A Deep Learning Approach for Probabilistic Security in Multi-Robot Teams

In this letter, we train a convolutional neural network (CNN) to predict the probability of security of a multi-robot system (MRS) when robot interactions are probabilistic. In the context of MRSs, probabilistic security is defined using the control-theoretic notion of left invertibility, a necessary and sufficient condition to avoid perfect attacks. As the probabilistic security problem is NP-Complete, current solutions fail to generalize as the size of the MRS increases. Fortunately, deep neural networks have shown promising results in the efficient computation of solutions to hard problems, which motivates our CNN-based approach. In this context, formulating a method for data generation is non-trivial due to the large space of available interaction graph topologies and training biases introduced by random sampling. As such, we use a two-step approach for data generation where we first explore the space of available topologies, then populate the sampled topologies with probability distributions, all while preventing any biases from occurring in the data. We then train a CNN with convolution layers specifically tailored for graph adjacency matrices. Finally, the validity of our results is demonstrated through simulations.