  This paper presents a new efficient algorithm which guarantees a solution for
a class of multi-agent trajectory planning problems in obstacle-dense
environments. Our algorithm combines the advantages of both grid-based and
optimization-based approaches, and generates safe, dynamically feasible
trajectories without suffering from an erroneous optimization setup such as
imposing infeasible collision constraints. We adopt a sequential optimization
method with \textit{dummy agents} to improve the scalability of the algorithm,
and utilize the convex hull property of Bernstein and relative Bernstein
polynomial to replace non-convex collision avoidance constraints to convex
ones. The proposed method can compute the trajectory for 64 agents on average
6.36 seconds with Intel Core i7-7700 @ 3.60GHz CPU and 16G RAM, and it reduces
more than $50\%$ of the objective cost compared to our previous work. We
validate the proposed algorithm through simulation and flight tests.
