  In this paper, we propose two novel decentralized optimization frameworks for
multi-agent nonlinear optimal control problems in robotics. The aim of this
work is to suggest architectures that inherit the computational efficiency and
scalability of Differential Dynamic Programming (DDP) and the distributed
nature of the Alternating Direction Method of Multipliers (ADMM). In this
direction, two frameworks are introduced. The first one called Nested
Distributed DDP (ND-DDP), is a three-level architecture which employs ADMM for
enforcing a consensus between all agents, an augmented Lagrangian layer for
satisfying local constraints and DDP as each agent's optimizer. In the second
approach, both consensus and local constraints are handled with ADMM, yielding
a two-level architecture called Merged Distributed DDP (MD-DDP), which further
reduces computational complexity. Both frameworks are fully decentralized since
all computations are parallelizable among the agents and only local
communication is necessary. Simulation results that scale up to thousands of
vehicles and hundreds of drones verify the effectiveness of the methods.
Superior scalability to large-scale systems against centralized DDP and
centralized/decentralized sequential quadratic programming is also illustrated.
Finally, hardware experiments on a multi-robot platform demonstrate the
applicability of the proposed algorithms, while highlighting the importance of
optimizing for feedback policies to increase robustness against uncertainty. A
video including all results is available in https://youtu.be/tluvENcWldw.
