Modular Specification of Hybrid Systems in CHARON

1. Modular Specification of Hybrid Systems in CHARON R. Alur, R. Grosu, Y. Hur, V. Kumar, I. Lee University of Pennsylvania SDRL and GRASP

2. Software Framework for the Deployment of Multiple Robots • 1. High-level modeling language • - platform independent • hierarchical and modular • specify modes and constraints • hierarchical and sequential composition of modes • parallel composition of agents

3. Software Framework for the Deployment of Multiple Robots • 2. Tools for design, programming, and analysis • simulation and execution • analysis and optimization • automated generation of code • 3. Demonstrate on multiple coordinating robots

4. Challenges in Coordinating Multiple Robots • Large number of modes • Individual modes are well understood, but not their interaction. • Software design • modes are designed bottom up. • coordination protocols are traditionally designed top down.

5. CharonFramework Architecture CHARON Code (High level language) Charon to Java Translator Java Libraries Drivers Java Code Simulator Code Generator Control Code Generator Analysis Human Interface

6. Charon Language • Individual components described as agents • Composition, Instantiation, and Hiding • Individualbehaviors described as modes • Encapsulation, Instantiation, and Scoping • Support for concurrency • Shared variables as well as message passing • Support for discrete and continuous behavior • Well-defined formal semantics

7. Robot Team Approaching a Target T

8. write diff analog position pos1, pos2 class position { float x; float y;} Robots pos1 pos2 Monitor Architectural Hierarchy • Variables Specifiers • Range: discrete/analog • Computation: diff/alg • Access: read/write/local

9. Robots r1Est1 Robot1 Robot2 Robots r1Est2 pos1 pos2 r2Est1 Monitor r2Est2 pos1 pos2 Architectural Hierarchy

10. pos = target local diff analog timer awTarget dPlan iAway atTarget dStop iAt arrive r2Est1 Robot1 dTimer r2Est2 . pos.x = v * cos(phi) pos.y = v * sin(phi) . r1Est1 r1Est2 timer/updateFreq = 0 . pos timer = 1 moving dSteer aOmega iFreq sense sensing dStop iConst arrive move omega = k * (theta – phi) Behavioral Hierarchy

11. Related Work • Hybrid automata [ACH+95] • Analysis, model checkers HyTech [AHH96, HHW95] • No compositional models, no hierarchy • I/O automata [LSVW96] and Hybrid Modules [AH97] • Compositional models • No behavioral hierarchy • SHIFT [DGS97] and HyCharts [GSB98] • Allow hierarchic specification of hybrid behavior • No concern for modular simulation • UML [BJR97]and (hybrid) Statecharts [Har87] • Hierarchical but not modular • Stateflow • Hierchic specification but only for dynamic behavior Charonis a modeling language for hybrid systems reflecting the current state of the art both in formal and object oriented methods(UML)

12. Modular Simulation • Goal • Simulation is efficient and accurate • Integration of modes at different time scales • Integration of agents at different time scales • Modes are simulated using local information • Submodes are regarded as black-boxes • Submodes are simulated independently of other ones • Agents are simulated using local information • Agents are regarded as black-boxes • Agents are simulated independently of other ones

13. Pick up the agents withminimum • andsecond minimumreached time. time 2. Compute the time round interval d for the minimum agent, such that its absolute time may exceed with at most dt the time reached by the second one t+dt d 3. The agent executes a time round. This ends before d if the invariants of the agent were violated. Then, an actual time increment would be e. e t Agents A1 A3 A2 The Simulator 4. The agent executes an update round to synchronize the discrete variables with the analog ones. 5. The state of the agent get visible to other agents

14. 1. Getintegration time d and invariants from the supermode (or the scheduler). d, xInv dt, yInv - Simplify all invariants. . . . - Predictintegration stepdt based on d and the invariants. x y z - Execute time round of the active submode and get state s and time elapsed e. e, sz - Integrate for time e and get new state s. t+e, sy - Returns and t+eif invariants were violated. Time Round of a Mode(Agent) 2. While(time t = 0; t <= d)do: - Increment t = t+e. 3. Returns and d

15. awTarget moving arrive atTarget sense move sensing Update Round of a Mode(Agent) • Innermost transitions • havehigher priority • Default transitionsare • taken ifall other • transitions are disabled • Group transitionsstart • at thedefault exit points • Transitions to history • are transitions to the • default entry point

16. . y = 2u x1 < a x2 = -1 strMinus dY iStrM aStrM Env . x1 = u u s2u Hyst up dY iUp aUp -a a+2 u2p 1 strPlus dY iStrP aStrP -1 -(a+2) a Hysteresis Example inc dX1 dec inc dec dX1

17. Global vs Modular Simulation

18. Modular Simulation Error

19. Current Implementation Status CHARON Specification CHARON Parser • Work to date • CHARON semantics • Parser for CHARON • Internal representation • Current work • Type checker • Modular simulation scheme • Internal representation generator Type Checker Syntax Tree Internal Representation Generator Internal Representation Control Code Generator Simulator Generator Model Checker

20. Ongoing Research • Distributed simulation • Accurate event detection • And modes and And/Or hierarchies • Exploiting the hierarchy in model checking

21. Wrap-Up • Charonis a language for embedded systems • reflecting the current state of the art both • in formal and object oriented methods(UML) • Its explicit support for a mixed visual/textual notation should improve communication among the various communities involved in an embedded system project.