Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

Abstract

In this work, we propose a novel safe and scalable decentralized solution for multi-agent control in the presence of stochastic disturbances. Safety is mathematically encoded using stochastic control barrier functions and safe controls are computed by solving quadratic programs. Decentralization is achieved by augmenting to each agent's optimization variables, copy variables, for its neighbors. This allows us to decouple the centralized multi-agent optimization problem. However, to ensure safety, neighboring agents must agree on what is safe for both of us, creating a need for consensus. To enable safe consensus solutions, we incorporate an ADMM-based approach. Specifically, we propose a Merged Consensus ADMM-OSQP implicit neural network layer, that solves a mini-batch of both, local quadratic programs as well as the overall consensus problem, as a single optimization problem. This layer is embedded within a Deep Forward-Backward Stochastic Differential Equations (FBSDEs) network architecture at every time step, to facilitate end-to-end differentiable, safe and decentralized stochastic optimal control. The efficacy of the proposed approach is demonstrated on several challenging multi-robot tasks in simulation. By imposing collision avoidance constraints, the safe operation of all agents is ensured during the entire training process. We also demonstrate superior scalability in terms of computational and memory savings as compared to a centralized approach.