Author Contributions
Conceptualization, Y.L. and S.L.; methodology, Y.L. and S.L.; software, S.L. and S.Q.; validation, S.L., J.G., and Z.C.; formal analysis, S.L. and S.Q.; investigation, Y.L., S.L., and J.G.; resources, Y.L. and Z.Y.; data curation, S.L.; writing—original draft preparation, Y.L. and S.L.; writing—review and editing, Y.L. and Z.Y.; visualization, S.L., J.G., S.Q., and Z.C.; supervision, Z.Y.; project administration, Z.Y.; funding acquisition, Y.L. and Z.Y. All authors have read and agreed to the published version of the manuscript.
Figure 1.
(a) The safety convex corridor established in the map in Figure 3c; (b) collision avoidance constraints are represented as linear constraints within the convex corridor region.
Figure 1.
(a) The safety convex corridor established in the map in Figure 3c; (b) collision avoidance constraints are represented as linear constraints within the convex corridor region.
Figure 2.
Different types of bounding boxes of the space rover.
Figure 2.
Different types of bounding boxes of the space rover.
Figure 3.
Illustration of the cluttered plenary surface and its 2D projection: (a) classical plenary surface scenario, (b) 3D modeling of the obstacles, (c) 2D projection of the obstacles.
Figure 3.
Illustration of the cluttered plenary surface and its 2D projection: (a) classical plenary surface scenario, (b) 3D modeling of the obstacles, (c) 2D projection of the obstacles.
Figure 4.
The space rover trajectory optimization framework based on safe convex corridors.
Figure 4.
The space rover trajectory optimization framework based on safe convex corridors.
Figure 5.
Geometric description of the space rover.
Figure 5.
Geometric description of the space rover.
Figure 6.
An example of polygon segmentation using the proposed convex decomposition algorithm: (a) decomposition of a nonconvex obstacle; (b) subconvex polygons after decomposition.
Figure 6.
An example of polygon segmentation using the proposed convex decomposition algorithm: (a) decomposition of a nonconvex obstacle; (b) subconvex polygons after decomposition.
Figure 7.
Comparison of Keil’s algorithm, Bayazit’s algorithm, and the proposed convex decomposition algorithm: (a) Keil’s algorithm, (b,c) Bayazit’s algorithm, (d–f) proposed. It can be observed that our proposed algorithm yields fewer subconvex polygons in the decomposition compared with the other two algorithms. Additionally, Bayazit’s algorithm is incapable of handling concave polygons in the case (c).
Figure 7.
Comparison of Keil’s algorithm, Bayazit’s algorithm, and the proposed convex decomposition algorithm: (a) Keil’s algorithm, (b,c) Bayazit’s algorithm, (d–f) proposed. It can be observed that our proposed algorithm yields fewer subconvex polygons in the decomposition compared with the other two algorithms. Additionally, Bayazit’s algorithm is incapable of handling concave polygons in the case (c).
Figure 8.
When the line segment between the points and intersects with an obstacle, we select the intermediate point , where .
Figure 8.
When the line segment between the points and intersects with an obstacle, we select the intermediate point , where .
Figure 9.
Safe convex corridor generation: (
a) The bounding rectangle Pr is generated to create the safe convex corridor, excluding obstacle nodes
located outside the rectangle. The obstacle nodes within the bounding rectangle are denoted as
. If there are no obstacle nodes within the bounding rectangle Pr, the next two steps (
Section 5.2 and
Section 5.3) are omitted. (
b) The tangent lines of the ellipse that are closest to the obstacle node
are used to exclude a portion of the obstacle nodes (represented by the black dots in the figure). (
c) The process of finding the nearest obstacle point
and
is repeated until
becomes empty. (
d) The final created safe convex corridor.
Figure 9.
Safe convex corridor generation: (
a) The bounding rectangle Pr is generated to create the safe convex corridor, excluding obstacle nodes
located outside the rectangle. The obstacle nodes within the bounding rectangle are denoted as
. If there are no obstacle nodes within the bounding rectangle Pr, the next two steps (
Section 5.2 and
Section 5.3) are omitted. (
b) The tangent lines of the ellipse that are closest to the obstacle node
are used to exclude a portion of the obstacle nodes (represented by the black dots in the figure). (
c) The process of finding the nearest obstacle point
and
is repeated until
becomes empty. (
d) The final created safe convex corridor.
Figure 10.
The figure illustrates a safe convex corridor (SCC) method, designed to mitigate the influence of redundant obstacles on trajectory planning problems.
Figure 10.
The figure illustrates a safe convex corridor (SCC) method, designed to mitigate the influence of redundant obstacles on trajectory planning problems.
Figure 11.
Importance of connectivity in the safe convex corridor: (a) constructing a safe convex corridor with a single point does not guarantee connectivity, which can potentially lead to collisions; (b) constructing a safe convex corridor with line segments (two points) ensures the connectivity.
Figure 11.
Importance of connectivity in the safe convex corridor: (a) constructing a safe convex corridor with a single point does not guarantee connectivity, which can potentially lead to collisions; (b) constructing a safe convex corridor with line segments (two points) ensures the connectivity.
Figure 12.
The bounding rectangle Pr.
Figure 12.
The bounding rectangle Pr.
Figure 13.
The depiction of constraints within the safe convex corridor (SCC) reveals that a set of waypoints resides within a convex polygon . These path points are generated during the path planning stage, but we specifically utilize the sampled points and to construct the convex polygon . The side of the line equation can be expressed as a linear constraint , where in the diagram, and .
Figure 13.
The depiction of constraints within the safe convex corridor (SCC) reveals that a set of waypoints resides within a convex polygon . These path points are generated during the path planning stage, but we specifically utilize the sampled points and to construct the convex polygon . The side of the line equation can be expressed as a linear constraint , where in the diagram, and .
Figure 14.
Display of optimal trajectory. The two coverage circle centers of the space rover need to stay within the corresponding safety corridors SCCf and SCCr. (a) The safe convex corridor SCCf is generated using the waypoints for the center of the front circle . (b) The safe convex corridor SCCr is generated using the waypoints for the center of the rear circle . (c) The trajectory is generated by utilizing these two safe convex corridors.
Figure 14.
Display of optimal trajectory. The two coverage circle centers of the space rover need to stay within the corresponding safety corridors SCCf and SCCr. (a) The safe convex corridor SCCf is generated using the waypoints for the center of the front circle . (b) The safe convex corridor SCCr is generated using the waypoints for the center of the rear circle . (c) The trajectory is generated by utilizing these two safe convex corridors.
Figure 15.
(a) The area of the convex polygon that makes up the safe convex corridor and the abscissa denotes the waypoint number from the start point to the end point. (b) Number of elliptic transformations in the process of generating the safe convex corridor.
Figure 15.
(a) The area of the convex polygon that makes up the safe convex corridor and the abscissa denotes the waypoint number from the start point to the end point. (b) Number of elliptic transformations in the process of generating the safe convex corridor.
Figure 16.
(a–g) Time profile of decision variables that are within the defined range.
Figure 16.
(a–g) Time profile of decision variables that are within the defined range.
Figure 17.
Four different unstructured cases: (a) case 1, (b) case 2, (c) case 3, (d) case 4.
Figure 17.
Four different unstructured cases: (a) case 1, (b) case 2, (c) case 3, (d) case 4.
Figure 18.
(a) Optimal value in case 1; (b) constraint violation in case 1.
Figure 18.
(a) Optimal value in case 1; (b) constraint violation in case 1.
Figure 19.
Influence of the parameter h: (a) objective; (b) CPU time.
Figure 19.
Influence of the parameter h: (a) objective; (b) CPU time.
Figure 20.
The impact of the parameter h on the optimal trajectory.
Figure 20.
The impact of the parameter h on the optimal trajectory.
Figure 21.
Optimized trajectory with different objectives and constraints.
Figure 21.
Optimized trajectory with different objectives and constraints.
Table 1.
Decomposition procedures of the proposed irregular polygon.
Table 1.
Decomposition procedures of the proposed irregular polygon.
Concave Point | Types of Scenarios | | | Processing Method |
---|
| Scenario 2 | | ∅ | connect |
| Scenario 1 | | | connect |
| Scenario 3 | ∅ | ∅ | connect |
| Connecting can eliminate the concave point condition without the need for processing |
Table 2.
Basic parameter settings for the rover in the simulation environment.
Table 2.
Basic parameter settings for the rover in the simulation environment.
Parameter | Description | Value | Unit |
---|
l | Space rover length | | m |
| Space rover width | | m |
| Front suspension length | | m |
| Rear suspension length | | m |
| Front and rear wheelbase | | m |
| Maximum speed | | |
| Maximum acceleration | | |
| Maximum angular velocity | | |
| Maximum jerk | | |
| Maximum angular jerk | | |
| Maximum steering angle | | |
r | Space rover coverage circle radius | 1.5 | |
N | Number of discrete points | 100 | - |
| Construction parameter of Pr | 0.1 | |
| Discretization accuracy of obstacle boundaries | 0.1 | |
| Discretization accuracy of inflated circles | 0.1 | |
| Weighting factor for time in the objective function | 10 | - |
Table 3.
Information of the obstacles.
Table 3.
Information of the obstacles.
Case ID | Number of Obstacles | Area | Vertices | Initial State
| Terminal State
|
---|
Case 1 | 30 | 1.092–13.418 | 4–8 | 25.601, 2.874, 1.047 | 24.656, 33.610, 0.785 |
Case 2 | 25 | 1.266–7.207 | 4–7 | 13.872, 14.086, 1.047 | 22.423, 31.805, 0 |
Case 3 | 20 | 4.482–17.977 | 4–6 | 30.119, 7.910, 2.443 | 25.938, 35.748, 1.222 |
Case 4 | 8 | 6.633–25.328 | 5–6 | 32.922, 17.933, 1.571 | 29.216, 36.651, 3.142 |
Table 4.
Comparison of experimental results of different methods.
Table 4.
Comparison of experimental results of different methods.
| Rectangle Safe Corridor | Our Work | Area Method |
---|
Case ID | Cost | CPU Time/s | | | | Cost | CPU Time/s | | | | Cost | CPU Time/s |
Case 1 | 51.227 | 1.905 | 8.715 | 17.013% | 103.434 | 42.881 | 0.838 | 0.369 | 0.861% | 236.408 | 42.512 | 198.948 |
Case 2 | 250.977 | 2.916 | 218.41 | 87.024% | 31.040 | 32.641 | 2.226 | 0.074 | 0.227% | 40.971 | 32.567 | 93.428 |
Case 3 | 59.749 | 1.578 | 12.720 | 21.289% | 67.118 | 42.505 | 2.238 | 1.668 | 3.924% | 47.029 | 40.837 | 107.490 |
Case 4 | 44.457 | 0.843 | 7.036 | 26.408% | 31.126 | 33.117 | 1.057 | 0.400 | 1.208% | 48.548 | 32.717 | 52.372 |
Mean | 101.602 | 1.811 | 64.444 | 63.428% | 54.838 | 37.784 | 1.590 | 0.626 | 1.657% | 62.901 | 37.158 | 101.124 |
Table 5.
Description of different trajectory optimization formulations.
Table 5.
Description of different trajectory optimization formulations.
Problem ID | Objective and Constraints Details |
---|
Problem 1 | |
Problem 2 | |
Problem 3 | |
Problem 4 | |
Problem 5 | |
Problem 6 | |
Problem 7 | Problem 2 with unconstraint |
Problem 8 | Problem 2 with unconstraint |
Problem 9 | Problem 2 with unconstraint |