Transcript Document

European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Trajectory Optimization Strategies for the
Simulation of the ADS-33 Mission Task Elements
C.L. Bottasso, F. Scorcelletti, G. Maisano, A. Ragazzi
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
OUTLINE
• Objectives and Motivations
• Introduction to Trajectory Optimization
• Description of the Trajectory Optimization Program (TOP)
• ADS-33 Mission Task Elements (MTEs)
• MTEs Simulation Strategy
• Numerical Examples
• Conclusions and Future Work
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Objectives
• Development of a tool for the simulations of Flight Mechanics
maneuvers specifically designed for the Handling Qualities
assessment of a generic Helicopter.
• The code should be conceptually interfaced to every kind of black-
box Flight Simulator.
Motivations
• Analytical Prediction of the Handling Qualities level of a specific
vehicle.
• Support to the Flight Test trials; extensive simulations can be
performed with no risk and zero cost.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Trajectory Optimization
• Flight Mechanics Simulators are typically used for dynamic response evaluation;
• The Trajectory Optimization process allows to evaluate the optimal control time
histories and the associated vehicle response minimizing an appropriate cost
function;
• The minimization must satisfy a series of constraints ( flight envelope limits, safety
requirements, etc. )
• Several Rotorcraft Maneuvers can be conveniently analyzed using a Trajectory
Optimization approach ( Category-A Certification, Optimal Autorotation, Emergency
Maneuvers, Handling Qualities Mission Task Elements ).
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
The Optimal Control Problem
Find the optimal control policy
and the associated state history
which minimize the following cost function:
The minimization is subjected to a set of constraints:
Model equations of motion ( FLIGHTLAB MODEL )
Boundary conditions - TRIM
Integral conditions
All-time conditions – FLIGHT ENVELOPE LIMITS,
PATH CONSTRAINTS, etc.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Numerical Solution Strategies
Optimal Control
Problem
Discretize
Optimal Control
Governing Eqs.
Indirect
Direct
Discretize
Numerical solution
NLP Problem
Indirect approach:
• Need to derive optimal control governing equations;
• Need to provide initial guesses for co-states;
• For state inequality constraints, need to define a priori constrained and unconstrained sub-arcs.
Direct approach:
• All above drawbacks are avoided.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Numerical Solution Strategies
Optimal Control
Problem
Discretization
Interface
• Direct Transcription
• Multiple Shooting
Computational tools involved:
 A Flight Simulator Code: FlightLab
( open to other codes like Europa, FDS, etc.);
 An interface scheme as much general as possible
NLP Problem
for the organization and elaboration of the NLP
Problem;
Solver
SQP or IP algorithm
A Solver for Non - Linear Parametric Optimization
Problems.
Numerical
Solution
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Direct Transcription Technique
• Partition of the simulation domain:
NLP variable
• Discretization of the Cost Function:
• Discretization of the Constraints:
NON LINEAR PROGRAMMING PROBLEM
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
ADS-33 Mission Task Elements
The MTEs are flight tests, precisely defined to quantify the Handling Qualities properties of a rotorcraft.
Slalom
Pirouette
Lateral Reposition
For each maneuver trajectory constraints
( constraints on the vehicle states ) and final
time are precisely defined in the ADS-33
specification.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Flight Mechanics Model
• The trajectory optimization code ‘works’ with a FLIGHTLAB ‘stand-alone’ model;
• Generic medium-size four-bladed utility helicopter in the 9 ton class;
• Three-dimensional rigid body dynamics;
• Rotor forces and moments are computed by an actuator disk model with uniform
inflow;
• Look-up tables for quasi-steady aerodynamics of the lifting surfaces;
• A ground effect is used to accurately reproduce the MTE flight tests;
• Inputs: MR collective, TR collective, Long. Cyclic, Lat. Cyclic.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Mission Task Elements as Optimal Control Problems
Specific constraints are then enforced to take
into account the ADS-33 trajectory constraints.
Depart Maneuver:
Aggressiveness parameter
Integral of the control rates
( e.g. the maneuver duration )
( to avoid ‘band-bang’ solutions)
transition from Hover to Forward Flight @50 Kts.
64
0
= 1
= 5
 = 10
62
-5
60
58
B1 [%]
 [deg]
-10
56
-15
54
=1
=5
 =10
-20
52
50
-25
0
2
4
6
8
t [s]
10
12
14
48
0
2
4
6
8
10
12
14
t [s]
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Lateral Reposition
• Lateral translation of 400 ft;
• Initial and final positions are 35 ft above ground (ground effect);
• Longitudinal and Vertical error of 10 ft;
• Heading misalignment of 10 deg;
• The maneuver must be accomplished within 18 s.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Lateral Reposition
• Minimum time maneuver;
• Path constraints are imposed through bounds on state variables:
• The simulation is computed over a Chebychev computational grid of 80 time elements;
• The guess solution is represented by a steady lateral flight condition.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Lateral Reposition
400
10
350
300
5
Y [ft]
X [ft]
250
0
200
150
-5
100
50
-10
0
2
4
6
8
10
0
12
0
2
4
6
t [s]
8
10
12
8
10
12
t [s]
12
-20
10
-25
 [deg]
-Z [ft]
8
-30
6
4
-35
2
-40
0
2
4
6
8
t [s]
10
12
0
0
2
4
6
t [s]
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Lateral Reposition
94
46
44
92
42
90
88
 TR [%]
 MR [%]
40
86
38
36
34
84
32
82
30
80
0
2
4
6
8
10
28
12
0
2
4
6
t [s]
8
10
12
8
10
12
t [s]
58
63
56
62
61
54
60
B1 [%]
A1 [%]
52
50
59
58
48
57
46
56
44
42
55
0
2
4
6
8
t [s]
10
12
54
0
2
4
6
t [s]
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Pirouette
• Radial constraints:
• Heading error:
• The reference circumference is 30 ft above ground;
• Vertical error of 10 ft;
• The maneuver must be accomplished within 45 s.
 The maneuver is divided in 3 phases
( 2 transitions & 1 steady state );
 Each transition is solved on a Chebychev grid of 50 time elements (minimum time);
 A turning trim in lateral flight is used as guess.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Pirouette
Path constraints:
REMARK: Note that for the transitions the final/initial position and heading are unknown.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Pirouette
6
0
4
-1
2
-2
 [deg]
-2
-4
-3
-4
-6
-5
-8
-6
-10
-12
0
5
10
15
20
25
30
35
-7
0
40
5
10
t [s]
15
20
25
30
35
40
t [s]
400
350
300
250
 [deg]
 [deg]
0
200
150
100
50
0
0
5
10
15
20
25
30
35
40
t [s]
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Pirouette
 (t) -  (t)
10
10
5
5
[deg]
[ft]
r(t) - R
0
0
-5
-5
-10
-10
0
5
10
15
20
t [s]
25
30
35
40
0
5
10
15
20
25
30
35
40
t [s]
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Slalom
• Obstacles are located at 500 ft intervals;
• Their distance form the centerline is  50 ft;
• A maximum lateral error of 100 ft is allowed;
• Flight below 100 ft w.r.t. ground;
• Flight Velocity | V | > 60 Kts.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Slalom
• The maneuver is computed on a uniform grid of 100 time elements (minimum time);
• The guess solution was assembled gluing a series of elementary turns.
Path constraints:
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements
European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK)
Conclusions
• A numerical algorithm for the Trajectory Optimization was implemented and tested.
The code can be easily coupled with complex Rotorcraft Simulators.
• TOP has been used with a FLIGHTLAB rotorcraft model in order to simulate the
ADS-33 MTE scenarios.
Future Work
• Simplified pilot models can be introduced in the optimization process in order to
improve the realism of the simulations.
• Multiple Shooting simulations will allow to use more sophisticated fine-scale Flight
Mechanics Models.
Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements