  We present a modular Bayesian optimization framework that efficiently
generates time-optimal trajectories for a cooperative multi-agent system, such
as a team of UAVs. Existing methods for multi-agent trajectory generation often
rely on overly conservative constraints to reduce the complexity of this
high-dimensional planning problem, leading to suboptimal solutions. We propose
a novel modular structure for the Bayesian optimization model that consists of
multiple Gaussian process surrogate models that represent the dynamic
feasibility and collision avoidance constraints. This modular structure
alleviates the stark increase in computational cost with problem dimensionality
and enables the use of minimal constraints in the joint optimization of the
multi-agent trajectories. The efficiency of the algorithm is further improved
by introducing a scheme for simultaneous evaluation of the Bayesian
optimization acquisition function and random sampling. The modular BayesOpt
algorithm was applied to optimize multi-agent trajectories through six unique
environments using multi-fidelity evaluations from various data sources. It was
found that the resulting trajectories are faster than those obtained from two
baseline methods. The optimized trajectories were validated in real-world
experiments using four quadcopters that fly within centimeters of each other at
speeds up to 7.4 m/s.
