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Abstract
We present a method for controlling a swarm using its spectral decomposition---that is, by describing the set of trajectories of a swarm in terms of a spatial distribution throughout the operational domain---guaranteeing scale invariance with respect to the number of agents both for computation and for the operator tasked with controlling the swarm. We use ergodic control, decentralized across the network, for implementation. We demonstrate the scale-invariance and dynamic response of our system in a field relevant simulator on a variety of tactical scenarios with up to 50 agents. (shown below). The code for our system can be found at: https://github.com/MurpheyLab/rover_decentralized_ergodic_control
Introduction
One of the biggest problems in the field of swarm robotics is that it is difficult for human users to reap the potential benefits of swarm robotic systems (i.e., robustness, information gains) due to the high cognitive load associated with controlling swarms. Cognitive load has been shown to scale with both the size of the swarm a user controls, as well as with the complexity of the environment in which the swarm and user operate (due to both agent-agent interactions and the length of time the operator has to reason about decisions). Swarm operators need interfaces and control algorithms that are scale-invariant to enable operators to specify the same objective to swarms of different sizes without modification. Two major components are needed to create such a system—an interface to transform user input into scale-invariant commands and a control algorithm to automatically and flexibly adapt user commands to changes in swarm size (which may occur due to communication dropouts, hardware failures, or newly available robots joining the swarm). Our work develops a method for scale-invariant swarm control with a touch interface and a decentralized control algorithm. The touch interface enables users to prescribe strategies at the swarm-level rather than at the individual agent-level. Gestures from the touch interface are converted to commands for the swarm using a decentralized ergodic coverage approach, which is invariant to swarm size. Each agent responds to the desired coverage map in real-time. These two components enable human operators to dynamically re-plan with a swarm for exploration and distributed sensing by using ergodicity as a quantitative measure of information in the environment. Using our system, the operator maps visual input from both their line of sight in the environment and from the command interfaces at their disposal to a spatial representation of information that they then send as a command to their swarm via their user interface. Each member of the swarm runs a decentralized ergodic coverage algorithm that transforms user commands into swarm trajectories. The combination of visual input the operator receives, the user interfaces they send swarm commands through, and the decentralized ergodic coverage algorithm running on each member of the swarm enables the swarm to converge to the operator’s spatial representation of information regardless of how many agents in the swarm the operator has at their disposal at any point in time. Since the internal process an operator uses to map visual input to expected information content is qualitative (in the sense that we do not have a model of how humans make these choices), our system affords flexibility to the operators—different operators can send different commands (representing spatial information) to their swarms based upon the same visual input.
Copy of multimodal_50agents_20xspeed.mp4Multimodal Target Specification
This video (20x speed) shows a swarm of 50 agents converging to a multimodal user target specification that contains two areas with high expected information content (shown in blue in the target distribution plot) and two areas with low expected information content (shown in red in the target distribution plot). The rest of the environment has medium expected information content (shown in white in the target distribution plot).
The plot on the left shows the normalized ergodic metrics for three different swarm sizes converging to the same multimodal target specified above. The normalized ergodic metric for all three swarm sizes converges to near zero at roughly the same time and has the same trend, indicating the operator can expect similar behavior for a given target across swarm size.
Copy of converge_repel_50agents_video_20x_speed.mp4Converge and Repel Target Specification
This video (20x speed) shows a swarm of 50 agents converging upon a specific area specified by the user at the center of the environment and then repelling from that same area after the user re-specifies this area as a region to avoid.
Copy of 50agents_bullseye_video_20x_speed.mp4Non-Trivial Multimodal Target Specification
This video (20x speed) shows a swarm of 50 agents converging on a non-trivial multimodal target specification that resembles a bullseye.
Copy of kill_agents_20xspeed_25agents.mp4Recovery from Agent Failure
This video (20x speed) shows a swarm of 25 agents converging to a multimodal target specification that has two areas with high expected information content in the northwest and southwest corners of the environment. A simulated EMP device disables most of the agents in the northwest corner of the environment after the swarm as a whole has converged to the initial target. Without any user intervention or additional target specifications, the swarm automatically adapts by reallocating some of the agents from the southwest corner to the northwest corner and converges back to the original target specification.
Graceful Degradation in the Amount of Information Collected Across Swarms of Different Sizes
The figure on the left shows the graceful degradation---our system continuing to operate under unexpected agent loss and enabling the operator to use the same strategy or mental model with swarms of different sizes---with respect to the amount of information the swarm collects. "Information" in this scenario are simulated April tags representing different entities relevant to the OFFSET program (IED, High Value Target, etc.). The April tags are randomly distributed throughout the bottom left corner of the environment. An operator specifies a target distribution that uniformly covers this area of the environment. Plot c shows the number of April tag detections over time for the three different swarm sizes. The largest swarm of 50 agents detects the highest number of April tags, however, the trend in the amount of information collected over time is similar for all three swarm sizes, indicating graceful degradation in the amount of information collected and that our system is suitable for uncovering information at any scale. The operator can use our system with different numbers of agents knowing that the amount of information collected will gracefully increase or decrease if new agents are added to the swarm or if agents are disabled during operation.
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