Distributed Spatial Awareness for Robot Swarms

TL;DR

This work uses local observations by robots of each other and Gaussian belief propagation message passing combined with continuous swarm movement to build a global and distributed swarm-centric frame of reference that allows new swarm algorithms to be built.

Abstract

Building a distributed spatial awareness within a swarm of locally sensing and communicating robots enables new swarm algorithms. We use local observations by robots of each other and Gaussian Belief Propagation message passing combined with continuous swarm movement to build a global and distributed swarm-centric frame of reference. With low bandwidth and computation requirements, this shared reference frame allows new swarm algorithms. We characterise the system in simulation and demonstrate two example algorithms.

Figures (7)

• Figure 1: Simulation of robots performing DSA-RW to locate cargo carriers, with various elements of the visualisation labelled. Within the carrier squares are overlayed the current swarm estimates of the carrier position, already showing good correspondence after two minutes of simulated time.
• Figure 2: Robots creating connected factor graphs. Left: Two robots move on trajectories, making odometry measurements, that bring them within sensing range of each other. Right: The internal factor graphs that are created on each robot, assuming $n_{window}=4$ and some time has passed. The oldest variable node in each graph, $x_3,y_3$, has an anchor factor. Between each variable node is an odometry measurement factor node. In timestep $ts_5$, robot $y$ has observed robot $x$, creating an outward-facing relative position measurement factor. In $ts_6$, both robots have observed each other.
• Figure 3: Illustration of shared reference frame convergence. 1) All robots start by thinking they are at the centre of the swarm. 2) Observation and communication imposes constraints on location of the swarm centroid; the top two robots communicate.. 3) .. and each robot updates its own estimate. 4) More communication imposes further constraints. 5) Origin estimates move closer.. 6) ..and approach convergence.
• Figure 4: Left: Convergence time with different factor graph update rates and different arena areas, with fixed robot density. Reduction in convergence time is minimal below 0.1s update period. Right: For a fixed update period of 0.1s and fixed arena area of 25m^2, computation, convergence time, and particularly bandwidth are dependent on robot density.
• Figure 5: The distribution of the robot encounter measure $t_{met\_half}$ over 2886 simulations with different numbers of robots between 5 and 100, and different arena sizes between 4m^2 and 100m^2. Using a constant $\beta=3$ ensures the proxy convergence time $t_{proxyconv}$ exceeds the true convergence time $t_{conv}$ in more than 95% of simulation. Right scatter plot coloured according to arena area.