On the Robustness of Consensus-based Behaviors for Robot Swarms

Autonomous Robots (Special Issue Foundations of Resilience for Networked Robotic Systems) Supplementary material

Model Performance


    VSKEY = 1
    vs_value = id
    ROBOTS = 10
     # The robot with the highest id (10) is elected as a leader 
    function init() {
         # Create a virtual stigmergy 
        vs = stigmergy.create(VSKEY)
         # Set onconflict manager 
        vs.onconflict(function(k,l,r) {
         # Return local value if 
         # - Remote value is smaller than local, OR 
         # - Values are equal, robot of remote record is smaller than local one 
        if(r.data < l.data or (r.data == l.data and r.robot < l.robot)) {
            return l
        }
        # Otherwise return remote value 
        else return r
        })
         # Initialize vstig 
        vs.put(VSKEY, vs_value)
        set_leds(255,0,0)
    }
    function step() {
         # Get current value 
        start_timer()
        vs_value = vs.get(VSKEY)
         # If the vs_value corresponds to the highest id 
        if (vs_value == ROBOTS) {
            stop_timer()
            log ("I am robot ", id , "my vs_value is", vs_value, "I reached consensus")
            set_leds(0,255,0)
        }
    }
    }

As discussed in the paper, we have used Statistical Model Checking (SMC) [1] to model and assess the robustness of consensus-based behaviors. In a nutshell, our solution models a robot swarm as a network of priced timed automata NPTA [2]. Each robot in the swarm is represented by a single PTA [2] and is able to communicate its state with its neighborhood. The model is weighted by a set of parameters used to assess the impact of the communication quality and robots’ defects on the consensus behavior of the swarm. Our model is depicted in the figure below. We have studied the performance of our solution by comparing it with a physics-based simulator (ARGoS) [3] and real-world experiments. We have collected the time to convergence while degrading the communication quality (i.e., increasing packet lost probability). The simulations in the three testing environments are performed on an elect leader scenario implemented in a domain specific language Buzz (see the code on the right). The packet loss value is selected from [0%; 25%; 50%; 75%; 95%] and the swarm size is chosen from [5,10].

In ARGoS, we have conducted 500 simulations on cluster, scale free and line swarms with different packet loss probabilities, that is 100 simulations for each packet loss probability. The same has been done in the real word experiments where we used a set of of Khepera IV robots [4] connected by a standard 2.4GHz wireless network.

The following figures depict a comparison between our proposed model (SMC model), ARGoS and real-world experiments. For the 3 studied topologies (Cluster, Scale-free and Line), the figures show that our model exhibits a convergence time similar to what was recorded using ARGoS and Kheperas. These results confirm that our SMC model is representative of the real robot behavior.

5-robot cluster topology align=

Cluster Topology

5-robot cluster topology

5-robot cluster topology

10-robot cluster topology

10-robot cluster topology

Line Topology

5-robot line topology

5-robot line topology

10-robot line topology

10-robot line topology

Scale-Free Topology

5-robot scale-free topology

5-robot scale-free topology

10-robot scale-free topology

10-robot scale-free topology

References


  1. Bulychev, Peter, et al. "UPPAAL-SMC: Statistical model checking for priced timed automata." arXiv preprint arXiv:1207.1272 (2012).
  2. David, Alexandre, et al. "Statistical model checking for networks of priced timed automata." International Conference on Formal Modeling and Analysis of Timed Systems. Springer, Berlin, Heidelberg, 2011.
  3. Pinciroli, Carlo, et al. "ARGoS: a modular, multi-engine simulator for heterogeneous swarm robotics." Intelligent Robots and Systems (IROS), 2011 IEEE/RSJ International Conference on. IEEE, 2011.
  4. Khepera IV, https://www.k-team.com/mobile-robotics-products/khepera-iv/introduction, Last Visit: 28-05-2018.

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