1. Optimal UAV Flight Path Selection
Da-Wei Gu
Control & Instrumentation Group
11/12/2018

2. Objectives considered
“Optimal” in terms of low risk and flight length
Real-time flight path for single/multiple vehicle
Avoidance of collision in multiple vehicle case
3-dimensional flight paths
Fixed (known a priori) and pop-up threats
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3. Scenario considered Operational range: [0 200]x[0 200] km
Altitude: 1 km
Risk threshold: 0.05
Threats: 18 (10 medium
and 8 short ranges)
Low risk path is preferable
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4. Hit probability for a medium range SAM (25 km)
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5. Path Planning Methods
Improved Voronoi graph method (a graph-based method)
Finite receding horizon with mixed integer linear programming (MILP) method
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6. Voronoi graph method Voronoi graph
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7. Weighted Cost Function
Objective functions: risk level & fuel cost
The cost on the ith edge:
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8. Dynamic Programming: Dijkstra’s Algorithm (1)
Starting node: ns , Ending node: ne
Label assignment of nodes: temporary/permanent
For Node p:
q: preceding node, r: cost(ns, p)
Connection matrix, cost vector, …
Initialisation: (0,0)  ns , (0,)  all other nodes
the permanent node variable k= ns
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9. Dynamic Programming: Dijkstra’s Algorithm (2)
Step 1: Let the label of k be k(p,q).
Consider all nodes connecting to k, y(r,s), in turn:
if q+cost(k,y) < s, y(r,s)  y(k,q+cost(k,y))
Step 2: From the set of temporary labels, select the one with
the smallest 2nd component and declare that label to
permanent. That node becomes the new node k. If
k= ne , goto Step 3; otherwise, goto Step 1, until no
new node can be found (“no feasible path” exit).
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10. Dynamic Programming: Dijkstra’s Algorithm (3)
Step 3: For the destination node ne(x,z), z is the optimal
cost from the starting node ns , x the preceding node.
Recover the selected path (a sequence of waypoints)
from ns to ne .
NB: Other dynamic programming algorithms can be applied (from ne to ns ). No obvious difference in terms of efficiency.
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11. Results of Voronoi graph method (without & with local minimisation)
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12. Voronoi graph method Pros and cons
Global optimality (needs global information)
Guaranteed convergence
Fast path generation
Highly simplified threat model (no strength information)
Possibly high risk
Combined with the local minimisation method
Path tracking needed
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13. Finite receding horizon with MILP Basic idea
LP (linear programming) with integer variables
All dynamic and relevant constraints are expressed as integer linear constraint in similar ways
The path planning problem becomes solving a MILP at each (or several) time step(s)
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14. Speed and acceleration constraints
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15. Modelling of the risk area with dynamical boundaries
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16. Cost function
where
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17. Receding Horizon Control Scheme
Reference Trajectory +
Current State
Model
Predicted Outputs -
Future
Inputs
UAV
CPLEX
Future Errors
Optimum input
Cost
Function
Constraints
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18. MILP method Result
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19. MILP method Pros and cons
Local optimality (only needs local information)
Guaranteed convergence with soft constraints
Full consideration of all necessary constraints
Relatively slow waypoint (path) generation
Simplified threat model
High risk when passes local minima
Could be combined with the graph based methods
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20. Flight Path Planning Package Software Developed at UL
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