Modified A-Star (A*) Approach to Plan the Motion of a Quadrotor UAV in Three-Dimensional Obstacle-Cluttered Environment
Abstract
:1. Introduction
2. Preliminaries
2.1. Modeling
2.2. Controller Design
2.2.1. Inner Loop Controller
2.2.2. Outer Loop Controller
3. Motion Planning
3.1. Three−Dimensional Path Search Using Modified A−Star Approach
Algorithm 1 A* algorithm for three-dimensional path search (with 6-sided search). |
1: Function P(n) = Astar3D(3D_Environment, start, goal) |
2: list_open = nodes to be evaluated; %initially only starting node is present |
3: list_closed = nodes which have been examined; % initially empty |
4: list_open (start_node) = 0; |
5: while (list_open =! empty) do |
6: search the node with least f in list_open % the value of h(n) is same only for 6 neighbors, here one can plan the strategy for 18-sided search as well. |
7: n = node with least value of f; |
8: remove n from the list_open |
9: search the adj_cells of n % adj_cells infer adjacent cells |
10: for (each adj_cell) |
% for three-dimensional case 6 adjacent cells have been visited in this work, however these can be up to 18 adjacent cells including the cells at the edges of a voxel holding the current vertex. |
11: if (adj_cell = goal) then |
12: stop the search |
13: adj_cell.g = n.g + dis_adj_cell; |
14: adj_cell.h = distance between adj_cell and goal; |
15: adj_cell.f = Adj_cell.g + Adj_cell.h; |
16: else if (node with same position as of adj_cell in list_open) |
17: if (node.f < adj_cell.f) |
18: skip adj_cell |
19: end if |
20: else if (node with same position as of adj_cell in list_closed) |
21: if (node.f < adj_cell.f) |
21: skip adj_cell |
22: else |
23: add node to list_open |
24: end if |
25: end if |
26: end for loop |
27: add n to list_closed |
28: end while |
29: P(n)= list_closed |
30: return P(n) |
31: end function |
Algorithm 2 Collision detection algorithm. |
1: input (3D_Environment, current vertex) |
2: E = 3D Environment; |
3: C(n) = current vertex; |
4: E_min = min(E.obstacles); %lower boundary of the obstacles |
5: E_max = max(E.obstacles); %upper boundary of the obstacles |
6: minEo = E_min – margins – UAV_size; |
7: maxEo = E.max + margins + UAV_size; |
8: minEb = lower boundary of 3D Environment; |
9: maxEb = upper boundary of 3D Environment; |
10: if (Cx(n), Cy(n), Cz(n) ≥ minEo && Cx(n), Cy(n), Cz(n) ≤ maxEo) |
11: return collision; |
12: else if (Cx(n), Cy(n), Cz(n) < minEb) |
13: return collision; |
14: else if (Cx(n), Cy(n), Cz(n) > maxEb) |
15: return collision; |
16: else |
17: return collision_free; |
18: End if |
Algorithm 3 Proposed algorithm to refine the path obtained from conventional A* approach |
1: function truncated_path = truncation(3D_Environment, P(n)) |
2: Truncated_path = P(1); |
3: E.obstacles = 3D_Environment.obstacles; |
4: for i = 2: length of path |
5: P = P(i) − P(1); |
6: if (collision between E.obstacles and P) |
7: Truncated _path = P(i − 1) % store the node explored just before collision-node into the truncated path list. |
8: else if (i == length of path) |
9: Truncated _path = P(i); % store last node in the truncated list |
10: else |
11: continue; |
12: end if |
13: end for loop |
3.2. Trajectory Generation
3.2.1. Constraints on Positions
3.2.2. Constraints on Derivatives
3.2.3. Constraints on Start and Goal Points
4. Simulations
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Parameter | Value | Unit |
---|---|---|
Mass (m) | 0.2 | kg |
Arm length (l) | 0.09 | m |
Inertia (Ix) | 0.00026 | kgm2 |
Inertia (Iy) | 0.00026 | kgm2 |
Inertia (Iz) | 0.00040 | kgm2 |
Gravity (g) | 9.81 | m/s2 |
Controller | Parameter | Value |
---|---|---|
Outer Loop Controller | (x, y, z) | 2 |
Outer Loop Controller | (x, y, z) | 1.4 |
Inner Loop Controller | ) | 7 |
Inner Loop Controller | () | 0.3 |
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Farid, G.; Cocuzza, S.; Younas, T.; Razzaqi, A.A.; Wattoo, W.A.; Cannella, F.; Mo, H. Modified A-Star (A*) Approach to Plan the Motion of a Quadrotor UAV in Three-Dimensional Obstacle-Cluttered Environment. Appl. Sci. 2022, 12, 5791. https://doi.org/10.3390/app12125791
Farid G, Cocuzza S, Younas T, Razzaqi AA, Wattoo WA, Cannella F, Mo H. Modified A-Star (A*) Approach to Plan the Motion of a Quadrotor UAV in Three-Dimensional Obstacle-Cluttered Environment. Applied Sciences. 2022; 12(12):5791. https://doi.org/10.3390/app12125791
Chicago/Turabian StyleFarid, Ghulam, Silvio Cocuzza, Talha Younas, Asghar Abbas Razzaqi, Waqas Ahmad Wattoo, Ferdinando Cannella, and Hongwei Mo. 2022. "Modified A-Star (A*) Approach to Plan the Motion of a Quadrotor UAV in Three-Dimensional Obstacle-Cluttered Environment" Applied Sciences 12, no. 12: 5791. https://doi.org/10.3390/app12125791