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Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements

European Rotorcraft Forum, September 16 th -19 th 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 16 th -19 th 2008, Liverpool (UK).

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Trajectory Optimization Strategies for the Simulation of the ADS-33 Mission Task Elements

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  1. 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

  2. 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

  3. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) • Objectives • Development of a tool for the simulations of Flight Mechanics maneuvers specificallydesigned 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.

  4. 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 ).

  5. 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.

  6. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) Numerical Solution Strategies Optimal Control Problem Optimal Control Governing Eqs. Indirect Discretize Discretize Direct 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.

  7. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) Numerical Solution Strategies Computational tools involved: • A Flight Simulator Code: FlightLab ( open to other codes like Europa, FDS, etc.); • An interface scheme as much general as possible for the organization and elaboration of the NLP Problem; • A Solver for Non - Linear Parametric Optimization Problems. Optimal Control Problem Discretization • Direct Transcription • Multiple Shooting Interface NLP Problem SQP or IP algorithm Solver Numerical Solution

  8. 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

  9. 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.

  10. 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.

  11. 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. Aggressiveness parameter ( e.g. the maneuver duration ) Integral of the control rates ( to avoid ‘band-bang’ solutions) Depart Maneuver:transition from Hover to Forward Flight @50 Kts.

  12. 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.

  13. 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.

  14. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) Lateral Reposition

  15. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) Lateral Reposition

  16. 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.

  17. 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.

  18. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) Pirouette

  19. European Rotorcraft Forum, September 16th-19th 2008, Liverpool (UK) Pirouette

  20. 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.

  21. 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:

  22. 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.

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