Dynamic obstacle avoidance method for mobile robot
By extracting dynamic obstacle features through multimodal perception and a bi-branch Transformer model, and combining obstacle priority scoring for path planning, the robustness of traditional methods in dynamic obstacle detection is solved, thereby improving the navigation safety and efficiency of mobile robots.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ANHUI TECHN COLLEGE OF MECHANICAL & ELECTRICAL ENG
- Filing Date
- 2026-04-02
- Publication Date
- 2026-07-21
AI Technical Summary
Existing obstacle detection methods are not robust enough when facing dynamic obstacles, especially in the case of occlusion, changes in lighting, or multiple overlapping obstacles. They are prone to feature misjudgment or target loss, resulting in low navigation safety and efficiency.
Multimodal perception fusion technology is adopted to collect environmental point clouds and images through LiDAR and binocular cameras, perform spatiotemporal alignment and fusion, use a two-branch Transformer model to extract local details and global temporal features of dynamic obstacles, combine attention gating mechanism to perform feature fusion, and perform path planning and control input based on obstacle priority scoring.
It improves the accuracy and real-time performance of dynamic obstacle detection, enhances the navigation safety and efficiency of mobile robots in complex environments, and avoids the feature loss and decision-making rigidity problems of traditional methods in complex scenarios.
Smart Images
Figure CN122431385A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of autonomous navigation technology, and more specifically, this invention relates to a dynamic obstacle avoidance method for a mobile robot. Background Technology
[0002] Autonomous navigation mobile robots are becoming increasingly widely used, and they have entered communities and some public places. When mobile robots operate in indoor and outdoor scenarios, they mostly first build a map containing static obstacles and then plan their paths based on the map. However, dynamic obstacles may appear during operation. Therefore, accurate detection and real-time obstacle avoidance of dynamic obstacles are the core keys to ensuring their navigation safety.
[0003] Most existing obstacle detection methods are based on traditional computer vision algorithms, such as optical flow or background subtraction. These methods mainly rely on low-dimensional features such as local texture, color, or contour of obstacles for identification. These methods are difficult to capture the motion correlation of dynamic targets in time series. Therefore, when encountering complex situations such as partial occlusion, drastic changes in lighting, or multiple overlapping obstacles, feature misjudgment or target loss are likely to occur, resulting in insufficient robustness. Summary of the Invention
[0004] This invention provides a dynamic obstacle avoidance method for mobile robots, aiming to solve at least one of the above-mentioned problems.
[0005] This invention is implemented as follows: a dynamic obstacle avoidance method for a mobile robot, the method being as follows:
[0006] (1) Collect environmental point cloud and environmental image under the current environment, perform spatiotemporal alignment on the environmental point cloud and environmental image, fuse the environmental point cloud and environmental image into a multimodal environmental representation, and identify dynamic obstacles under the current environment based on the multimodal environmental representation.
[0007] (2) Extract local detail features and global temporal features of dynamic obstacles from the multimodal environmental representation corresponding to dynamic obstacles, respectively, and fuse the local detail features and global temporal features through an attention gating mechanism, and then predict the category and motion state of dynamic obstacles through a multi-task prediction head;
[0008] (3) Take the obstacle in motion as the target obstacle, and perform obstacle avoidance path planning and its corresponding optimal control input based on the target obstacle priority score.
[0009] Furthermore, the process of extracting local detail features of obstacles is as follows:
[0010] Environmental images Divide into N groups of size The image patch is flattened, and the flattened pixels are used to form a pixel feature vector. This pixel feature vector is then linearly projected and positionally encoded to obtain the initial feature embedding. Embed the initial features The L-th layer Transformer encoder is used for feature extraction. The feature corresponding to the [cls] token in the output of the L-th layer Transformer encoder is taken, and after LN normalization, the local detail features are obtained. .
[0011] Furthermore, the global temporal feature extraction process is as follows:
[0012] Extract the obstacle state of the same dynamic obstacle in T consecutive frames to form a temporal input sequence, and process the temporal sequence. Perform linear projection and temporal position encoding to obtain the initial temporal feature embedding. Embed the initial time series features Feature extraction is performed on the L-th layer temporal Transformer encoder. The feature corresponding to the [cls] token in the output of the L-th layer temporal Transformer encoder is taken, and the global temporal feature is obtained after layer normalization. .
[0013] Furthermore, the fusion process of local detail features and global temporal features is as follows:
[0014] Calculate the attention weights for feature fusion, based on the attention weights Perform local detail features With global temporal features The fusion yields fusion characteristics. .
[0015] Furthermore, the target obstacle priority score is obtained as follows:
[0016] The priority score of the target obstacle is calculated based on its category, speed, direction of movement, and relative distance to the robot.
[0017] Based on the acceleration and state prediction uncertainty of the target obstacle, the adjustment factor of the corresponding target obstacle is determined. The corresponding priority base score is adjusted based on the adjustment factor to form the priority score of the corresponding target obstacle.
[0018] Furthermore, the priority base score of the i-th target obstacle The calculation formula is as follows:
[0019] ;
[0020] in, , , , These are the weighting coefficients, and ; This represents the class weight of the i-th target obstacle in the output of the two-branch Transformer model; This represents the estimated speed of the i-th target obstacle. , This represents the estimated three-dimensional velocity of the i-th target obstacle; This indicates the preset upper limit threshold for obstacle speed; This represents the angle between the direction of motion of the i-th target obstacle and the straight line between the robot and the i-th target obstacle; This represents the Euclidean distance between the i-th target obstacle and the robot; This indicates the preset safe distance value.
[0021] Furthermore, the dynamic adjustment factor for the i-th target obstacle. The specific calculation formula is as follows;
[0022] ;
[0023] in, This represents the estimated three-dimensional acceleration of the i-th target obstacle. , This represents the estimated acceleration of the i-th target obstacle. ; This indicates the preset upper limit threshold for dynamic obstacle acceleration; This represents the uncertainty in predicting the motion state of the i-th target obstacle; , This represents the adjustment coefficient.
[0024] Furthermore, the specific optimization objective of model predictive control (MPC) is as follows:
[0025] ;
[0026] in, This represents the robot's operating state at step k, including its three-dimensional position, three-dimensional velocity, and motion direction angle. This represents the reference trajectory state of the robot at step k; This represents the prediction time domain of MPC; This indicates the robot's operating state at step N. This represents the robot's reference trajectory state at step N; , , These are the weight matrices with state error respectively. Control weight matrix Terminal weight matrix The quadratic form; This represents the control input of the robot at step k, which includes three-dimensional acceleration and steering angular velocity. The collision cost weights are represented. ; This represents the predicted state of the i-th target obstacle at step k; This represents the predicted state of the robot at step k. The predicted state of the i-th target obstacle at step k. The cost of detected collisions; Indicates the number of target obstacles.
[0027] Furthermore, the cost of collision as follows:
[0028] ;
[0029] in, Let represent the Euclidean distance between the robot and the i-th target obstacle at step k; Indicates the collision cost threshold. This represents the width coefficient of the Gaussian function.
[0030] This invention extracts the local spatial features and global temporal motion features of dynamic obstacles using a dual-branch Transformer model. Through feature fusion, it achieves accurate prediction of the category and motion state of dynamic obstacles. The prediction results are then used to perform adaptive path planning using a multi-objective priority obstacle avoidance decision model. This effectively improves the problems of poor robustness of feature extraction, rigid decision-making, and insufficient real-time performance of traditional methods in scenarios with occlusion, changes in lighting, and multiple obstacles. This enhances the navigation safety and efficiency of mobile robots in dynamic and complex environments. Attached Figure Description
[0031] Figure 1 A flowchart illustrating the dynamic obstacle avoidance method for a mobile robot provided in an embodiment of the present invention. Detailed Implementation
[0032] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, so as to help those skilled in the art to have a more complete, accurate and in-depth understanding of the inventive concept and technical solution of the present invention.
[0033] Figure 1 This is a flowchart of a dynamic obstacle avoidance method for a mobile robot provided in an embodiment of the present invention. The method includes:
[0034] (1) Collect environmental point cloud and environmental image under the current environment, perform spatiotemporal alignment on the environmental point cloud and environmental image, fuse the environmental point cloud and environmental image to form a multimodal environmental representation, and extract and identify dynamic obstacles in the current environment based on the multimodal environmental representation;
[0035] The mobile robot is equipped with a multimodal perception unit consisting of LiDAR and binocular cameras. This unit collects current multimodal environmental data, preprocesses and fuses the collected data, and constructs a unified multimodal environmental representation. Specifically, this includes:
[0036] Environmental point cloud preprocessing: Voxel grid filtering is used to downsample the environmental point cloud collected by lidar, and a statistical outlier removal algorithm is used to filter out noise points. Finally, Euclidean clustering algorithm is used to extract candidate regions of obstacles to obtain the three-dimensional position information of obstacles.
[0037] Environmental image preprocessing: Stereo matching and depth estimation are performed on the environmental images acquired by the binocular camera to generate a dense depth map. The pixel coordinates are then converted to world coordinates using the camera intrinsic parameters to obtain the visual depth and position information of the obstacles.
[0038] The preprocessed environmental point cloud and environmental image are spatiotemporally synchronized. An extended Kalman filter is used to fuse the environmental point cloud with visual depth information to form a unified multimodal environmental representation. Based on the multimodal environmental representation, dynamic obstacles such as pedestrians, vehicles and other moving objects in the current environment are identified.
[0039] (2) The local detail features and global temporal features of the dynamic obstacle are extracted from the multimodal environmental representation corresponding to the dynamic obstacle by the dual-branch Transformer model. The local detail features and global temporal features are fused by the attention gating mechanism, and then the category and motion state of the dynamic obstacle are predicted by the multi-task prediction head.
[0040] (21) Extraction of local detailed features of dynamic obstacles;
[0041] Based on the View Transformer (ViT) architecture, the environment image in the multimodal environment representation corresponding to dynamic obstacles is integrated. The image is segmented into fixed-size patches, which are then linearly embedded and positionally encoded before being input into a multi-layer Transformer encoder. The mathematical expression for this branch is as follows:
[0042] Input environment image Where H, W, and C represent the environmental images, respectively. Height, width, and number of channels will affect the environmental image. Divide into N groups of size The image patch, in which, The size of the image patch, the total number of image patches , image blocks Add to image patch set middle.
[0043] The image patch is flattened, and the pixels of the flattened patch are used to form a pixel feature vector. The pixel feature vector is then linearly projected and positionally encoded to obtain the initial feature embedding. , means as follows:
[0044] ;
[0045] in, Represents the linear projection matrix. Represents a learnable category vector. This represents vector concatenation; D is the feature dimension. Indicates positional encoding;
[0046] Embed the initial features Feature extraction is performed on the input L-layer Transformer encoder. Each Transformer encoder layer includes a multi-head self-attention mechanism (MHA) and a feedforward network (MLP), and residual connections and layer normalization (LN) are introduced. The process is as follows:
[0047] ;
[0048] ;
[0049] in, , They represent the first , The output of the layer Transformer encoder.
[0050] The features corresponding to the [cls] token in the output of the Lth layer Transformer encoder are extracted, and after layer normalization (LN), local detail features are obtained. Local details It is expressed as follows:
[0051] ;
[0052] in, This represents the feature vector corresponding to the [cls] token in the output of the L-th layer Transformer encoder. The [cls] token is an additional learnable vector added to the ViT input sequence.
[0053] (22) Extraction of global temporal features of dynamic obstacles;
[0054] Extract the obstacle state of the same dynamic obstacle in T consecutive frames to form a temporal input sequence, and process the temporal sequence. Perform linear projection and temporal position encoding to obtain the initial temporal feature embedding. The details are as follows:
[0055] ;
[0056] in, Represents a learnable category vector. Represents the time-series linear projection matrix. It is represented as a timing position code.
[0057] In this embodiment of the invention, the obstacle state in the current t-th frame is: ,in, This represents the three-dimensional position of the obstacle in frame t. The three-axis velocity of the obstacle in frame t is represented by the obstacle state in consecutive frames T, which constitutes the temporal input sequence. ,
[0058] Embed the initial time series features Feature extraction is performed using an L-layer temporal Transformer encoder, with each layer containing a temporal multi-head self-attention mechanism. and temporal feedforward network The process is as follows:
[0059] ;
[0060] ;
[0061] in, , They represent the first , The output of the layer-time Transformer encoder;
[0062] The features corresponding to the [cls] token in the output of the L-th temporal Transformer encoder are extracted and normalized to obtain the global temporal features. Global temporal features Specifically as follows:
[0063] ;
[0064] in, This represents the feature vector corresponding to the [cls] token in the output of the L-th temporal Transformer encoder.
[0065] Using attention gating mechanism to achieve local detail features With global temporal features The adaptive fusion is then used, followed by obstacle category classification and motion state regression via a multi-task prediction head. The specific process is as follows:
[0066] Calculate the attention weights for feature fusion to achieve local detail features. With global temporal features Weighted fusion, attention weight The formula for expressing this is as follows:
[0067] ;
[0068] in, , For learnable parameters, For the Sigmoid function, Representing local detail features With global temporal features splicing.
[0069] Based on attention weights Perform local detail features With global temporal features The fusion yields fusion characteristics. fusion features as follows:
[0070] ;
[0071] Based on fusion features Implement dynamic obstacle category prediction and output the probability distribution of each category. , as shown below;
[0072] ;
[0073] in, , Learnable parameters for classification tasks The preset number of dynamic obstacle categories, Represents the normalization function;
[0074] Based on fusion features Realizing the future motion state of dynamic obstacles Prediction, motion status Includes three-dimensional velocity Three-dimensional acceleration , direction angle of motion , means as follows:
[0075] ;
[0076] in, , This represents the learnable parameters for the regression task. This indicates the predicted motion state of an obstacle.
[0077] We design multiple loss functions to perform end-to-end training of the two-branch Transformer model, with the total loss function being the classification loss. Regression loss Future state prediction loss The weighted sum, the total loss function It is expressed as follows:
[0078] ;
[0079] in, , , For the weighting coefficients, satisfying + + =1.
[0080] In this embodiment of the invention, classification loss Cross-entropy loss is used to measure the difference between the predicted and the true class, and its calculation formula is as follows:
[0081] ;
[0082] in, Category labels for dynamic obstacles, This represents the predicted probability of the i-th type of dynamic obstacle.
[0083] Regression loss The SmoothL1 loss is used to measure the difference between the predicted and actual motion states. The specific calculation formula is as follows:
[0084] ;
[0085] in, The number of obstacle samples. , These represent the actual motion state and the predicted motion state of the i-th obstacle, respectively.
[0086] Future state prediction loss Using L2 norm loss to measure future The difference between the predicted frame motion state and the actual state is calculated using the following formula:
[0087] ;
[0088] in, The number of predicted frames representing the future motion state of a dynamic obstacle. express The actual and predicted motion states of obstacles at all times. For time step, This represents the L2 norm.
[0089] (3) Take the obstacle in motion as the target obstacle, and perform obstacle avoidance path planning and its corresponding optimal control input based on the target obstacle priority score.
[0090] Based on the identified obstacle categories and predicted motion states, a multi-objective priority obstacle avoidance decision model is constructed. First, the priority of each dynamic obstacle is calculated, and then adaptive path planning is implemented based on model predictive control (MPC). Specifically, this includes:
[0091] (31) Calculate the priority score of each target obstacle. The higher the priority score, the greater the navigation threat to the robot. The priority score is determined as follows:
[0092] The priority base score of the target obstacle is calculated based on its category, speed, direction of motion, and relative distance to the robot. The priority base score of the i-th target obstacle is... The calculation formula is as follows:
[0093] ;
[0094] in, , , , These are the weighting coefficients, and ; This represents the class weight of the i-th target obstacle in the output of the two-branch Transformer model; This represents the estimated speed of the i-th target obstacle. , This represents the estimated three-dimensional velocity of the i-th target obstacle; This indicates the preset upper limit threshold for the speed of dynamic obstacles; This represents the angle between the direction of motion of the i-th target obstacle and the straight line between the robot and the i-th target obstacle; This represents the Euclidean distance between the i-th target obstacle and the robot; This indicates the preset safe distance value.
[0095] Based on the acceleration and state prediction uncertainty of the target obstacle, the adjustment factor of the corresponding target obstacle is determined, and the corresponding priority base score is adjusted based on the adjustment factor to form the priority score of the corresponding target obstacle;
[0096] In this embodiment of the invention, the dynamic adjustment factor of the i-th target obstacle The specific calculation formula is as follows;
[0097] ;
[0098] in, This represents the estimated three-dimensional acceleration of the i-th target obstacle. , This represents the estimated acceleration of the i-th target obstacle. ; This indicates the preset upper limit threshold for obstacle acceleration; This represents the uncertainty in predicting the motion state of the i-th target obstacle; , This represents the adjustment coefficient.
[0099] Priority score of the i-th target obstacle .
[0100] (32) Introduce the priority score of the target obstacle into the model predictive control (MPC) to perform obstacle avoidance path planning and its optimal control input, thereby achieving adaptive obstacle avoidance.
[0101] With the optimization objectives of minimizing trajectory tracking error, smoothing control input, and minimizing collision cost, an MPC optimization problem is constructed as follows:
[0102] ;
[0103] in, This represents the robot's operating state at step k, including its three-dimensional position, three-dimensional velocity, and motion direction angle. This represents the reference trajectory state of the robot at step k; This represents the prediction time domain of MPC; This indicates the robot's operating state at step N. This represents the robot's reference trajectory state at step N; , , These are the weight matrices with state error respectively. Control weight matrix Terminal weight matrix The quadratic form; This represents the control input of the robot at step k, which includes three-dimensional acceleration and steering angular velocity. The collision cost weights are represented. ; This represents the predicted state of the i-th target obstacle at step k; This represents the predicted state of the robot at step k. The predicted state of the i-th target obstacle at step k. The cost of detected collisions; Indicates the number of target obstacles.
[0104] A global path from the starting point to the target point is pre-planned based on global path planning (such as the A* algorithm). When MPC is executed, it extracts discrete path points within a predicted time domain of N based on the robot's current pose along the global path. After local smoothing optimization, a reference trajectory state is generated.
[0105] Constraints: When solving the optimization problem, the following constraints must be satisfied to ensure the feasibility and safety of path planning, including system dynamics constraints: ,in, The dynamic model of the mobile robot; control input constraints: , , Lower and upper limits for robot control inputs; state constraints: , , Lower and upper limits for robot motion states; safety distance constraints: , Let be the adaptive safe distance for the i-th obstacle.
[0106] In this embodiment of the invention, the collision cost A Gaussian function is used to achieve continuous quantification of collision risk, and the specific calculation formula is as follows:
[0107] ;
[0108] in, Let represent the Euclidean distance between the robot and the i-th target obstacle at step k; This represents the collision cost threshold; exceeding this distance incurs a higher collision cost. , This represents the width coefficient of the Gaussian function, which is positively correlated with the obstacle priority score. The smaller the value, the faster the collision cost decreases with distance.
[0109] This invention significantly improves upon the limitations of single sensors by deeply fusing LiDAR and visual data, enabling stable operation even in harsh visual environments and enhancing environmental adaptability. It utilizes a dual-branch Transformer model to collaboratively extract local details and global temporal features of dynamic obstacles, greatly improving the feature loss problem of traditional methods under occlusion and lighting changes, while also increasing processing speed. Furthermore, it introduces a priority scoring mechanism based on dynamic obstacle category and real-time motion state, achieving differentiated obstacle avoidance decisions and avoiding the drawbacks of a "one-size-fits-all" strategy. In scenarios with multiple dynamic obstacles, it can make more reasonable and safer path planning, reducing collision risks.
[0110] The present invention has been described by way of example. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution of the present invention to other occasions without modification, are all within the protection scope of the present invention.
Claims
1. A dynamic obstacle avoidance method for a mobile robot, characterized in that, The method is as follows: (1) Collect environmental point cloud and environmental image under the current environment, perform spatiotemporal alignment on the environmental point cloud and environmental image, fuse the environmental point cloud and environmental image into a multimodal environmental representation, and identify dynamic obstacles under the current environment based on the multimodal environmental representation. (2) Extract local detail features and global temporal features of dynamic obstacles from the multimodal environmental representation corresponding to dynamic obstacles, respectively, and fuse the local detail features and global temporal features through an attention gating mechanism, and then predict the category and motion state of dynamic obstacles through a multi-task prediction head; (3) Take the obstacle in motion as the target obstacle, and perform obstacle avoidance path planning and its corresponding optimal control input based on the target obstacle priority score.
2. The dynamic obstacle avoidance method for a mobile robot as described in claim 1, characterized in that, The process of extracting local detail features of obstacles is as follows: Environmental images Divide into N groups of size The image patch is flattened, and the flattened pixels are used to form a pixel feature vector. This pixel feature vector is then linearly projected and positionally encoded to obtain the initial feature embedding. Embed the initial features The L-th layer Transformer encoder is used for feature extraction. The feature corresponding to the [cls] token in the output of the L-th layer Transformer encoder is taken, and after LN normalization, the local detail features are obtained. .
3. The dynamic obstacle avoidance method for a mobile robot as described in claim 1, characterized in that, The process of extracting global temporal features is as follows: Extract the obstacle state of the same dynamic obstacle in T consecutive frames to form a temporal input sequence, and process the temporal sequence. Perform linear projection and temporal position encoding to obtain the initial temporal feature embedding. Embed the initial time series features Feature extraction is performed on the L-th layer temporal Transformer encoder. The feature corresponding to the [cls] token in the output of the L-th layer temporal Transformer encoder is taken, and the global temporal feature is obtained after layer normalization. .
4. The dynamic obstacle avoidance method for a mobile robot as described in claim 1, characterized in that, The process of fusing local detail features and global temporal features is as follows: Calculate the attention weights for feature fusion, based on the attention weights Perform local detail features With global temporal features The fusion yields fusion characteristics. .
5. The dynamic obstacle avoidance method for a mobile robot as described in claim 1, characterized in that, The target obstacle priority score is obtained as follows: The priority score of the target obstacle is calculated based on its category, speed, direction of movement, and relative distance to the robot. Based on the acceleration and state prediction uncertainty of the target obstacle, the adjustment factor of the corresponding target obstacle is determined. The corresponding priority base score is adjusted based on the adjustment factor to form the priority score of the corresponding target obstacle.
6. The dynamic obstacle avoidance method for a mobile robot as described in claim 5, characterized in that, The priority base score of the i-th target obstacle The calculation formula is as follows: ； in, , , , These are the weighting coefficients, and ; This represents the class weight of the i-th target obstacle in the output of the two-branch Transformer model; This represents the estimated speed of the i-th target obstacle. , This represents the estimated three-dimensional velocity of the i-th target obstacle; This indicates the preset upper limit threshold for obstacle speed; This represents the angle between the direction of motion of the i-th target obstacle and the straight line between the robot and the i-th target obstacle; This represents the Euclidean distance between the i-th target obstacle and the robot; This indicates the preset safe distance value.
7. The dynamic obstacle avoidance method for a mobile robot as described in claim 5, characterized in that, Dynamic adjustment factor for the i-th target obstacle The specific calculation formula is as follows: ； in, This represents the estimated three-dimensional acceleration of the i-th target obstacle. , This represents the estimated acceleration of the i-th target obstacle. ; This indicates the preset upper limit threshold for dynamic obstacle acceleration; This represents the uncertainty in predicting the motion state of the i-th target obstacle; , This represents the adjustment coefficient.
8. The dynamic obstacle avoidance method for a mobile robot as described in claim 1, characterized in that, The specific optimization objective of Model Predictive Control (MPC) is as follows: ； in, This represents the robot's operating state at step k, including its three-dimensional position, three-dimensional velocity, and motion direction angle. This represents the reference trajectory state of the robot at step k; This represents the prediction time domain of MPC; This indicates the robot's operating state at step N. This represents the robot's reference trajectory state at step N; , , These are the weight matrices with state error respectively. Control weight matrix Terminal weight matrix The quadratic form; This represents the control input of the robot at step k, which includes three-dimensional acceleration and steering angular velocity. The collision cost weights are represented. ; This represents the predicted state of the i-th target obstacle at step k; This represents the predicted state of the robot at step k. The predicted state of the i-th target obstacle at step k. The cost of detected collisions; Indicates the number of target obstacles.
9. The dynamic obstacle avoidance method for a mobile robot as described in claim 8, characterized in that, Collision Cost The body is as follows: ； in, Let represent the Euclidean distance between the robot and the i-th target obstacle at step k; Indicates the collision cost threshold. This represents the width coefficient of the Gaussian function.