Outline

1. NAVIGATION AND CONTROL OF AUTONOMOUS VEHICLES WITH INTEGRATED FLIGHT ENVELOPE PROTECTIONC.L. BottassoPolitecnico di MilanoWorkshop CRUI-ACARE Napoli, July 14, 2006

2. Outline • Background on flight envelope protection; • Proposed research: model-based optimal control with integrated flight envelope protection; • - Envelope-aware path planning (tactical control layer); • - Envelope-aware path tracking (reflexive control layer); • - Adaptive reduced vehicle model; • Preliminary results; • Conclusions and outlook.

3. Background on Flight Envelope Protection • Care-Free Maneuvering (CFM): • Monitor and maintain vehicle operation within an operational envelope (Massey 1992). • Example: n n V V Pull-up with flight envelope violation Pull-up within the flight envelope

4. Background on Flight Envelope Protection n 1) Predict limit onset • CFM working principle: • Piloted flight: • CFM cues pilot (often tactile cues through force-feel feedback on active control stick, which can be overridden by the pilot), and/or • CFM interacts with Flight Control System (FCS), which in turn corrects the command inputs. • Autonomous flight: • CFM interacts with trajectory planner (tactical controller) so as to generate a safe-to-be-tracked response profile, and/or • Interacts with trajectory tracker (reflexive controller), by correcting the command inputs. 2) Cue pilot and/or modify control actions so as to avoid boundary violation V

5. Background on Flight Envelope Protection • CFM systems: • Indispensable for utilizing full flight envelope without exceeding aerodynamic, structural, propulsive and controllability limits; • Avoid need for conservative envelope limits (reduced weight, cost, etc. and/or improved performance, safety, handling qualities, etc.); • Contribute to the reduction of pilot work-load in piloted systems; • but difficult … • Due to high agility and maneuverability of modern high-performance vehicles; • Because of need to monitor multiple flight envelope limits, which depend on multiple vehicle states and control inputs.

6. Background on Flight Envelope Protection • Previous work: • dynamic trim (Calise & Prasad), peak-response estimation (Horn), non-linear function response (Horn), reactionary envelope protection (Prasad). • Available methods suffer from various limitations and approximations, especially for UAVs: • FCS can not typically deal directly with constraints ⇨ coupling with CFM not trivial, possibly inefficient/ineffective; • Adaptive limit parameter estimation does not exploit adaptive capabilities of FCS; • Trajectory planning typically very simple (interpolation of way-points), unable to deal directly with constraints ⇨ no guarantee of feasible within-the-boundary profile.

7. Optimal Control CFM • Proposed work: • Optimal-control model-based tactical and reflexive control architecture with integrated flight envelope protection. • Highlights: • Optimal control can rigorously deal with constraints; • Optimal-control planning of trajectories (tactical layer) ⇨ guaranteed feasibility; • Optimal-control tracking (reflexive layer) ⇨ constraints accounted for also at the level of the FCS; • Adaptive reduced model ⇨ improves both FCS and CFM performance.

8. UAV Control Architecture Hierarchical three-layer control architecture (Gat 1998): • Strategic layer: assign mission objectives (typically relegated to a human operator); • Tactical layer: generate vehicle guidance information, based on input from strategic layer and sensor information; • Reflexive layer: track trajectory generated by tactical layer, control, stabilize and regulate vehicle. Vision/sensor range Obstacles Target

9. Tactical Layer: Path Planning • Goal: • Plan paths compatible with the flight envelope boundaries for high performance vehicles in complex/unstructured environments. • Approach: at each time step • Discretize space and identify candidate way-points; • Compute path by connecting way-points (A* search); • Smooth path so as to make it compatible with flight envelope boundaries, using motion primitives. Obstacles Target

10. Tactical Layer: Motion Primitives • Vehicle model: maneuver automaton (Frazzoli et al. 2001), only two possible states: trim or maneuver (finite-time transition between two trims). • Highlights: • Highly efficient transcription of the vehicle dynamics in small solution space; • Transcribed dynamics compatible with flight envelope boundaries. T6: high speed right turn T5: high speed left turn T2: high speed level flight All maneuvers designed using optimal control with envelope protection constraints M21: deceleration from T2 to T1 T1: low speed level flight T4: low speed right turn T3: low speed left turn

11. T l l l p a n Z ( ( ( ( ( ( ) ) ) ) [ [ ) ) [ ] ] ] à à f à à à à ¤ ¤ _ T T T p a n p a n 0 2 2 2 g y y y y y y u u p g g = T T l 0 0 0 ¯ i ( ) ( ) p a n ; ; ; ; ; ; ; ; ; ; ; : Á d i i J L m a x t m n + m m n n m m a a x x y u y u = ¯ ; ; ; T T 0 Tactical Layer: Maneuver Planning • Goal: plan a maneuver which is compatible with the flight envelope boundaries. • Optimal control: min • Subjected to: • Reduced model equations: • Boundary conditions: (initial) • (final) • Constraints: Trajectory to be tracked by reflexive controller

12. k t r a c k k k k T t t t t ( ( ( ) ) ) [ ] e f ¤ T _ T r a c r a c r a c r a c 0 Z 2 y g y y y u u p y g g = = 0 i 0 ; ; ; ; ; ; ; ; : k m a x m n t ( j j j j j j j j ) ¤ d J _ r a c t ¡ + y y u = k k t t S S r a c r a c ; _ y u k t T r a c 0 Reflexive Layer: Trajectory Tracking Goal: track trajectory while satisfying flight envelope constraints. Prediction window Prediction window Tracking cost Tracking cost Prediction window Tracking cost Reference trajectory Steering window Steering window Plant response Predictive solutions (reduced model) Steering window 2. Steering 1. Tracking • Optimal Control: min • Subjected to: • Reduced model equations: • Initial conditions: • Constraints:

13. Reduced Model Adaption • Goal: • Develop reduced model capable of predicting the behavior of the plant with minimum error (same outputs when subjected to same inputs) ⇨ critical for faithful flight envelope protection; • Reduced model must be self-adaptive (capable of learning) to adjust to varying operating conditions. Prediction window Prediction window Tracking cost Tracking cost Prediction window Tracking cost Reference trajectory Prediction error Prediction error Steering window Steering window Prediction error Plant response Predictive solutions Steering window 1. Tracking 2. Steering 3. Reduced model update

14. Reduced Model Adaption • Approach: • Neural-augmented reference model (Bottasso et al. 2004), using extended Kalman parameter identification. • Idea: • A non-linear parametric function is identified online to capture the mismatch (defect) between the plant and a non-linear reference vehicle model. Reference model Plant • Highlights: • Good predictions even before any learning has taken place (otherwise would need extensive pre-training); • Easier and faster adaption: the defect is typically a small quantity, if the reference model is well chosen. Augmented reference Short transient = fast adaption

15. Preliminary Results Procedures tested in a virtual environment using a high-fidelity helicopter flight simulator. Rotorcraft trajectory Acceleration, climb, aggressive turn, descent, deceleration, with prescribed state and control limits: Planned path Rotorcraft trajectory when tracking non-compatible path

16. Preliminary Results

17. Conclusions • Proposed a procedure for navigation and control of vehicles which respects the flight envelope; • Flight envelope constraints are accounted for directly both at the planning and tracking levels for the first time; • Applicable to both fixed and rotary wing vehicles; • Full system applicable to UAVs, but components applicable to piloted flight to provide cues to pilots; • On-line model adaption improves performance and limit avoidance; • Basic concept demonstrated in a virtual environment.

18. Outlook • Real-time implementation and integration in a rotorcraft UAV (in progress) at the Autonomous Flight Lab at PoliMI; • Testing and extensive experimentation; • Integration with vision for fully autonomous navigation in complex environments. • Develop cueing system and test in the future flight simulation lab at PoliMI.

19. Acknowledgements Work in collaboration with: A. Croce (Post-Doc), L. Fossati (Graduate student), D. Leonello (Ph.D. candidate), G. Maisano (Ph.D. candidate), R. Nicastro (Graduate student), L. Riviello (Ph.D. candidate), B. Savini (Ph.D. candidate).