On Path Generation, Path Following On Path Generation, Path - PowerPoint PPT Presentation

On Path Generation, Path Following On Path Generation, Path Following and Time Coordination for and Time Coordination for Small UAVs UAVs Small I. Kaminer I. Kaminer Department of Mechanical and Astronautical Astronautical Engineering, Engineering, Department of Mechanical and Naval Postgraduate School Naval Postgraduate School Monterey, CA Monterey, CA Joint work with Joint work with NPS: Dobrokhodov, Yakimenko, Jones NPS: Dobrokhodov, Yakimenko, Jones IST: Pascoal, Ghabcheloo, Silvestre IST: Pascoal, Ghabcheloo, Silvestre VPI: Hovakimyan, Chu, Patel VPI: Hovakimyan, Chu, Patel

INTRODUCTION INTRODUCTION UAV Wing span, m Wing type Max takeoff weight, kg Endurance, hour Payload, kg FOG-R 3.2 high wing 41 1 Tern 3.5 high wing 59 4 Rascal 2.8 high wing 8 3 Telemaster 2.5 high wing 8 3 MAV 0.23 flapping-wing 0.015 0.3 -

Introduction Mobile UAV Operations Testbed Runway at Camp Roberts Flight Test Architecture

Time Coordinated Control of Multiple UAVs • Time Coordinated Applications for Multiple UAVs (small) • Sequential Autoland • Coordinated Strike • Coordinated Road Following • Coordinate on the arrival of the leader subject to deconfliction and network constraints Wind drection Segment 2: Stabilized glideslope tracking Top of glideslope • Net or wire 4000 3500 3000 UAV 3 Bring each UAV from formation UAV 2 2500 to the top of the glideslope at a y(m) 2000 given point in time 1500 UAV 1 Segment 1: Glideslope capture 1000 UAV n (from any initial condition) 500 UAV 1 0 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 x(m)

Outline Outline � Generation of feasible trajectories using direct methods Generation of feasible trajectories using direct methods � � Path following for a single UAV � Path following for a single UAV � Coordination of multiple of Coordination of multiple of UAVs UAVs � � Simulation results � Simulation results � Flight Test results Flight Test results � � Conclusions. � Conclusions.

Generation of Feasible Trajectories Generation of Feasible Trajectories • Assume polynomial trajectories defined using virtual length – decouples time and space domains Impact of changing total Impact of changing total path length path length and initial jerk

Generation of Feasible Trajectories Generation of Feasible Trajectories τ d ( ) • Let λ τ = dt ( ) ( ) • Then ′ ′ ′ ′ τ = λ τ τ + τ + τ = λ τ τ 2 2 2 v ( ) x ( ) x ( ) x ( ) ( ) p 1 2 3 c ( ) ( ) ( ) ( ) ′′ ′ ′ τ = τ λ τ + τ λ τ λ τ 2 a p ( ) p ( ) c c • Boundary conditions ( ) ( ) ( ) ( ) • given p 0 , p 0 , p t , p t & && & && , c c c f c f ( ) ( ) ( ) ( ) ( ) ( ) ( ) • let ′ ′ λ = λ = λ τ = λ τ = τ 0 v 0 , 0 a (0) and v t , a f f f f • then ( ) ( ) ( ) ( ) ′′ ′ ′ = − λ λ 2 p (0) p 0 p (0) 0 / 0 && c c c ( ) ( ) ( ) ( ) ′′ ′ ′ τ = − λ τ λ τ 2 p ( ) p t p t ( ) / && c f c f c f f f

Generation of Feasible Trajectories Generation of Feasible Trajectories • Feasible trajectory for single UAV ( ) ′ ≤ λ τ τ ≤ v ( ) p v min c max ( ) ( ) ( ) ′′ ′ ′   τ λ τ + τ λ τ λ τ ≤ ∀ ∈  τ τ 2 p ( ) p ( ) a 0,  c c max f • Multiple UAVs , ( ) ( )  ′ ′  τ τ τ τ p d p d • 1 st UAV arrives in τ τ T ∫ ∫   c c = =  f 1 f 1 , ith in T t , t ,    i 1 f 1 f 1 v v min max  0 0    1 1 min max • therefore must guarantee ∩ ≠ ∅ ∀ = ≠ T T , i j , 1, , n i j • i j ( ) ( ) 2 ( ) • τ − τ ≥ ∀ τ τ ∈ τ × τ j k 2 min p p E , , [0, ] [0, ] c j c k j k fj fk = j k , 1,..., n ≠ j k

Generation of Feasible Trajectories Generation of Feasible Trajectories • Optimization Problem ∑  min w J i i  τ = , i 1, n i fi = 1, n  [ ] ∈ subject to (4) for each i 1, n and    ( ) ( ) 2 ( ) τ − τ ≥ ∀ τ τ ∈ τ × τ j k 2 min p p E , , [0, ] [0, ]  c j c k j k fj fk = j k , 1,..., n  ≠ j k  ≤ ≤ ≤ = t t t , t t , i 2,... n  ,  f 1 fi f 1 f 1 fi min min max max max • where, for example the cost τ t f f ( ) ( ) 3 ∫ ∫ ′ = ρ = ρλ τ τ τ 3 3 J c c v t dt c c ( ) p d i f D ci f D i ci 0 0 represents the total fuel spent

Generation of Feasible Trajectories Generation of Feasible Trajectories 4000 3500 800 3000 600 UAV 3 UAV 2 Z(m) 2500 400 UAV 2 UAV 1 200 y(m) 2000 0 1500 UAV 3 0 UAV 1 1000 1000 2000 -2000 Y(m) 3000 500 0 2000 4000 4000 0 X(m) -3000 -2000 -1000 0 1000 2000 3000 4000 5000 5000 6000 x(m) • 2D and 3D view , UAV1 speed (m/sec) 20 T 1 UAV 1 18 16 0 1000 2000 3000 4000 5000 6000 T UAV2 speed (m/sec) 2 25 UAV 2 20 15 T 10 3 0 1000 2000 3000 4000 5000 6000 7000 8000 UAV 3 UAV3 speed (m/sec) 25 20 15 ∩ ∩ T T T 1 2 3 10 0 2000 4000 6000 8000 10000 12000 path length (m) • arrival intervals • feasible velocity profiles

Network Control Flight Test Architecture • UAV – Hardware • Airframe; Sig Rascal 110 – 2.8 meter span, 8 kg, 26 cc gas engine – 2-3 hour endurance – 15-30 m/s velocity • Payload : – PTZ color camera with AF and 10:1 zoom – PC104 with WLAN Mesh Networks card – PC104 for gimbal control and AP interface – PELCO network video server

UAV Path Following UAV Path Following • Problem : follow polynomial trajectories defined using virtual pathlength – time independent – must use UAV attitude – leaves velocity as a degree of freedom for time coordination • Inner/Outer Loop Solution L 1 adaptive controller polynomial Path following Trajectory Pitch rate Onboard A/P (Outer loop) Generation path (Inner loop) Yaw rate commands Onboard PC104 Boundary condiitons User Laptop

UAV Path Following UAV Path Following Key idea: use virtual target to determine desired location on the path Path Q s 1 q y 1 {I} : Inertial Frame Virtual Target P {F} : Serret-Frenet Frame

UAV Path Following UAV Path Following Control the evolution of the virtual target : added degree of freedom Path Q {I} : Inertial Frame P

UAV Path Following (Outer Loop) UAV Path Following (Outer Loop) F φ θ ψ , , φ θ ψ , , Coordinate e e e c c c systems γ ψ , I W 3D Case: Kinematic Kinematic equations equations 3D Case: Kinematic Error equations Error equations Kinematic  = γ ψ  x v cos cos = − τ − κ + θ ψ & s & & (1 y ) v cos cos  1 1 e e  = − γ ψ y v cos sin = − τ κ − ς + θ ψ & y ( s z ) v cos sin  & &  1 1 1 e e   = γ z v sin & = = − ςτ − θ  G z & y v sin  & e 1 1 e    γ      1 0 q & & θ = u   = θ e         ψ − γ 1  0 cos r &      ψ =  & u  ψ e where τ − − 1 torsion φ − φ γ  cos sin cos   ψ ςτ    e e u  sin    q &     θ e = φ φ − sin cos . κ −       curviture   ( )   γ − τ ς θ ψ + κ e cos e u tan cos r &           ψ θ θ e e   cos cos   e e

UAV Path Following (Outer Loop) UAV Path Following (Outer Loop) π /2 δ(ρ) Kinematic Control Law Control Law Kinematic 0 1 1 1 ( ) Let ( ) 2 2 = 2 + 2 + 2 + θ − δ + ψ − δ V ( s y z ) . θ ψ 1 1 1 e e 2 2 c 2 c ρ 1 2 - π/2 -25 -20 -15 -10 -5 0 5 10 15 20 25 Shaping function     z y − − δ = 1 θ δ = 1 ψ sin  1  and sin  1  where     θ ψ d d + ε + ε z y     1 1 τ = + θ ψ & K s v cos cos 1 1 e e θ − δ then sin sin ( ) & = − θ − δ + + δ θ u K c z v e & ≤ − λ V V θ θ θ 2 e 1 1 θ − δ θ e ψ − δ sin sin ( ) ψ & = − ψ − δ − θ e + δ u K c y v cos ψ ψ ψ 3 e 2 1 e ψ − δ ψ e Choose K K 1 , K 2 , K 3 to provide time- -scale separation between scale separation between Choose 1 , K 2 , K 3 to provide time inner and outer loops inner and outer loops

UAV Path Following: Inner Loop UAV Path Following: Inner Loop L 1 adaptive controller polynomial Path following Trajectory Pitch rate Onboard A/P (Outer loop) Generation path (Inner loop) Yaw rate commands Onboard PC104 Boundary condiitons User Laptop

L 1 Adaptive Output Feedback Controller for Systems of Unknown Dimension � System dynamics: � Assumptions: � � � � � Control objective: Courtesy of Naira Hovakimyan, VPI, Blacksburg, VA