1. POLI di MI tecnicolano NAVIGATION AND CONTROL OF AUTONOMOUS VEHICLES WITH INTEGRATED FLIGHT ENVELOPE PROTECTION C.L. Bottasso Politecnico di Milano Workshop CRUI-ACARE Napoli, July 14, 2006

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

4. Flight Envelope Protection for UAVs POLITECNICO di MILANO Background on Flight Envelope Protection CFM CFM working principle: Piloted flight 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 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. V n 1) Predict limit onset 2) Cue pilot and/or modify control actions so as to avoid boundary violation

5. Flight Envelope Protection for UAVs POLITECNICO di MILANO CFM systems CFM systems: full flight envelope Indispensable for utilizing full flight envelope without exceeding aerodynamic, structural, propulsive and controllability limits; conservative 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; difficult but difficult … high agilitymaneuverability Due to high agility and maneuverability of modern high- performance vehicles; multiple multiple Because of need to monitor multiple flight envelope limits, which depend on multiple vehicle states and control inputs. Background on Flight Envelope Protection

6. Flight Envelope Protection for UAVs POLITECNICO di MILANO Previous work Previous work: dynamic trim (Calise & Prasad), peak-response estimation (Horn), non-linear function response (Horn), reactionary envelope protection (Prasad). limitationsapproximations 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. Background on Flight Envelope Protection

7. Flight Envelope Protection for UAVs POLITECNICO di MILANO Optimal Control CFM Proposed work Proposed work: Optimal-control model-based tactical and reflexive control architecture with integrated flight envelope protection. Highlights 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. Flight Envelope Protection for UAVs POLITECNICO di MILANO UAV Control Architecture Target Obstacles Hierarchical three-layer control architecture Hierarchical three-layer control architecture (Gat 1998): Vision/sensor range 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.

9. Flight Envelope Protection for UAVs POLITECNICO di MILANO Goal Goal: Plan paths compatible with the flight envelope boundaries for high performance vehicles in complex/unstructured environments. Tactical Layer: Path Planning Target Approach 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

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

11. Flight Envelope Protection for UAVs POLITECNICO di MILANO Goal 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 Constraints: Tactical Layer: Maneuver Planning à ( y ( T 0 )) 2 [ à 0 m i n ; à 0 max ] ; à ( y ( T )) 2 [ à T m i n ; à T max ] ; J p l an = Á ( y ; u ) ¯ ¯ T + Z T T 0 L ( y ; u ) d t ; f ( _ y ; y ; u ; p ¤ ) = 0 ; g p l an ( y ; u ; T ) 2 [ g p l an m i n ; g p l an max ] : Trajectory to be tracked by reflexive controller y ¤

12. Flight Envelope Protection for UAVs POLITECNICO di MILANO Reflexive Layer: Trajectory Tracking 1. Tracking Plant response Predictive solutions (reduced model) 2. Steering Prediction window Steering window Tracking cost Prediction window Tracking cost Steering window Tracking cost Prediction window Steering window Reference trajectory Optimal Control: min Subjected to: Reduced model equations: Initial conditions: Constraints Constraints: f ( _ y ; y ; u ; p ¤ ) = 0 ; y ( T t rac k 0 ) = e y 0 ; g t rac k ( y ; u ; T ) 2 [ g t rac k m i n ; g t rac k max ] : Goal Goal: track trajectory while satisfying flight envelope constraints. J t rac k = Z T t rac k T t rac k 0 ( jj y ¡ y ¤ jj S t rac k y + jj _ u jj S t rac k _ u ) d t ;

13. Flight Envelope Protection for UAVs POLITECNICO di MILANO Reduced Model Adaption 1. Tracking Plant response 3. Reduced model update Predictive solutions 2. Steering Prediction window Steering window Tracking cost Prediction error Prediction window Tracking cost Steering window Prediction error Tracking cost Prediction window Steering window Prediction error Reference trajectory Goal Goal: reduced modelpredicting the behavior of the plant 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; self-adaptive Reduced model must be self-adaptive (capable of learning) to adjust to varying operating conditions.

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

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

16. Flight Envelope Protection for UAVs POLITECNICO di MILANO Preliminary Results

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

18. Flight Envelope Protection for UAVs POLITECNICO di MILANO 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. Flight Envelope Protection for UAVs POLITECNICO di MILANO 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).