvable linearized estimation problem in the current iteration, the two-dimensional Navier-Stokes equations are Picard linearized, i.e., the convection velocity term is fixed near the velocity estimation of the current or previous iteration, and the result is obtained with respect to the state vector. The linearized fluid control equation residuals are then constructed. Further, boundary condition residuals are constructed based on the boundary type of the two-dimensional flow field region. These boundary condition residuals constrain the velocity or pressure relationships at the boundary locations. Regularized residuals are constructed based on the stability requirements of the estimation problem to suppress non-physical solutions or excessive oscillations in ill-posed estimation problems. Using preset residual weight matrices, the measurement residuals, fluid control equation residuals, boundary condition residuals, and regularized residuals are weighted, and the weighted residuals are stacked to form the linearized residual matrix for the current round. and corresponding vector Therefore, a weighted maximum a posteriori estimation problem is constructed: to obtain the state vector. ,make and The weighted residuals between them are minimized. Solving the weighted maximum a posteriori estimation problem yields the current flow field estimate reflecting the current actual distribution of the physical flow field, and the a posteriori accuracy matrix is ​​formed from the linearized residual matrix:

[0042]

[0043] The posterior accuracy matrix This is used to represent the locally linearized posterior information formed in the current round under the combined effects of velocity measurement, fluid control equations, boundary conditions, and regularization. In this embodiment, when actually calculating the covariance column matrix, it can be equivalently solved by... It is a linear equation of the coefficient matrix, without requiring explicit formation of a complete inverse matrix.

[0044] In step S4, refer to Figure 1 and combined Figure 2 The illustration is shown in the probability road diagram. In this context, the current position node of the mobile robot is denoted as... .from The process begins by generating a set of candidate paths through a bundle search. Candidate path set Each candidate path in the list is denoted as:

[0045]

[0046] Furthermore, the total length of each candidate path does not exceed the maximum expansion depth in the beam search. For each candidate path , and include Each path node corresponds to its respective discrete flow field node. These discrete flow field nodes form a set of pseudo-measurements used to evaluate information gain. The proposed measurement set represents the set of locations where velocity measurements could be collected if the mobile robot moves along the candidate path.

[0047] In a preferred embodiment, step S4 above, which involves starting from the current position node of the mobile robot... A candidate path set is generated using beam search. The specific process is as follows: Set the beam width parameter and initialize the expansion depth The set of times At each extended depth For the current set of retention Each candidate path prefix in The adjacent nodes are expanded to generate an extended prefix set for the next depth. For each candidate path prefix in the extended prefix set... Calculate the corresponding task-weighted posterior uncertainty reduction score. Combined with subsequent information gain estimation Calculate the candidate path prefix The overall priority score is:

[0048]

[0049] in, For preset weighting coefficients, This is the upper bound of information gain within the remaining extended depth, calculated based on single-point independent observation evaluation. It is based on the comprehensive priority score. Sort the extended prefix set in descending order and retain the first few prefixes. The candidate path prefixes constitute the reserved set for the next depth. The above expansion and retention process is executed iteratively until the preset maximum expansion depth is reached. The paths generated during the search process are then added to the candidate path set. .

[0050] In step S5, for each candidate path Based on the set of measurements to be measured Construct the observation matrix The observation matrix is ​​used to analyze the state vector. Two velocity components corresponding to each discrete node of the flow field in the set to be measured are selected. Simultaneously, the set to be measured is defined as... Construct a positive definite measurement noise covariance matrix , used to represent the measurement noise uncertainty of the velocity value to be measured. According to the first Posterior accuracy matrix of the wheel Calculate candidate paths The corresponding covariance column matrix:

[0051]

[0052] Then, based on the calculated matrices, jointly calculate the prediction covariance matrix:

[0053]

[0054] The joint prediction covariance matrix simultaneously contains the prediction variance and cross covariance of multiple measurement nodes in the set of proposed measurements, and is used to jointly evaluate multiple proposed measurement points on the candidate path.

[0055] In a preferred embodiment, for step S5, if the set to be measured... Includes non-repeating For the nth discrete node of the flow field, for the nth node... For each discrete node in the flow field, a velocity component selection operator is constructed. The observation matrix is ​​obtained by vertically stacking the selection operators for each velocity component, as shown below:

[0056]

[0057] For the For each discrete node in the flow field, a noise covariance matrix corresponding to the two velocity component observations is set. By assembling the noise covariance matrices into a block diagonal matrix, we obtain the measurement noise covariance matrix:

[0058]

[0059] in Through the above construction, the observation matrix and the measurement noise covariance matrix can simultaneously represent the joint observation structure of multiple nodes to be measured on the candidate path.

[0060] In step S6, the task weight matrix is ​​constructed:

[0061]

[0062] The first two sets of weights correspond to the state vectors respectively. The two velocity components in the equation have zero weight corresponding to pressure. For each candidate path... Calculate the candidate path The task-weighted posterior uncertainty reduction score is:

[0063]

[0064] in, This represents the matrix trace operation. The score indicates the result if the candidate path is followed. The collection of velocity measurements at the target location is expected to reduce the posterior uncertainty of the velocity field in the understanding of the global physical flow field.

[0065] In a preferred embodiment, regarding the task weight matrix in step S6 The weights It is based on the current flow field estimate at the 1st Two velocity components at a discrete node in the flow field and The speed is generated by normalizing the speed magnitude, and the formula for calculating the speed magnitude is:

[0066]

[0067] Specifically, the velocity magnitude of each discrete node in the flow field can be divided by the maximum velocity magnitude among all discrete nodes in the current round to obtain a normalized weight within a preset range. This allows for adaptive adjustment of the relative importance of different discrete nodes in the path scoring based on the flow field estimation results of the current round.

[0068] In step S7, in the candidate path set The candidate path with the largest reduction score for task-weighted posterior uncertainty is selected as the candidate path. The mobile robot executes the selected candidate path. The former Step, and collect new velocity measurements during execution, where The preset execution number of steps is used. The new speed measurement is added to the speed measurement set. This will form the speed measurement set for the next round of planning. Determine if the preset termination condition is met. If it is, end the path planning and output the final flow field estimation result; otherwise, set... The robot then returns to step S2 to proceed to the next round of planning. The termination conditions include: the number of planning rounds reaches a preset maximum total number of rounds, or the global uncertainty of the current flow field estimation is lower than a preset threshold. Therefore, after collecting new velocity measurements in each round, the mobile robot can re-estimate the flow field and continuously select the optimal path.

[0069] The specific embodiments described above have detailed the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the present invention is not limited to the above embodiments. 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 Bayesian inference-based online flow field estimation path planning method for a mobile robot to collect velocity measurements and select subsequent motion paths within a two-dimensional flow field region, characterized in that... Includes the following steps: S1. The two-dimensional flow field region to be measured is discretized using a mesh generation method to generate a region containing... The physical computational grid for discrete nodes of the flow field; Randomly select nodes from the discrete nodes of the flow field to form the road map node set. And establish a set of connecting edges based on the drivability between the nodes in the road map. Constructing a probabilistic roadmap ; S2, Initialize planning rounds And the initial position of the robot, to obtain the first Speed ​​measurement sets collected before wheel planning , among which when hour, For the initial velocity measurement set; S3. Express the state of the flow field to be estimated as follows: ,in, and The respective Two velocity components at discrete nodes in the flow field For the Pressure at discrete nodes in the flow field; based on the velocity measurement set A measurement residual term is constructed, and based on the fluid control equation residual term, boundary condition residual term, and regularization residual term obtained by Picard linearization of the two-dimensional Navier-Stokes equations, a weighted maximum a posteriori estimation problem for the current round is constructed. Using preset residual weight matrices, the weighted measurement residual term, fluid control equation residual term, boundary condition residual term, and regularization residual term are stacked into a linearized residual matrix. and corresponding vector Solving the weighted maximum a posteriori estimation problem yields the current flow field estimate to reflect the actual distribution of the physical flow field, and the linearized residual matrix is ​​used to obtain the estimate. Forming the posterior accuracy matrix ; S4, in the probability roadmap In, from the current position node of the mobile robot A candidate path set is generated using beam search. The candidate path set Each candidate path in is denoted as And the total length of each candidate path does not exceed the maximum expansion depth in the beam search. For each of the candidate paths , and include Each path node is mapped to its corresponding discrete flow field node to form a set of pseudo-measurements for evaluating information gain. ; S5. For each of the candidate paths... Based on the set of measurements to be measured Construct the observation matrix and positive definite measurement noise covariance matrix And based on the posterior accuracy matrix Calculate the covariance column matrix and joint prediction covariance matrix ; S6. Construct the task weight matrix The first two weights correspond to two velocity components, while the weight corresponding to pressure is zero; for each candidate path... According to the formula Calculate the candidate path The task-weighted posterior uncertainty reduction score is used to quantitatively assess the degree of uncertainty reduction in the mobile robot's perception of the global physical flow field after moving along the candidate path. S7, in the candidate path set The candidate path with the largest weighted posterior uncertainty reduction score for the task is selected as the chosen candidate path. Execute the selected candidate path The former Step and collect new velocity measurements, among which, To preset the number of execution steps; add the new speed measurement to the speed measurement set. This will form the speed measurement set for the next round of planning. Determine if the preset termination condition is met. If it is, end the path planning and output the final flow field estimation result; otherwise, set... Then return to step S2 to enter the next round of planning; the termination conditions include: the number of planning rounds reaches the preset maximum total number of rounds, or the global uncertainty of the current flow field estimation is lower than the preset threshold.

2. The method according to claim 1, characterized in that, In step S5, for each of the candidate paths The set of measurements to be measured Includes non-repeating Discrete nodes in the flow field: The observation matrix According to the corresponding description Two velocity component selection operators for each node The result of vertical stacking is represented as: ； The measurement noise covariance matrix The noise covariance matrix corresponding to the two velocity component observations of each node. The resulting block diagonal matrix is ​​represented as: ； in, .

3. The method according to claim 1, characterized in that, In step S6, the task weight matrix In Based on the current flow field estimate at the... Two velocity components at a discrete node in the flow field and speed magnitude Normalized generation.

4. The method according to claim 1, characterized in that, In step S4, the current position node of the mobile robot... A candidate path set is generated using beam search. Specifically, it includes: Set beam width parameters Initialize the expansion depth The set of times ; At each extended depth For the current set of retention Each candidate path prefix in The adjacent nodes are expanded to generate the extended prefix set for the next depth; For each candidate path prefix in the extended prefix set Calculate the corresponding task-weighted posterior uncertainty reduction score. ; Combined with subsequent information gain estimation Calculate the candidate path prefix Overall priority score ,in, The subsequent information gain estimation uses preset weighting coefficients. This is the upper bound of the information gain within the remaining extended depth, calculated based on single-point independent observation evaluation. Based on the comprehensive priority score Sort the extended prefix set in descending order and retain the first few prefixes. The candidate path prefixes constitute the reserved set for the next depth. ; The expansion and retention process described above is executed iteratively until the maximum expansion depth is reached. The paths generated during the search process are included in the candidate path set. .

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