  We propose a new formulation of optimal motion planning (OMP) algorithm for
robots operating in a hazardous environment, called adaptive Gaussian-process
based stochastic trajectory optimization (AGP-STO). It first restarts the
accelerated gradient descent with the reestimated Lipschitz constant (L-reAGD)
to improve the computation efficiency, only requiring 1st-order momentum.
However, it still cannot infer a global optimum of the nonconvex problem,
informed by the prior information of Gaussian-process (GP) and obstacles. So it
then integrates the adaptive stochastic trajectory optimization (ASTO) in the
L-reestimation process to learn the GP-prior rewarded by the important samples
via accelerated moving averaging (AMA). Moreover, we introduce the incremental
optimal motion planning (iOMP) to upgrade AGP-STO to iAGP-STO. It interpolates
the trajectory incrementally among the previously optimized waypoints to ensure
time-continuous safety. Finally, we benchmark iAGP-STO against the numerical
(CHOMP, TrajOpt, GPMP) and sampling (STOMP, RRT-Connect) methods and conduct
the tuning experiment of key parameters to show how the integration of L-reAGD,
ASTO, and iOMP elevates computation efficiency and reliability. Moreover, the
implementation of iAGP- STO on LBR-iiwa, multi-AGV, and rethink-Baxter
demonstrates its application in manipulation, collaboration, and assistance.
