Coordinating multiple legged robots on rough terrain is a centralized optimization problem that scales poorly. Zeng, Sambhus, Imran, Kim, Pastore, and Hamed decompose it. Their method reformulates trajectory planning for multi-robot quadrupedal locomotion as an ADMM-based distributed model predictive control problem with control barrier functions encoding safety constraints. Each robot solves its own subproblem using only information from immediate neighbors, communicated through the ADMM consensus mechanism. The architecture is hierarchical: trajectory planning feeds into nonlinear MPC, which feeds into whole-body control. On Unitree Go2 hardware with up to four agents, the distributed system matches the centralized solution's performance while reducing per-cycle planning time by 51% in the four-agent case --- the gap between real-time feasibility and infeasibility for onboard computation.
The barrier function integration is the structural innovation. Safety constraints in multi-robot systems are inherently coupling constraints --- robot A's safe region depends on robot B's position. ADMM decomposes the optimization into independent subproblems, but safety cannot be decomposed independently; it requires consensus on the shared constraint. The control barrier functions encode this shared constraint as a continuously differentiable function whose sign determines safety, making it compatible with the ADMM dual variable update. The result is that safety is enforced through the same communication channel as trajectory consensus, not through a separate coordination layer. No robot has global information, yet the collective satisfies global safety guarantees.
Decentralization succeeds when the coupling between agents is sparse enough that local information suffices for global guarantees. The mechanism is always the same: identify the minimal shared variable that encodes the coupling, and route consensus through that variable alone. Barrier functions work here because safety is a scalar constraint --- one number separating safe from unsafe --- and scalar constraints decompose efficiently. The 51% speedup is not an optimization trick; it is the quantitative signature of the coupling being lower-dimensional than the full state space. Sparsity in the constraint structure is the resource that makes decentralization possible.
(arXiv:2603.19170)