Aiming at multi-agent coordinated scheduling problems in power systems under uncertainty, a generic projection and decomposition (P&D) approach is proposed in this letter. The canonical min-max-min two-stage robust optimization (TSRO) model with coupling constraints is equivalent to a concise robust optimization (RO) model in the version of mixed-integer linear programming (MILP) via feasible region projection. The decentralized decoupling of the non-convex MILP problem is realized through a dual decomposition algorithm, which ensures the fast convergence to a high-quality solution in the distributed optimization. Numerical tests verify the superior performance of the proposed P&D approach over the existing distributed TSRO method.