  This paper presents an adaptive online distributed optimal control approach
that is applicable to optimal planning for very-large-scale robotics systems in
highly uncertain environments. This approach is developed based on the optimal
mass transport theory. It is also viewed as an online reinforcement learning
and approximate dynamic programming approach in the Wasserstein-GMM space,
where a novel value functional is defined based on the probability density
functions of robots and the time-varying obstacle map functions describing the
changing environmental information. The proposed approach is demonstrated on
the path planning problem of very-largescale robotic systems where the
approximated layout of obstacles in the workspace is incrementally updated by
the observations of robots, and compared with some existing state-of-the-art
approaches. The numerical simulation results show that the proposed approach
outperforms these approaches in aspects of the average traveling distance and
the energy cost.
