A blockchain-based information market to incentivise cooperation in swarms of self-interested robots

Abstract

Robot swarms are generally considered to be composed of cooperative agents that, despite their limited individual capabilities, can perform difficult tasks by working together. However, in open swarms, where different robots can be added to the swarm by different parties with potentially competing interests, cooperation is but one of many strategies. We envision an information market where robots can buy and sell information through transactions stored on a distributed blockchain, and where cooperation is encouraged by the economy itself. As a proof of concept, we study a classical foraging task, where exchanging information with other robots is paramount to accomplish the task efficiently. We illustrate that even a single robot that lies to others-a so-called Byzantine robot-can heavily disrupt the swarm. Hence, we devise two protection mechanisms. Through an individual-level protection mechanism, robots are more sceptical about others' information and can detect and discard Byzantine information, at the cost of lower efficiency. Through a systemic protection mechanism based on economic rules regulating robot interactions, robots that sell honest information acquire over time more wealth than Byzantines selling false information. Our simulations show that a well-designed robot economy penalises misinformation spreading and protects the swarm from Byzantine behaviour. We believe economics-inspired swarm robotics is a promising research direction that exploits the timely opportunity for decentralised economies offered by blockchain technology.

Figure 1

We simulate a swarm of 25 robots (blue circles) that move between food and nest sites (green and yellow circles). Robots filter out odometry noise and improve navigation efficiency implementing a social odometry algorithm based on local exchange of messages (the grey circles show the communication range). Through social odometry, the robots form a dynamic chain around the shortest patch connecting food and nest. The robots’ outline is the colour of their last visited site and the white line indicates the robot’s motion orientation. The simulator is easily extendable, open source, and available at https://github.com/ludericv/information-market.

Figure 2

Box plots of the total number of items collected by each robot after 15 000 timesteps in 128 simulations per condition. Swarm size is kept constant at 25 robots in all our experiments, and we varied the swarm composition (indicated under each panel). The blue and red boxes show the results for honest and Byzantine robots, respectively. The boxes indicate the range between the data distribution’s first and third quartiles, the horizontal lines show the median, the whiskers extend in both directions to the last datapoint up to 1.5 IQR, and finally, the outliers are marked black diamonds. (A–B) Naive robot’s performance has a big decrease when a single saboteur is present. (C–D) Sceptical robots are instead more resilient to the presence of a saboteur.

Figure 3

Box plots of the proportion of wealth of each robot after 15 000 timesteps in experiments with the outlier penalisation payment scheme (128 simulations per condition). We varied the swarm composition (indicated under each panel) in swarms composed of 25 robots. The blue and red boxes show the results for honest and Byzantine robots, respectively (see full description of the box plots in the caption of Fig. 2). In all tested conditions, the blue distribution is significantly higher than the red one (Mann-Whitney U test, p-value < 0.001 in all cases). The outlier penalisation payment scheme penalises more heavily the wealth of Byzantine robots when they are few, however the difference between the blue and red distribution decreases as the number of Byzantine robots increases.

Figure 4

Results of the experiments with the outlier penalisation with staking payment scheme (128 simulations per condition). We varied the swarm composition (indicated under each panel) in swarms composed of 25 robots (see description of the box plots in the caption of Fig. 2). In all tested conditions, the blue distribution (honest robots) is significantly higher than the red one (Byzantine robots); Mann–Whitney U test (p-value < 0.001 in all cases). Including the staking mechanism reduces considerably the Byzantine robots’ wealth.

Figure 5

Average robot’s wealth in a swarm of 20 sceptical and 5 scaboteur robots using the outlier penalisation with staking payment scheme in 32 simulations. The transparent shades show the 95% confidence interval. (A) The absolute wealth of honest sceptical robots constantly increases at a high pace compared with the scaboteurs that remains with relatively low, almost null, wealth. (B) The proportion of total wealth rapidly converges to a relatively stable situation where wealth is mainly distributed among honest robots, approximately equally.

Figure 6

Relationship between odometry error (indicated as the mean angular drift on the x-axis) and robot’s wealth (indicated as wealth proportion on the y-axis), for swarms of 25 robots after 15 000 timesteps (results of 32 simulations, data reported only for the honest robots subgroup). The two measures are correlated both in case of (A) Byzantine-free swarms and (B) swarms with 5 scaboteurs, with Pearson correlation coefficients of $-0.54$ and $-0.64$ respectively (solid lines with the 95% confidence interval shown as transparent shades).

Figure 7

Collective performance comparison between robot swarms that only use individual protection and swarms that use both individual and systemic protection through outlier penalisation with staking. The collective performance (y-axis) is measured as the number of items collected by a swarm of 25 robots in the last 10 000 timesteps of an experiment 30 000 timesteps long (results of 32 simulations). We only record the collective performance in the last part of the experiment in order to study the dynamics once the robot chain—connecting nest and food—is formed. The swarm comprises one Byzantine robot (panel A) or three Byzantine robots (panel B) which consistently send incorrect path information by rotating the navigation vector by the angle indicated on the x-axis (note that when the rotation angle is equal to zero there are no Byzantine robots in the swarm).

Figure 8

The process of information exchange between the selling and the buying robots comprises four steps. Step 1: A selling robot makes an offer to a buying robot. This offer includes the target (food or nest), information age, and a maximum block number which specifies when the light contract must be included in the blockchain at the latest. Step 2: If a buying robot agrees on the offer, it returns its signature of the offer and its corresponding public key. In addition, it returns its relative position to the selling robot. Both parties now possess a double-signed light contract. The light contract is an off-chain agreement between two robots that is fast to perform since it does not require a transaction on the blockchain network. Step 3: The selling robot creates a blockchain transaction that includes both the light contract and the now revealed path information to the target site in the buyer’s reference frame. Step 4: The smart contract performs three security checks before it adds the transaction to the blockchain. These checks ensure that the terms of the light contract were not violated. If one of the checks fails, the transaction is discarded.

Figure 9

UML diagram of the developed smart contract. The smart contract enables the robots to buy and sell information and the market to buy items. The variable contributors is a mapping from robot addresses to a list of the Information structure. This mapping ensures that the smart contract keeps track of who sold which information to whom; the mapping is used for rewarding all contributors when the item is deposited in the nest and the market buys it.