The 2008 ICRA Workshop on Cooperative Control of Multiple Heterogeneous UAVs for Coverage and Surveillance Time-Optimal UAV Trajectory Planning for 3D Urban Structure Coverage Peng Cheng Jim Keller Vijay Kumar Lab 1
Motivation Intelligence Surveillance and Reconnaissance (ISR) tasks ONR, Code 30 2
Motivation 3D city maps, such as Google Maps New York, Google Maps 3
Motivation An FAA approved UAV for city law enforcement in Miami 4
Goal 3D Coverage for Reconnaissance and Surveillance in Urban Environments Two Problems: 1. Cooperative coverage with multiple UAVs Task allocation with minimal communication in finite time Scalable and decentralized Ad-hoc organization An Almost Communication-Less Approach to Task Allocation for Multiple UAVs Peng Cheng Vijay Kumar ThA1: Path Planning Algorithms; Thur. 10:20-10:40am 2. 3D coverage of urban structures Complete coverage with optimality guarantee Dynamic constraints of fixed-wing UAVs Limited field of view of the onboard camera 5
Task 2 needs 20% UAVs Task 1 needs 10% UAVs Task 4 needs 40% UAVs Task 3 needs 30% UAVs A group of unknown number of UAVs 6
Each UAV: Does not know the total number of UAVs Does know the task specification and bounded region Has GPS provide compass and synchronized clock Has fixed-wings must fly forward (Dubin s car) Has limited omni directional sensing range Has no communication between UAVs Limited turning rate Limited turning rate Positive min. fwd. speed Objective: Determines a task to accomplish in finite time 7
An Example 1 Task Allocation 2 3 Initial configurations Video 4 Intended task allocation Allocate the UAVs to provide persistent coverage of the border of the sea. 25% of UAVs are respectively allocated to the 1 st and 2 nd closed curves, 37.5% for the 3 rd curve, and 12.5% for the 4 th curve. 8
Our Solution Decentralized and scalable with minimal communication (O(1) computation time and O(1) memory with respect to the number of UAVs) Establishes consensus on the total number and task allocation of UAVs in finite time Applicable for a large group of fixed-wing UAVs with ad-hoc organization Thur. 10:20-10:40am ThA1: Path Planning Algorithms 9
3D Coverage Problem φ Achieve a complete coverage of a building with an onboard camera on a fixed-wing UAV 10
Challenges Complicated and coupled dynamics of the UAV Complicated to compute the covered surface area of the building Hard to provide performance guarantee on Complete coverage Time optimality 11
Sensor footprint of the onboard camera A Search-Based Solution Area of interest Expensive to compute a solution Hard to provide guarantee on complete coverage 12
Sensor footprint of the onboard camera Pattern-Based Solutions - I Area of interest 13
Pattern-Based Solutions - II Sensor footprint of the onboard camera Area of interest Hard to quantify the time optimality while incorporating system dynamics 14
Our Objectives Compute a coverage plan in real-time Applicable for the fixed-wing UAVs Provide performance guarantee Complete coverage Time optimality Simplified dynamics and building models + Improved pattern-based coverage 15
A Simplified UAV Model Decoupled dynamics In x-y plane, the Dubin s car model ( v f has a positive lower bound for the fixed-wing UAVs) In z direction, the double integrator model 16
Simplified Building Models O B ( F ) The hemisphere model The cylinder model 17
Constant Coverage Rate A C B D O Tight lower bound on the time to achieve complete coverage of the hemisphere 18
The Lower Bound on Coverage Time 19
Coverage Plan for the Hemisphere Model Constant factor optimality: T k T L k T opt 20
21 Constant Factor Optimality max ' min max min max ' ' ',,, 2 2 1 2 8 5 10 2 2 z z z z z z z L f z z L i i i h t i v t L t h all v v a a a a a T v v a T T T T T T T = + = + + + + + + + = π π π
Multiple UAV Persistent Coverage T n = T T f all f : refreshing rate n : the number of UAVs 22
Multiple UAV Multiple Buildings r B O B ( F ) O B ( F ) O B ( F ) O B ( F ) 23
Multiple UAV Multiple Buildings r B r B r B O B O B ( F ) r G O O B ( F B ) r B O O B r G B O ( F ) ( F ) B r G O B O B ( F ) r G 24
Multiple UAV Multiple Buildings r B r B r B O B O B ( F ) r G O O B ( F B ) r B O O B r G B O ( F ) ( F ) B r G O B O B ( F ) r G 25
Preliminary Results with Dynamic Models 26
Active Waypoint Aircraft location Offset view of aircraft from simulator Overview of System Autopilot connected for hardwarein-the-loop testing in lab 27
Power Required for Maneuvering Flight Assumption of Decoupled Requirements for Turning and Climbing Segments Appropriate for Simulated Flight Conditions: Velocity near minimum power required Maximum angle of bank low in magnitude 500 Power Required - Watts 450 400 350 300 250 25 20 Bank Angle - degrees 15 10 Navigation Limits 5 0 0 5 10 15 Flight Path Angle - degrees 28
Trim Angle of Attack for Maneuvering Flight 8 7.5 7 6.5 6 25 Flight Plan entirely within range of linear aerodynamics 20 15 10 5 0 5 15 10 29 Trim Angle of Attack - degrees Flight Path Angle - degrees Bank Angle - degrees
Simulation Data for Hemispherical Flight Path Over a Building in Lower Manhattan (17 State St.) Simulation Model: Nonlinear Equations of Motion Linear Aerodynamic Forces and Moments Visualization: FlightGear v9.9 Air Vehicle Configuration: Quarter scale Piper Cub J3 Piccolo TM Autopilot Hardware-in-the-loop Flight Conditions: Sea Level/Standard Day Ambient Conditions Cruise Airspeed set to 15 m/s Maximum Commanded Angle of Bank set to 15 o (minimum radius of turn = 85.7m) Target Climb Angle: 15 o (maximum power) No winds Building Height: 208m } Camera FOV: 35 o Dictates 4 Tiers for Complete Coverage; 96 waypoints Trajectory Requirements for Air Vehicle: increase in power required to climb (φ = 0) = mgvη prop sin(γ) ~ 820*sin(γ) [Watts] increase in power required to turn (γ = 0) = (mg) 2 Vη prop ~ 33*sec2 (φ)) [Watts] qsπaecos 2 (φ) 30
FlightGear Scenery Sparse Compared to Reality Permits Execution of Hemispherical Flight Plan 31
Map-view of Simulated Flight Path Launch point T =0 @ first waypoint Flight Plan Actual Path Last point in time history Reference Point for δnorthing, δeasting measurements 32
Cartesian view of flight plan Alt. - m North - m East - m 33
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deltanorthing, deltaeasting and Altitude from reference - m 600 500 400 300 200 Time History Data δnorthing from Reference: Flight Plan: Actual Path: δeasting from Reference: Flight Plan: Actual Path: 100 δaltitude from Reference: Flight Plan: Actual Path: 0 0 50 100 150 200 250 300 350 400 450 Time - sec Trajectory Following Performance: Within expected limits for Piccolo except during transition phases 35
Autonomous UAV Flight Test Data/Imagery 6August06 Pipersville, PA Trajectories for Time Optimal Surveillance 36
Flight Field Pipersville, Pennsylvania 37
Autopilot and Camera Installation on Aircraft GPS Antenna Autopilot Housing Airspeed/Altitude Sensor Ground Station Antenna Fixed forward-looking camera: 30 o down from level attitude 38
Coverage of Flightline 39
Landing/Recovery 40
Conclusion Real-time trajectory design for fixed-wing UAVs for coverage of urban structures Performance guarantee Complete coverage Constant-factor time optimality Verified with the hardware-in-the-loop simulation results Thank you! Questions! An Almost Communication-Less Approach to Task Allocation for Multiple UAVs Thur. 10:20-10:40am ThA1: Path Planning Algorithms 41