A method and system for rapid autonomous exploration of unmanned aerial vehicles for narrow dynamic environments
By generating grid maps, extracting leading cluster features, and implementing dynamic obstacle avoidance in narrow dynamic environments, the problem of UAVs being unable to explore deeply in narrow environments has been solved, achieving rapid autonomous exploration and low collision reduction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HANGZHOU DIANZI UNIV
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-05
AI Technical Summary
Drones cannot identify key passages in narrow and dynamic environments, making it impossible to explore in depth. Furthermore, existing trajectory optimization algorithms fail to plan in narrow areas or move conservatively, affecting exploration efficiency. Moreover, obstacle avoidance strategies lack prediction and are prone to collisions.
By generating a grid map, extracting the channel features of the leading cluster, constructing a utility function, dynamically adjusting the safety distance, predicting dynamic obstacle trajectories for obstacle avoidance, and optimizing the path to enable the UAV to explore rapidly and autonomously.
The drone can identify and prioritize exploring narrow passages, reduce unnecessary movement, improve exploration efficiency, reduce collision rate, and quickly resume exploration after obstacle avoidance.
Smart Images
Figure CN122149474A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mobile robot autonomous navigation and artificial intelligence technology, specifically relating to a method and system for rapid autonomous exploration of unmanned aerial vehicles (UAVs) in narrow dynamic environments. Background Technology
[0002] Currently, mainstream autonomous exploration solutions for drones typically employ a cyclical framework of "perception-planning-execution." The core strategy is largely based on the frontier point, i.e., finding the boundary between the known free region and the unknown region as the target point. For trajectory generation, optimization is often achieved using Euclidean symbolic distance fields combined with B-spline curves. Traditional methods, when evaluating the frontier point, only consider "distance cost" and "expected information gain (how much volume can be seen)." However, in post-earthquake rubble search and rescue or underground mine / tunnel inspection, due to the environment often being narrow triangular spaces (narrow geometry) or long, narrow tunnels (channel-type frontier), drones cannot identify "this is a key passage to a new area." They often ignore narrow areas because of their low information gain (small volume), causing drones to circle in open areas, unable to explore deeply, and easily trapped in local optima. Meanwhile, existing trajectory optimization algorithms typically set a fixed, large safety expansion radius (e.g., 0.5 meters) to ensure safety. When the width of the environmental passage (e.g., 0.8 meters) is less than twice the safety radius, the algorithm will determine it as "impassable," leading to planning failure. Alternatively, to maintain a safe distance, the drone moves extremely conservatively and slowly, severely impacting exploration efficiency. Furthermore, many solutions assume a static environment or only employ reactive obstacle avoidance (immediately stopping or randomly avoiding obstacles), lacking prediction of obstacle trajectories, making collisions more likely. Moreover, obstacle avoidance actions are disconnected from the overall exploration task; after obstacle avoidance, the drone often "loses its way" or remains stationary for extended periods, unable to quickly resume exploration. Summary of the Invention
[0003] The purpose of this invention is to provide a method and system for rapid autonomous exploration by unmanned aerial vehicles (UAVs) in narrow dynamic environments.
[0004] In a first aspect, the present invention provides a method for rapid autonomous exploration by unmanned aerial vehicles (UAVs) in confined dynamic environments, the method comprising:
[0005] A grid map is generated based on the surrounding environment information used by the drone;
[0006] Front voxels are extracted based on a raster map, and each front voxel is clustered to form a front cluster; channel features of each front cluster are extracted; the channel features include the length and width of the front cluster; the utility function value of each front cluster is obtained based on each front cluster and its channel features; target front clusters are selected based on the utility function values of each front cluster, and exploration points are selected from the target front clusters;
[0007] The path planning algorithm is used to obtain the seed path from the current position of the UAV to the exploration point, and the motion control of the UAV is performed based on the seed path;
[0008] Repeat the process of selecting exploration points and controlling the drone's motion until the drone reaches the destination.
[0009] Preferably, the method for obtaining the channel features is as follows:
[0010] Obtain the coordinate set of all voxels contained in the current front cluster and calculate the covariance matrix of the coordinate set; perform eigenvalue decomposition on the covariance matrix to obtain multiple principal components and their corresponding eigenvalues; use the eigenvalues corresponding to the first principal component as the length of the front cluster and the eigenvalues corresponding to the second principal component as the width of the front cluster.
[0011] Preferably, the utility function is obtained by weighted summation of the geometric feature term, distance feature term, and information gain term of the front cluster; the weights of each term in the utility function are adjusted based on the channel features of the corresponding front cluster; the adjustment method is as follows: if the aspect ratio of the front cluster is greater than the aspect ratio threshold and the width is less than the width threshold, then the weight corresponding to the geometric feature is increased and the weight corresponding to the distance feature is decreased; otherwise, the weight corresponding to the information gain feature is increased.
[0012] Preferably, the geometric feature term is constructed based on the ratio of the length to the width of the leading edge cluster; the distance feature term is constructed based on the current position of the UAV and the coordinates of the leading edge voxels in the leading edge cluster; and the information gain term is constructed based on the number of leading edge voxels in the leading edge cluster.
[0013] Preferably, during the motion control of the drone, if the drone detects a dynamic obstacle, dynamic obstacle avoidance processing is performed on the path tracked by the drone. The specific process is as follows:
[0014] The uniform acceleration model is used to predict the area occupied by dynamic obstacles in the future time period. If the path tracked by the UAV does not cross the occupied area, the UAV continues to move along the original path. Otherwise, the minimum collision time is obtained, and the original path is adjusted based on the minimum collision time.
[0015] As a preferred method, the original path can be adjusted as follows:
[0016] If the minimum collision time is less than the collision time threshold and the width of the local free space corresponding to the collision point is less than the minimum passage distance, the drone will continue to move along the original path and will slow down or hover by allocating time parameters to wait for the dynamic obstacle to pass.
[0017] If the minimum collision time is less than the collision time threshold and the width of the local free space corresponding to the collision point is greater than or equal to the minimum passage distance, then the predicted trajectory of the dynamic obstacle is regarded as the obstacle adjusting the original path, and the drone is controlled by the adjusted original path.
[0018] If the minimum collision time is greater than or equal to the collision time threshold, the drone continues to move along the original path.
[0019] Preferably, the local free space width is obtained based on the distance from the UAV to the nearest obstacle; the minimum passage distance is obtained based on the UAV's fuselage radius and the fitted radius of the dynamic obstacle.
[0020] As a preferred approach, after obtaining the seed path, the seed path is split into multiple local paths, and path optimization and path tracking are performed on each local path in turn. The target front cluster is updated in each iteration until the UAV reaches the exploration point.
[0021] As a preferred embodiment, the path optimization method is as follows:
[0022] Set a safe distance for the UAV to fly; generate a convex polyhedron containing the local path based on the safe distance, and convert the convex polyhedron into a hard solution space constraint; use spline curves to smooth and optimize the local path, and map the spline control points to the hard solution space constraint to complete the path optimization of the local path.
[0023] Secondly, the present invention provides a rapid autonomous exploration system for unmanned aerial vehicles (UAVs) in narrow dynamic environments, which is used to execute the aforementioned rapid autonomous exploration method for UAVs. The rapid autonomous exploration system includes a perception module, an exploration decision module, and a motion generation and execution module. The perception module includes a depth camera and an inertial measurement unit (IMU). The depth camera is used to perceive the three-dimensional environment; the IMU is used to perceive its own motion; the exploration decision module is used to select exploration points based on the three-dimensional environment information; and the motion generation and execution module is used to generate a path from the UAV's current position to the exploration point and control the UAV to move along that path.
[0024] The beneficial effects of this invention are:
[0025] 1. This invention uses the coordinate values of the front voxels in the front cluster to construct the channel features of different front clusters, and constructs a utility function based on the front clusters and their channel features. Compared with the prior art that only considers distance cost and expected information gain, this invention can identify and prioritize the exploration of narrow channels, thereby breaking the local optimum in the autonomous exploration of UAVs and reducing ineffective round-trip motions. At the same time, this invention dynamically adjusts the weighted weights of different features in the utility function through the channel features of the front clusters, thereby enabling the UAV to adjust its priority exploration plan according to the channel features of the front clusters, that is, to explore deep channels or explore unknown areas in a large direction, so as to quickly cover the airspace and ground.
[0026] 2. This invention dynamically adjusts the safety distance based on the width of the environment, thereby enabling the drone to fly more easily in wide areas and to squeeze through narrow gaps in narrow areas while ensuring physical safety.
[0027] 3. This invention obtains the occupied area of dynamic obstacles by predicting their trajectories, and executes obstacle avoidance strategies in a hierarchical manner based on the occupied area, enabling the UAV to maintain an extremely low collision rate in highly dynamic scenarios. At the same time, this invention quickly resumes exploration after obstacle avoidance, avoiding the UAV from executing a target path with low efficiency after obstacle avoidance. Attached Figure Description
[0028] Figure 1 This is the overall flowchart of the present invention.
[0029] Figure 2 This is a schematic diagram of geometric feature analysis in this invention.
[0030] Figure 3 This is a schematic diagram of the adaptive safety distance in this invention.
[0031] Figure 4 This is the dynamic obstacle avoidance logic diagram in this invention.
[0032] Figure 5 This is a schematic diagram comparing the exploration space of the present invention with that of existing mainstream technologies.
[0033] Figure 6 This is a schematic diagram comparing the exploration paths of the present invention with those of existing mainstream technologies. Detailed Implementation
[0034] The present invention will be further described below with reference to the accompanying drawings.
[0035] A rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments is proposed. The UAV rapid autonomous exploration system comprises a perception module, an exploration decision module, and a motion generation and execution module. The perception module includes a depth camera and an inertial measurement unit (IMU); the depth camera is used to perceive the 3D environment, and the IMU is used to perceive the UAV's own motion. The exploration decision module generates a target path based on the 3D environment information and the UAV's own motion. The motion generation and execution module controls the UAV to move along the target path.
[0036] In this embodiment, the depth camera has a sensing range of 5m; the maximum speed of the drone is 2.0 m / s.
[0037] like Figure 1 As shown, the rapid autonomous exploration method for this drone includes the following steps:
[0038] Step 1: Acquire 3D point cloud data using visual inertial odometry; allocate the 3D point cloud data to different voxels to construct a voxel map. Map the 3D voxel data in the voxel map onto a 2D raster to construct a raster map.
[0039] Step 2: Extract channel features
[0040] 2-1. Extraction of cutting-edge voxels
[0041] like Figure 2 As shown, all voxels in the raster map are traversed, and voxels with the state "known-free" are identified. For each "known-free" voxel, the states of its neighboring (6-neighborhood) voxels are checked. If there is at least one voxel with the state "unknown" in the neighborhood of a "known-free" voxel, then the "known-free" voxel is marked as a leading voxel.
[0042] 2-2. Frontier Clustering
[0043] The connected component labeling algorithm is used to group all the extracted front voxels. The specific process is as follows: randomly select an unvisited front voxel as a seed point, search for other front voxels in its neighborhood and add them to the current cluster. This process is recursively executed until it cannot be expanded, thus forming an independent front cluster. Repeat the above process until all front voxels are visited, that is, all front voxels are assigned to the corresponding front clusters.
[0044] 2-3. Obtain the length and width of the front cluster.
[0045] For each frontier cluster ( , (This refers to the number of frontal clusters), obtaining the set of three-dimensional coordinates of all voxels contained within them. Calculate the set of three-dimensional coordinates. The covariance matrix is obtained, and eigenvalue decomposition is performed on the covariance matrix to obtain multiple principal components and their corresponding eigenvalues; the eigenvalues corresponding to the first principal component are used as the basis for further analysis. As the length of the frontier cluster, the eigenvalue corresponding to the second principal component The width of the frontier cluster.
[0046] Step 3: Select exploration points
[0047] The utility function corresponding to each front cluster is obtained based on the geometric feature term, distance feature term, and information gain term of each front cluster. It is represented as:
[0048]
[0049] in, Geometric weights; Information gain weights; Distance weights; As a geometric feature term, it is determined by the aspect ratio. ( The value is obtained by normalization. For channel-type environments, the larger the value, the more it conforms to the "narrow channel" characteristic. For information gain, it represents the number of leading voxels in the leading cluster; The distance feature term represents the Euclidean distance from the current position of the UAV to the geometric center of the leading cluster.
[0050] In some embodiments, the information gain term is the volume of an unknown voxel.
[0051] In some embodiments, the distance feature represents the Euclidean distance from the current position of the UAV to the nearest point of the leading edge cluster.
[0052] In the process of obtaining the utility functions of each front cluster, if the aspect ratio of the front cluster is... Greater than the aspect ratio threshold (i.e., slender shape) and width If the width is less than the threshold, then the geometric weight will be adjusted. Set the distance weight to 2-3 times the initial geometric weight. Set the information gain weight to half of the initial distance weight to allow the drone to ignore the greater distance cost in order to explore deeper passages; otherwise, set the information gain weight to 1 to 2 times the initial information gain weight, so that it can prioritize the direction with a large unexplored area to quickly cover the ground.
[0053] In this embodiment, the aspect ratio threshold The value is 2.5; the width threshold is 1.5.
[0054] Select the frontier cluster with the highest utility function as the target frontier cluster, and obtain the geometric center of the target frontier cluster. If the geometric center is located in free space, directly select it as the exploration point; otherwise, search for the frontier voxel closest to the geometric center within the target frontier cluster as the exploration point, or backtrack a certain distance along the current line of sight until a collision-free viewpoint is found as the exploration point.
[0055] Step 4: Generate seed path
[0056] The A* algorithm is used to output an initial discrete geometric path from the UAV's current position to the exploration point as a seed path. The seed path is only collision-free at the geometric level and is a broken line composed of a series of discrete waypoints. It does not have dynamic information in the time dimension such as velocity and acceleration, and there is a problem of derivative discontinuity at the inflection points.
[0057] Step 5: Path Optimization and Flight Control
[0058] like Figure 3 As shown, the seed path is broken down into multiple local paths, and path optimization and path tracking are performed sequentially on each local path until the drone reaches the exploration point. The specific process of performing path optimization and path tracking on the local paths is as follows:
[0059] Step 5-1. Establish a safe distance
[0060] A safe distance can be established based on the drone's fuselage radius and the distance between the drone and the nearest obstacle, enabling the drone to fly safely. Its expression is:
[0061]
[0062] in, The physical limit of safe distance, ; The radius of the drone's fuselage; Minimum safety margin; The maximum safe distance; This is the proportionality coefficient; The width of the local free space around the drone. , This represents the Euclidean distance from the drone to the nearest obstacle.
[0063] In this embodiment, minimum safety margin for .
[0064] In this embodiment, the scaling factor is 0.4, which means it occupies less than half of the channel width.
[0065] By adaptively setting the safety distance, the safety distance can be increased in wide areas. This allows for more controlled drone flight and reduces the safe distance in narrow spaces. To approach the physical limit of safe distance This allows drones to fly close to the edge.
[0066] Step 5-2. Generate flight corridor
[0067] Using sampling points on the local path as central seed points, a region dilation algorithm is used to deduce the region in free space until a preset safe distance constraint is met, thus constructing a convex polyhedron (hyperplane). If the convex polyhedron overlaps with an obstacle, the target front cluster is discarded, and step two is repeated to select a new target front cluster. During the generation of the convex polyhedron, a directional constraint is introduced: the principal axis extension direction of the convex polyhedron is required to be aligned with the principal direction (first principal component) of the target front cluster (i.e., the dot product of the direction vectors is maximized). Safe distance. The dynamic threshold at which hyperplane expansion stops determines the lateral envelope of the corridor. In open areas, the safe distance... A larger value results in a more spacious convex polyhedron, which is beneficial for trajectory smoothing optimization; in narrow regions, a safe distance is crucial. Automatically move to the physical limit safe distance The contraction forces the generated convex polyhedron to fit tightly to the physical limits of the environment, thus ensuring that the drone can accurately pass through narrow gaps.
[0068] Step 5-3. Local Path Optimization
[0069] The generated convex polyhedron is transformed into a linear inequality constraint as a hard solution space constraint. By mapping B-spline control points to the corresponding linear inequality constraints of the convex polyhedron, the control points are constrained within the convex polyhedron, thus transforming the complex obstacle avoidance constraints into linear inequality constraints. This allows for the solution of a spatiotemporally continuous and smooth trajectory (locally optimized path) that satisfies UAV dynamic constraints (such as maximum speed and acceleration limits) while ensuring absolute trajectory safety.
[0070] Step 5-4. Dynamic obstacle avoidance
[0071] like Figure 4 As shown, the UAV is motion-controlled based on a locally optimized path, and the target leading edge cluster is reacquired after motion control is completed. During the motion control process, if the UAV does not detect any dynamic obstacles, it continues to move according to the locally optimized path; otherwise, the UAV performs dynamic obstacle avoidance operations, the specific process of which is as follows:
[0072] For detected dynamic obstacles, a uniform acceleration model is used to predict their bounding box over a future period (e.g., 2-3 seconds). The drone's locally optimized path is then checked to see if it crosses the predicted bounding box at some future point in time. If it does not cross the predicted bounding box, the drone continues moving along the locally optimized path; otherwise, a set collision time period is obtained. Internally, the local optimization path of the drone With dynamic obstacle prediction occupied area The earliest moment of overlap is taken as the minimum collision time. ,Right now The optimized path is adjusted based on the minimum collision time, as follows:
[0073] (1) If the minimum collision time The distance is less than the collision time threshold, and the width of the local free space corresponding to the predicted collision point is less than the minimum passage distance. The drone continues to move along a locally optimized path, and by allocating time parameters, it slows down or hovers when approaching obstacles, waiting for the dynamic obstacles to pass. Minimum clearance distance. The method to obtain it is as follows:
[0074]
[0075] in, The fitted radius of the dynamic obstacle; For safety buffering.
[0076] (2) If the minimum collision time PTTC is less than the collision time threshold, and the width of the local free space corresponding to the predicted collision point is greater than or equal to the minimum passage distance. The dynamic obstacle prediction trajectory is then regarded as the obstacle adjusting the current local optimized path, and the UAV is motion controlled by the adjusted local optimized path.
[0077] (3) If the minimum collision time PTTC is greater than or equal to the collision time threshold, the UAV continues to move along the local optimization path.
[0078] In this embodiment, after completing dynamic obstacle avoidance, local path optimization and trajectory tracking are immediately re-performed to ensure that the drone does not "stand still" after obstacle avoidance.
[0079] Step 6: Repeat steps 2 to 5 until the drone reaches the destination, completing the autonomous exploration of the drone.
[0080] Step 7: Method Evaluation
[0081] The invention and existing mainstream technologies (such as the FUEL algorithm and traditional frontier methods) were used to control the UAV, and the results are as follows: Figure 5 and Figure 6 As shown. From Figure 5 and Figure 6 As can be seen, this invention reduces exploration time by 21.2% to 27.7% in complex, dynamic, and narrow maze environments, thanks to geometry perception which allows the drone to avoid unnecessary detours. Simultaneously, the total flight path length is reduced by 12.9% to 15.3%, minimizing ineffective back-and-forth movements; furthermore, it can traverse narrow gaps only slightly wider than the drone's fuselage, where traditional fixed-parameter methods typically fail to plan. Moreover, this invention maintains an extremely low collision rate in highly dynamic scenarios while preserving a high exploration coverage (close to 100%).
Claims
1. A method for rapid autonomous exploration by unmanned aerial vehicles (UAVs) in confined dynamic environments, characterized by: The method includes: A grid map is generated based on the surrounding environment information used by the drone; Front voxels are extracted based on a raster map, and each front voxel is clustered to form a front cluster; channel features of each front cluster are extracted; the channel features include the length and width of the front cluster; the utility function value of each front cluster is obtained based on each front cluster and its channel features; target front clusters are selected based on the utility function values of each front cluster, and exploration points are selected from the target front clusters; The path planning algorithm is used to obtain the seed path from the current position of the UAV to the exploration point, and the motion control of the UAV is performed based on the seed path; Repeat the process of selecting exploration points and controlling the drone's motion until the drone reaches the destination.
2. The rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 1, characterized in that: The method for obtaining the channel features is as follows: Obtain the coordinate set of all voxels contained in the current frontier cluster, and calculate the covariance matrix of the coordinate set; perform eigenvalue decomposition on the covariance matrix to obtain multiple principal components and their corresponding eigenvalues; The eigenvalues corresponding to the first principal component are used as the length of the front cluster, and the eigenvalues corresponding to the second principal component are used as the width of the front cluster.
3. The rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 1, characterized in that: The utility function is obtained by weighted summation of the geometric feature term, distance feature term, and information gain term of the front cluster; the weights of each term in the utility function are adjusted based on the channel features of the corresponding front cluster; the adjustment method is as follows: if the aspect ratio of the front cluster is greater than the aspect ratio threshold and the width is less than the width threshold, then the weight corresponding to the geometric feature is increased and the weight corresponding to the distance feature is decreased; otherwise, the weight corresponding to the information gain feature is increased.
4. The rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in narrow dynamic environments according to claim 3, characterized in that: The geometric feature term is constructed based on the ratio of the length to the width of the leading edge cluster; the distance feature term is constructed based on the current position of the UAV and the coordinates of the leading edge voxels in the leading edge cluster; the information gain term is constructed based on the number of leading edge voxels in the leading edge cluster.
5. The rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 1, characterized in that: During the motion control of the drone, if the drone detects a dynamic obstacle, dynamic obstacle avoidance processing is performed on the path tracked by the drone. The specific process is as follows: The uniform acceleration model is used to predict the area occupied by dynamic obstacles in the future time period. If the path tracked by the UAV does not cross the occupied area, the UAV continues to move along the original path. Otherwise, the minimum collision time is obtained, and the original path is adjusted based on the minimum collision time.
6. The rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 5, characterized in that: The method for adjusting the original path is as follows: If the minimum collision time is less than the collision time threshold and the width of the local free space corresponding to the collision point is less than the minimum passage distance, the drone will continue to move along the original path and will slow down or hover by allocating time parameters to wait for the dynamic obstacle to pass. If the minimum collision time is less than the collision time threshold and the width of the local free space corresponding to the collision point is greater than or equal to the minimum passage distance, then the predicted trajectory of the dynamic obstacle is regarded as the obstacle adjusting the original path, and the drone is controlled by the adjusted original path. If the minimum collision time is greater than or equal to the collision time threshold, the drone continues to move along the original path.
7. A rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 6, characterized in that: The local free space width is obtained based on the distance from the UAV to the nearest obstacle; the minimum passage distance is obtained based on the UAV's fuselage radius and the fitted radius of the dynamic obstacle.
8. The rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 1, characterized in that: After obtaining the seed path, the seed path is split into multiple local paths. Path optimization and path tracking are performed on each local path in turn, and the target front cluster is updated in each iteration until the UAV reaches the exploration point.
9. A rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in confined dynamic environments according to claim 1, characterized in that: The path optimization method is as follows: Set a safe distance for the UAV to fly; generate a convex polyhedron containing the local path based on the safe distance, and convert the convex polyhedron into a hard solution space constraint; use spline curves to smooth and optimize the local path, and map the spline control points to the hard solution space constraint to complete the path optimization of the local path.
10. A rapid autonomous exploration system for unmanned aerial vehicles (UAVs) in confined dynamic environments, characterized in that: This system is used to execute the rapid autonomous exploration method for unmanned aerial vehicles (UAVs) in narrow dynamic environments as described in claim 1. The rapid autonomous exploration system includes a perception module, an exploration decision module, and a motion generation and execution module. The perception module includes a depth camera and an inertial measurement unit (IMU). The depth camera is used to perceive the three-dimensional environment; the IMU is used to perceive its own motion; the exploration decision module is used to select exploration points based on the three-dimensional environment information; and the motion generation and execution module is used to generate a path from the UAV's current position to the exploration point and control the UAV to move along that path.