Route-Planning for Real-Time Safety-Assured Autonomous Aircraft (RTS3A)

Transcription

1 Route-Planning for Real-Time Safety-Assured Autonomous Aircraft (RTS3A) Raghvendra V. Cowlagi 1 Jeffrey T. Chambers 2 Nikola Baltadjiev 2 1 Worcester Polytechnic Institute, Worcester, MA. 2 Aurora Flight Sciences Corp., Mannassas, VA. Session MAO-14, AIAA Aviation 2016 Conference. June 16, Washington, DC.

2 About WPI and WPI-AE Est. 1865; third oldest private technological university in the U.S. 4,100 UG students; 1,900 graduate students; 478 faculty members Aerospace Engineering (AE) Program: est UG students; 30 graduate students; 9 faculty members Degrees offered: B.S., M.S., Combined B.S./M.S., Ph.D. Active research in fluids and plasmas; dynamics, control, and UAVs; renewable energy; mechanics of materials R. V. Cowlagi (WPI) RTS3A Route-Planning 1 / 19

3 Introduction Aurora Orion unmanned aircraft. Self-aware Aerial Vehicle: c 2016 Aurora Flight Sciences Corp. All rights reserved. Autonomously adapts to evolving conditions in environment and own physical health conditions. R. V. Cowlagi (WPI) RTS3A Route-Planning 2 / 19

4 Introduction Aurora Orion unmanned aircraft. Self-aware Aerial Vehicle: c 2016 Aurora Flight Sciences Corp. All rights reserved. Autonomously adapts to evolving conditions in environment and own physical health conditions. Informed by onboard prognostics and health monitoring (PHM) systems: propulsion and airframe stucture. R. V. Cowlagi (WPI) RTS3A Route-Planning 2 / 19

5 Introduction Aurora Orion unmanned aircraft. Self-aware Aerial Vehicle: c 2016 Aurora Flight Sciences Corp. All rights reserved. Autonomously adapts to evolving conditions in environment and own physical health conditions. Informed by onboard prognostics and health monitoring (PHM) systems: propulsion and airframe stucture. Seeks additional information as required for planning and control. R. V. Cowlagi (WPI) RTS3A Route-Planning 2 / 19

6 Scope of RTS3A and Block Diagram Route-planning and PHM systems to enable a self-aware vehicle. Current focus: cruise-phase, constant altitude route-planning. Mission defined by linear temporal logic (LTL) specifications. Simulation demonstration planned for Aurora s Orion platform. Current status: unidirectional interface between PHM systems and route planner. Human Supervisor Propulsion PHM Environment T max Map, no-fly areas, weather φ LTL Specifications Route-Planning Algorithm n struct Airframe Structure PHM R. V. Cowlagi (WPI) RTS3A Route-Planning 3 / 19

7 Linear Temporal Logic Specifications Formal system that can be used to concisely describe a mission. Previously used in software development to describe desired behavior. R. V. Cowlagi (WPI) RTS3A Route-Planning 4 / 19

8 Linear Temporal Logic Specifications Formal system that can be used to concisely describe a mission. Previously used in software development to describe desired behavior. In addition to usual and ( ), or ( ), and not ( ), includes temporal operators such as always ( ), eventually ( ), and until ( ). R. V. Cowlagi (WPI) RTS3A Route-Planning 4 / 19

9 Linear Temporal Logic Specifications Formal system that can be used to concisely describe a mission. Previously used in software development to describe desired behavior. In addition to usual and ( ), or ( ), and not ( ), includes temporal operators such as always ( ), eventually ( ), and until ( ). An LTL formula φ can be represented by a finite state transition system called a Büchi automaton B φ. R. V. Cowlagi (WPI) RTS3A Route-Planning 4 / 19

10 Linear Temporal Logic Specifications Formal system that can be used to concisely describe a mission. Previously used in software development to describe desired behavior. In addition to usual and ( ), or ( ), and not ( ), includes temporal operators such as always ( ), eventually ( ), and until ( ). An LTL formula φ can be represented by a finite state transition system called a Büchi automaton B φ. Example Mission 1: Perform persistent surveillance in region A, visit region B at least once, and avoid no-fly zone C. LTL formula: C B A. R. V. Cowlagi (WPI) RTS3A Route-Planning 4 / 19

11 Linear Temporal Logic Specifications Formal system that can be used to concisely describe a mission. Previously used in software development to describe desired behavior. In addition to usual and ( ), or ( ), and not ( ), includes temporal operators such as always ( ), eventually ( ), and until ( ). An LTL formula φ can be represented by a finite state transition system called a Büchi automaton B φ. Example Mission 1: Perform persistent surveillance in region A, visit region B at least once, and avoid no-fly zone C. LTL formula: C B A. Mission 2: If target found in region A, then report the data at location B; in any case return to base. LTL formula: A (Target A B) (Base) R. V. Cowlagi (WPI) RTS3A Route-Planning 4 / 19

12 State of the Art Discrete abstractions of dynamical systems to design control laws for satisfying LTL specs (Alur et al, 2000; Tabuada & Pappas, 2003) Differential drive robots (Fainekos et al, 2005; Belta et al, 2007) Continuous- and discrete-time linear systems (Kloetzer & Belta, 2008) Traffic networks (Coogan et el, 2015) Low-dimensional nonlinear systems (Zamani et al, 2012) R. V. Cowlagi (WPI) RTS3A Route-Planning 5 / 19

13 State of the Art Discrete abstractions of dynamical systems to design control laws for satisfying LTL specs (Alur et al, 2000; Tabuada & Pappas, 2003) Differential drive robots (Fainekos et al, 2005; Belta et al, 2007) Continuous- and discrete-time linear systems (Kloetzer & Belta, 2008) Traffic networks (Coogan et el, 2015) Low-dimensional nonlinear systems (Zamani et al, 2012) Significant scope for improvements Abstractions of nonlinear systems (e.g. aircraft) have too many states Current methods do not update abstraction when new data is available (e.g. degraded health conditions) Current methods cannot update control laws/plans accordingly R. V. Cowlagi (WPI) RTS3A Route-Planning 5 / 19

14 RTS3A Route-Planning Algorithm Based on square cell decomposition of the environment map (a.k.a. occupancy grid). Each cell is a vertex in a graph G. Main innovation: lifted graphs (Cowlagi & Tsiotras, 2012) G G H Edge transitions in lifted graph G H can encode certain reachability characteristics of an underlying model of aircraft motion. These reachability calculations can be pre-processed offline (Cowlagi & Tsiotras, 2014; Cowlagi & Zhang, 2016) R. V. Cowlagi (WPI) RTS3A Route-Planning 6 / 19

15 RTS3A Route-Planning Algorithm Based on square cell decomposition of the environment map (a.k.a. occupancy grid). Each cell is a vertex in a graph G. Main innovation: lifted graphs (Cowlagi & Tsiotras, 2012) G G H Edge transitions in lifted graph G H can encode certain reachability characteristics of an underlying model of aircraft motion. These reachability calculations can be pre-processed offline (Cowlagi & Tsiotras, 2014; Cowlagi & Zhang, 2016) The lifted graph is a discrete abstraction of aircraft motion, and is used for finding routes that satisfy LTL specifications. The integer parameter H controls the number of states in G H. R. V. Cowlagi (WPI) RTS3A Route-Planning 6 / 19

16 RTS3A Route-Planning Algorithm (continued) Route plan is a discrete plan: channel of square cells. Guarantee that a trajectory satisfying kinematic and dynamic constraints exists within this channel. R. V. Cowlagi (WPI) RTS3A Route-Planning 7 / 19

17 Aircraft Model and Relation to PHM Systems ξ = (x, y, ψ) D := R 2 S 1 is the state of the aircraft model: position of the C.M. and the direction of its velocity vector. Airspeed v assumed constant. Control input u is the steering rate. Bounded control input: u(t) U := [ 1 r, 1 ] r, where r > 0. ẋ(t) = v cos ψ(t), ẏ(t) = v sin ψ(t), ψ(t) = u(t). Note that r is the minimum turn radius. R. V. Cowlagi (WPI) RTS3A Route-Planning 8 / 19

18 Aircraft Model and Relation to PHM Systems ξ = (x, y, ψ) D := R 2 S 1 is the state of the aircraft model: position of the C.M. and the direction of its velocity vector. Airspeed v assumed constant. Control input u is the steering rate. Bounded control input: u(t) U := [ 1 r, 1 ] r, where r > 0. ẋ(t) = v cos ψ(t), ẏ(t) = v sin ψ(t), ψ(t) = u(t). Note that r is the minimum turn radius. We relate r to the structural and propulsive capabilities. R. V. Cowlagi (WPI) RTS3A Route-Planning 8 / 19

19 Minimum Radius of Turn The radius of a coordinated level turn is related to the load factor n Radius of turn = v 2 g n 2 1. R. V. Cowlagi (WPI) RTS3A Route-Planning 9 / 19

20 Minimum Radius of Turn The radius of a coordinated level turn is related to the load factor n Radius of turn = v 2 g n 2 1. Airframe structural load bearing capability places a direct upper bound n struct on the load factor. R. V. Cowlagi (WPI) RTS3A Route-Planning 9 / 19

21 Minimum Radius of Turn The radius of a coordinated level turn is related to the load factor n Radius of turn = v 2 g n 2 1. Airframe structural load bearing capability places a direct upper bound n struct on the load factor. The maximum thrust available T max also restricts the load factor (Anderson, 2000): n prop = q K ( ) Tmax W qc D,0, q := 1 2 ρv 2 /(W /S). Define n max := min(n struct, n prop ), and r := v 2 g n 2 max 1. R. V. Cowlagi (WPI) RTS3A Route-Planning 9 / 19

22 Sample Result #1 Effects on the resultant route of changes in r. 1 unit = cell size. φ 1 = λ 1 λ 2 λ 3 λ 4. λ 1, λ 2, λ 3, λ 4 correspond to all, gray, red, yellow cells, respectively. (a) Spec. φ 1 and r = 0.6 units. (b) Spec. φ 1 and r = 3.0 units. R. V. Cowlagi (WPI) RTS3A Route-Planning 10 / 19

23 Sample Result #2 Effects on the resultant route of changes in the initial state. φ 2 := λ 1 λ 2 λ 3, r = 3.5 units. R. V. Cowlagi (WPI) RTS3A Route-Planning 11 / 19

24 Dynamic Route Modifications Degraded structural and/or propulsive health may require modifications to the planned route and/or trajectory (for same route). R. V. Cowlagi (WPI) RTS3A Route-Planning 12 / 19

25 Dynamic Route Modifications Degraded structural and/or propulsive health may require modifications to the planned route and/or trajectory (for same route). R. V. Cowlagi (WPI) RTS3A Route-Planning 12 / 19

26 Dynamic Route Modifications Degraded structural and/or propulsive health may require modifications to the planned route and/or trajectory (for same route). Fast incremental replanning algorithm: (Zhang & Cowlagi, 2015). R. V. Cowlagi (WPI) RTS3A Route-Planning 12 / 19

27 Probabilistic Feasibility Decisions Recall n struct and T max are parameters that affect the route planner. R. V. Cowlagi (WPI) RTS3A Route-Planning 13 / 19

28 Probabilistic Feasibility Decisions Recall n struct and T max are parameters that affect the route planner. These parameters are estimated by PHM systems, therefore uncertain. R. V. Cowlagi (WPI) RTS3A Route-Planning 13 / 19

29 Probabilistic Feasibility Decisions Recall n struct and T max are parameters that affect the route planner. These parameters are estimated by PHM systems, therefore uncertain. Let N struct and T be random variables representing the estimated parameters. The characteristics of these r.v.s are determined by the PHM systems. R. V. Cowlagi (WPI) RTS3A Route-Planning 13 / 19

30 Probabilistic Feasibility Decisions Recall n struct and T max are parameters that affect the route planner. These parameters are estimated by PHM systems, therefore uncertain. Let N struct and T be random variables representing the estimated parameters. The characteristics of these r.v.s are determined by the PHM systems. The feasibility decisions in the previous flowchart are therefore inherently probabilistic, and must be characterized accordingly. R. V. Cowlagi (WPI) RTS3A Route-Planning 13 / 19

31 Probabilistic Feasibility Decisions Recall n struct and T max are parameters that affect the route planner. These parameters are estimated by PHM systems, therefore uncertain. Let N struct and T be random variables representing the estimated parameters. The characteristics of these r.v.s are determined by the PHM systems. The feasibility decisions in the previous flowchart are therefore inherently probabilistic, and must be characterized accordingly. R. V. Cowlagi (WPI) RTS3A Route-Planning 13 / 19

32 Probabilistic Feasibility Decisions (continued) Based on the physical relationships between r and the parameters n struct and T max, we can find a derived distribution R for the minimum radius of turn: where F R (r) = F Rstruct (r)f Rprop (r), f R (r) = f Rstruct (r)f Rprop (r) + f Rprop (r)f Rstruct (r), F Rstruct (r) = 1 F Nstruct ( v 2 + gr gr ), f Rstruct (r) = v 2 + gr F Rprop (r) = 1 F Nprop ( gr ), f Rprop (r) = f Nprop (n) = 2WKn q f T ( W (Kn2 + C D,0 q 2 ) q 2 ). v 2 gr 2gr 2 v 2 + gr f N struct ( v 2 gr 2gr 2 v 2 + gr f Nprop ( v 2 + gr ), gr v 2 + gr ), gr R. V. Cowlagi (WPI) RTS3A Route-Planning 14 / 19

33 Probabilistic Feasibility Decisions (continued) Based on the physical relationships between r and the parameters n struct and T max, we can find a derived distribution R for the minimum radius of turn: where F R (r) = F Rstruct (r)f Rprop (r), f R (r) = f Rstruct (r)f Rprop (r) + f Rprop (r)f Rstruct (r), F Rstruct (r) = 1 F Nstruct ( v 2 + gr gr ), f Rstruct (r) = v 2 + gr F Rprop (r) = 1 F Nprop ( gr ), f Rprop (r) = f Nprop (n) = 2WKn q f T ( W (Kn2 + C D,0 q 2 ) q 2 ). v 2 gr 2gr 2 v 2 + gr f N struct ( v 2 gr 2gr 2 v 2 + gr f Nprop ( F R (r ) > p threshold Planned route is still feasible. v 2 + gr ), gr v 2 + gr ), gr R. V. Cowlagi (WPI) RTS3A Route-Planning 14 / 19

34 Conclusions and Future Work Road to the self-aware aerial vehicle: user-friendly LTL specifications, route-planning algorithm to satisfy these specifications. Method of lifted graphs enables such a route-planning algorithm, whereas other methods from the literature do not suffice. Dynamic modifications to route are based on probabilistic decision of whether existing route is still feasible. Implementation in progress. R. V. Cowlagi (WPI) RTS3A Route-Planning 15 / 19

35 Conclusions and Future Work Road to the self-aware aerial vehicle: user-friendly LTL specifications, route-planning algorithm to satisfy these specifications. Method of lifted graphs enables such a route-planning algorithm, whereas other methods from the literature do not suffice. Dynamic modifications to route are based on probabilistic decision of whether existing route is still feasible. Implementation in progress. Future work: particle dynamical model of aircraft; similar connections between health parameters and route planner. Future work: Bidirectional interactions between route planner and PHM systems; Route planner queries PHM systems for critical parameter estimate updates. PHM systems use planned route in predictive models to update estimates. R. V. Cowlagi (WPI) RTS3A Route-Planning 15 / 19

36 Acknowledgements Graduate students at WPI: Zetian Zhang. Benjamin S. Cooper. Ruixiang Du. US Air Force SBIR Phase 2 Award #FA P-0034; program manager F. Zahiri. Aurora Flight Sciences Corp. personnel: Jeffrey T. Chambers (PI for SBIR-P2 award). Nikola Baltadjiev. Gray Riley. Sachin Jain. rvcowlagi@wpi.edu wpi.edu/ rvcowlagi. R. V. Cowlagi (WPI) RTS3A Route-Planning 16 / 19

37 Additional Technical Details R. V. Cowlagi (WPI) RTS3A Route-Planning 17 / 19

38 Workspace Cell Decomposition Environment decomposed into convex regions called cells, which are either free or full of obstacles. Each cell associated with a vertex in a graph G = (V, E), and geometrically adjacent pairs of cell associated with edges. A path in this graph is a sequence of vertices (v 0, v 1,..., v P ), which corresponds to a sequence of successively adjacent cells: the route. Cell decomposition transforms route-planning to a graph search problem, for which several fast algorithms are available. R. V. Cowlagi (WPI) RTS3A Route-Planning 18 / 19

39 Lifted Graph Vehicle kinematic and dynamic motion characteristics cannot be encoded in edge transitions in G. Alternative: consider successions of edges in G; leads to lifted graph G H = (V H, E H ) with vertices V H := {(v 0,..., v H ) : (v k 1, v k ) E, k = 1,..., H, v k v m, for k, m {0,..., H}, with k m}. = R. V. Cowlagi (WPI) RTS3A Route-Planning 19 / 19