Trajectory Optimization for Safe, Clean and Quiet Flight

Transcription

1 ENRI International Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 29) Trajectory Optimization for Safe, Clean and Quiet Flight Shinji Suzuki, Takeshi Tsuchiya and Adriana Andreeva Dept. of Aeronautics and Astronautics The University of Tokyo Trajectory Optimization Trajectory Optimization is formulated as an optimal control problem that finds the solution that maximizes or minimizes an objective function within constrained boundaries. 1

2 Calculus of variations Find the curve between two points that is covered in the least time by a body that starts at the first point with zero speed. A B Brachistochrone curve Johann Bernoulli Numerical Optimization Pontryagin's Minimum Principle Bellman s Dynamic Programming Direct Numerical Optimization Method Minimize : J Subject to : dx / dt f ( x, u) x( t t t f g( x, u) dt ) x, a( x, u) x( t f h( t ) x f f ) 2

3 Air Trafic Manegement NextGen Trajectory Management: Trajectory management includes any function that affects aircraft trajectory. These functions include trajectory optimization and negotiation with air traffic management, navigation algorithms, delegated aircraft separation applications, or trajectory constraints to avoid weather. The integration of these functions is key to NextGen aircraft functionality. FAA, Aircraft and Operator Requirements Solution Set Smart Sheet Flight Trajectory Optimization Safe Trajectory Trajectory Generation for Emergency Landing Quiet Trajectory Low Noise Trajectory Generation for Helicopter Landing Approach Clean Trajectory Flight Management of Multiple Aircraft for Co2 Reduction 3

4 Real-time Optimization in Emergency Landing Approach Ref: Y. Sakai, S. Suzuki., M. Miwa, T. Tsuchiya, and K. Maui, and H. Tomita, Flight Test Evaluation of Non-Linear Dynamic Inversion Controller, 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV/USA, Purpose In an emergency, as part of a faulttolerant flight control system, generate an optimal flight trajectory to the nearest airport in real time. Funded by the Ministry of Economy, Trade, and Industry (METI) and organized by the Society of Japanese Aerospace Companies. Joint Research Between the Univ of Tokyo and JAXA 4

5 Real-Time Trajectory Optimization method Flight initiation Stage 1 Initial condition Leading path Acquisition of Precise trajectory flight environment and aircraft condition Dense nodes Rough trajectory Sparse nodes Terminal condition Real-Time Trajectory Optimization method Stage 1 Stage 2 Update of flight environment and aircraft condition Precise trajectory Sparse nodes Dense nodes Rough trajectory Terminal condition 5

6 Real-Time Trajectory Optimization method Stage 2 Stage 3 Update of flight environment and aircraft condition Precise trajectory Dense nodes Sparse nodes Rough trajectory Terminal condition Real-Time Trajectory Optimization method Stage 3 Stage 4 Dense nodes Initial condition Update of flight environment and aircraft condition Precise trajectory Terminal condition 6

7 Real-Time Trajectory Optimization method Stage 4 Terminal condition Flight-test results Flight initiation Wind 7

8 Flight-test results Flight initiation Wind Flight Testing 16 8

9 Auto Pilot + Auto Throttle using 4D Navigation Indicated and Tracking Flight Path Indicated path Tracking result m m m X Y Z c c c c pc e c qc a c rc r Slow Medium Fast Flight p Dynamics X q Y Z r Fault Tolerant Flight Control Neural Network can learn the change of dynamic characteristic due to failure in flight. 9

10 Flight Demonstration Small Electric Power UAV Takeoff weight 2 kg Automatic Flight Capability Developed by U of Tokyo and Mitsubishi Electric Co. Ground Noise Reduction in Helicopter Landing Approach Ref: T. Tsuchiya, H. Ishii, J. Uchida, H. Ikaida, H. Gommi, N. Matayoshi, and Y. Okuno, Flight Trajectory Optimization to Minimize Ground Noise in Helicopter Landing Approach, J. Guidance, Control and Navigation (to appear) 1

11 Introduction A major problem in helicopter operations is noise. Operation limit due to the noise Reduction of the ground noise of aircrafts Designing silent aircrafts Flying the existing aircrafts silently Flight reducing the noise generation Flight-path decision regarding land use Purpose Optimizing helicopter flight trajectories to reduce ground noise in the landing approach Trajectory optimization (University of Tokyo) Flight demonstration (JAXA) Collaborative Research 11

12 Flight test field Taiki Multi-Purpose Aeronautical Park Problem definition 4 Runway x y 5 Terminal 1 NM NM Initial 3 NM Measurement Point noise measurement points 1NM=1.852km The Pacific Ocean Find optimal trajectories minimizing the noise levels measured at the five measurement points The optimal trajectories are computed before flight, and a pilot tracks it manually. 12

13 Helicopter dynamics model h Thrust Horizontal-velocity limit 5 horizontal velocity 1 [kt] Climb rate limit climb rate 8 [fpm] Altitude h 48 [ft] y Gravity 3DOF (point-mass model) x Velocity 5 [fpm] 3 h Acceleration limit horizontal acceleration 1.5 [kt/sec] vertical acceleration Roll angle limit roll angle 15 [deg] Altitude h 48 [ft] 1 [fpm/sec] Define the constraint conditions from pilot comments JAXA Simulator Noise source model microphone Noise level L ref [db] Microphone array system The level at a distance of 1 m from the helicopter 13

14 Attenuation model Distance absorption Distance r [m] Atmospheric absorption Sound level [db] Frequency [Hz] Flight-test results Altitude [m] Case 1 Free ascent flight Case 2 No ascent flight Case 3 Normal approach

15 Flight-test results Flight-path angle [deg] Airspeed [m/sec] [sec] Case 1 Free ascent flight Case 2 No ascent flight Case 3 Normal approach Flight scene 15

16 Flight scene Noise-reduction result 7 Temporal-mean noise level L A [db] Test results (Measurement) Optimal solutions 59.3 db (Simulation) 55.7 db 53.9 db 54.1 db 65.6 db Noise reduction 9.9 db 5 Case 1 Free ascent flight Case 2 No ascent flight Case 3 Normal approach 15 16

17 Multiple Aircraft Descent Trajectory Optimization with Air Traffic Constraints for Minimal Fuel Consumption Adriana Hristova Andreeva, Shinji Suzuki (Univ of Tokyo) Eri Itoh (ENRI) Ref: A. Andreeva, S. Suzuki, and E. Ito, Multiple Aircraft Descent Trajectory Optimization with Air Traffic Constraints for Minimal Fuel Consumption, International Conference on Mathematical Problems in Engineering, Aerospace and sciences, ICNPAA-28, Genoa, 28. Optimal Decent Trajectory of Single Aircraft 4 x 14 M(1): OBJECTIVE FUNCTION Top Of Descent z(1)= 33 ft Waypoint i position (x(i), y(i), z(i)) x(n+1)-x(1)= 13nm max = 3 deg z(n+1)= 5 ft M(N+1): dependent on aircraft type Sequential Qudratic ProgrammingSQP MATLAB 34 17

18 Optimal Decent Trajectory of Single Aircraft Higher for longer 6.5 h 1 1 T g 1 K T R M M M 1265 lb fuel _ B747 initial final t total _ B s 35 Two Aircraft Case 36 18

19 Two Aircraft Case 37 Summary A numerical method for trajectory optimization problem Application to real flights Ground noise reduction in helicopter landing approach Trajectory generation in emergency landing approach Air traffic management 19