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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners Case Study: Modelling and Analysis in Real-Time ABS Silvia Lizeth Tapia Tarifa Precise Modelling and Analysis University of Oslo

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

The Cooperative Cleaners Case Study: Modelling and Analysis in Real-Time ABS

Silvia Lizeth Tapia Tarifa

Precise Modelling and Analysis University of Oslo sltarifa@ifi.uio.no

29.11.2013

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Outline

1

Motivation Swarm Robotics ABS Problem Statement

2

The Cooperative Cleaners Case Study Definition The Floor The Cleaning Robots The CLEAN Protocol

3

Results The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

4

Conclusions

5

Future Work

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Swarm Robotics ABS Problem Statement

Swarm Robotics

Group of autonomous, simple and similar robots is coordinated in a way that leads to useful behaviour of the swarm itself. Advantages

Parallelism: robots cooperate and synchronise intelligently. Decentralised: robots operate on local information to accomplish global goals. Adaptability: changing environment. Scalability: e.g., number of robots. Fault-tolerance: robots complete the task, even if some of them fail.

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Swarm Robotics ABS Problem Statement

ABS – Abstract Behavioural Specification Language

ABS is a language for modelling object-oriented systems at an abstract, yet precise level.

Targets software systems that are: concurrent, distributed and object-oriented. Offers a wide variety of modelling options in one framework. (datatypes, functions, classes, concurrency, distribution, etc.). Clear and simple concurrency model that permits synchronous as well as asynchronous communication. Abstracts from implementation choices of data structures. Fully executable with code generators into e.g., Java and Maude. Has a formal semantics.

Real-Time ABS extends the syntax and semantics of ABS in order to allow models with time dependent behaviour.

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Swarm Robotics ABS Problem Statement

About This Thesis

Questions:

1

How can Real-Time ABS be used to naturally model autonomous, decentralised and self-organised systems such as swarm robotics?

2

To what extent can the simulation tool of Real-Time ABS help to analyse the collective behaviour of such systems?

Approach:

Develop a case study from the swarm robotics domain that exploits features of Real-Time ABS such as concurrency, distribution, object-orientation and so forth. Evaluate how well Real-Time ABS can be applied to model and analyse this case study.

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Definition The Floor The Cleaning Robots The CLEAN Protocol

The Cooperative Cleaners Case Study

A group of cleaning robots cooperate to clean a dirty floor

Floor: connected dirty area in Z2. Cleaner:

restricted amount of memory, indirect communication (signals and sensing), local knowledge (e.g., overall topology

  • f the dirty floor is unknown),

movement follows a protocol.

Cleaning the whole floor is an emerging property of the cleaning robots cooperation

Original definition: Cooperative cleaners: A study in ant robotics. Israel A. Wagner, Yaniv Altshuler, Vladimir Yanovski, and Alfred M. Bruckstein, 2008.

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Definition The Floor The Cleaning Robots The CLEAN Protocol

Definition of the Problem: The Floor

Shape: undirected graph G in Z2 with vertices v = (x, y) representing positions connected with edges e = (v, w) following a 4-neighbours relation. Concepts: 4-neighbours, 8-neighbours, boundary, single connected component, critical vertex. The dirty floor Ft is a subgraph of G, t represents time. Initial state: assume G is a single connected component without holes or obstacles, and F0 = G.

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X y

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Definition The Floor The Cleaning Robots The CLEAN Protocol

Definition of the Problem: The Cleaners

Group of identical cleaners moving across Ft. (using 4-neighbours relation). Cleaners can only observe their local environment. Goal: clean the dirty floor (not prior knowledge of the shape or size of the dirty floor). All the cleaning robots start and stop in the same position. Initial position: at the boundary of F0.

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X y

Initial position Local knowledge of diameter 5 Dirty position Clean position RED cleaner BLUE cleaner

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work Definition The Floor The Cleaning Robots The CLEAN Protocol

Definition of the Problem: The CLEAN Protocol

Common protocol: moving and cleaning (non-critical positions) along the boundary of Ft. Cyclic algorithm: in each discrete time step, each cleaner executes one outer cycle. The cleaners “peel” layers from the boundary of Ft, until Ft is cleaned entirely. Protocol must preserve the connectivity of the dirty floor.

From: Cooperative cleaners: A study in ant robotics. Wagner et al.

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Model in Real-Time ABS

1. User-defined datatypes and their associated functions. To represent and manipulate the information of the floor and the cleaners. To record monitoring information.

type Pos = Pair<Int, Int>; type Graph = Set<Pos>; ... type CleanersPerPos = Map <Pos,Cleaners>; ... type FloorPath = List<Triple<Time,Pos,String>>; ... type CleanerPath = List<Pair<Time,Pos>>; ...

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Model in Real-Time ABS

  • 2. Abstracting hardware of cleaners and environment.

Abstracted using method calls. Modelling entity environment. Passive floor vs. reactive environment. Environment Cleaner 1 Cleaner N

. . .

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Model in Real-Time ABS

3. Interpretation and implementation of informal concepts as functions.

(7,3)

(x,y) (x+1,y+1) (x-1,y-1) (x+1,y) (x-1,y) (x-1,y+1) (x+1,y-1) (x,y+1) (x,y-1)

up down left right up right up left down right down left

def PosSet eightNbr(Pos p, Graph g) = let (Pos u)=up(p) in let (Pos ul)=upleft(p) in let (Pos ur)=upright(p) in let (Pos l)=left(p) in let (Pos r)=right(p) in let (Pos d)=down(p) in let (Pos dl)=downleft(p) in let (Pos dr)=downright(p) in dirtySet(set[u,ul,ur,l,r,d,dl,dr],g); def PosSet dirtySet ...

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Model in Real-Time ABS

  • 4. Ambiguities of the CLEAN protocol.

Unexplained “Check Near Completion of Mission” subtask. SWEEP Protocol. Adaptation of the “Calculate waiting dependencies” subtask. Implicit synchronisation: we used fixed timers to guarantee homogeneous

  • progress. We restricted the execution of the CLEAN protocol to only one

cycle per time step.

Task completed? task near completion? Calculate next position Signal next position Resting? Waiting? Move to next position Stop yes no yes no no no yes yes May clean current postion sense sense broadcast sense /broadcast update floor broadcast

(synchronise) (synchronise) (synchronise) (synchronise) (synchronise)

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Model in Real-Time ABS

  • 4. Ambiguities of the CLEAN protocol.

Task completed? task near completion? Calculate next position Signal next position Resting? Waiting? Move to next position Stop yes no yes no no no yes yes May clean current postion

sense sense broadcast sense /broadcast update floor broadcast

(synchronise) (synchronise) (synchronise) (synchronise) (synchronise)

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Analysis and Simulations

During the modelling process:

1

Validate that the manipulation of user-defined datatypes is correct.

2

Validate that the implementation of the concepts given in the problem description is adequate.

3

Observe that the recording of the monitoring information was consistent.

4

Observe that the model satisfies the considered safety properties.

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Analysis and Simulations

Cleaning a five per five square floor using one cleaner

5

4 5 6 7 8

4

3 20 21 22 9

3

2 19 32 23 10

2

1 18+26+30+34 25+31+33 24 11

1

0+16+28+36 15+17+27+29+35 14 13 12

1 2 3 4 5

Path of the cleaner

5 4 5 6 7 8 4 3 20 21 22 9 3 2 19 32 23 10 2 1 34 33 24 11 1 36 35 14 13 12 1 2 3 4 5

Progress of cleaning the floor Total time: 36

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Analysis and Simulations

Cleaning a five per five square floor using two cleaners

5

4 5 6$7$8 9$10 11$12

4

3 13

3

2 26$27 14

2

1 23$24$25$28 15

1

0$20$31 19$21$30 18$22$29 17 16

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8#9 10#11 12#13

4

6 7 16 14#15

3

5 27 17

2

4 19#25#26#28 18

1

2#22#31 3#21#23#30 20#24#29

1 2 3 4 5 5 4 5 9 11 13 4 3 6 7 16 15 3 2 5 27 17 14 2 1 4 28 18 15 1 31 30 29 17 16 1 2 3 4 5

Total time: 31

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Analysis and Simulations

Cleaning a five per five square floor using three cleaners

5

4 5 6 7%8%%9%10%11 12%13%14

4

3 15

3

2 16

2

1 26%27%28%%29%30 17

1

0%22 21%23 20%24%32 19%25%31 18

1 2 3 4 5 5

8#9 10#11#12 13#14#15

4

6 7 16#17

3

5 18

2

4 21#30#31#32 19#20

1

2#26 3#25#27 23#24#28 22#29

1 2 3 4 5 5

11#12#13 14#15#16#17#18

4

10 19

3

8 9 20#21#22

2

7 24#25#26# 23

1

4#30 5#29#31 6#28#32 27

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work The Cooperative Cleaners: Model in Real-Time ABS The Cooperative Cleaners: Analysis and Simulations

The Cooperative Cleaners: Analysis and Simulations

Summary of simulation results.

5x5 ( size = 25) Time 1 cleaner 36 2 cleaners 31 3 cleaners (before livelock) 23 10x10 ( size = 100) 1 cleaner 140 2 cleaners 129 3 cleaners (before livelock) 83 20x20 ( size = 400) 1 cleaner 580 2 cleaners 587

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Conclusions

  • Q1. How can Real-Time ABS be used to naturally model

autonomous, decentralised and self-organised systems such as swarm robotics?

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Conclusions

Real-Time ABS & modelling of swarm robotic systems

Special hardware. Entity environment. Passive environment. Entity environment. Implicit communication. Entity environment. State representation. User-defined datatypes. Work flow. Functional + Imperative. Monitoring information. User-defined datatypes.

  • Synchronisation. Modelling a suitable synchronisation mechanism for a

given concurrent problem represents a challenge on its own (e.g., fixed timers).

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Conclusions

  • Q1. How can Real-Time ABS be used to naturally model

autonomous, decentralised and self-organised systems such as swarm robotics?

  • A1. From the cooperative cleaners case study:

almost naturally model in Real-Time ABS (simple concurrent model, functional layer, imperative layer), it required fairly advanced modelling skills.

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Conclusions

  • Q2. To what extent can the simulation tool of Real-Time

ABS help to analyse the collective behaviour of such systems?

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Conclusions

RTABS & analysis of swarm robotic systems Simulations.

Useful while modelling the case study. Limitations with respect to handling large amount of data.

Analysis of monitoring information.

Insights about the behaviour of the system. Manual analysis. Output format from the tool is not user friendly. Hard to scale in the size of the floor and in the number of cleaners.

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Conclusions

  • Q2. To what extent can the simulation tool of Real-Time

ABS help to analyse the collective behaviour of such systems?

  • A2. From the cooperative cleaners case study:

can be analysed using simulations, restricted analysis to small scenarios, requires reformatting and reorganisation of

  • btained monitoring data.
  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

Future Work

Possible changes to the model and to the protocol itself.

Group of robots with coordinators. Different synchronisation mechanisms (e.g., flexible timers).

Possible extensions to the analysis, using symbolic execution.

Reasoning about invariants using KeY. Reasoning about cost analysis using COSTA.

  • S. Lizeth Tapia Tarifa

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Motivation The Cooperative Cleaners Case Study Results Conclusions Future Work

THANK YOU

  • S. Lizeth Tapia Tarifa

The Cooperative Cleaners Case Study