Abstract: Physical stochastic disturbances, such as wind,
often affect the motion of robots that perform complex tasks in
real-world conditions. These disturbances pose a control challenge
because resulting drift induces uncertainty and changes
in the robot's speed and direction. This paper presents an
online control policy based on supervised machine learning,
Least Squares Axial Sum Policy Approximation (LSAPA), that
generates trajectories for robotic preference-balancing tasks
under stochastic disturbances. The task is learned offline with
reinforcement learning, assuming no disturbances, and then
trajectories are planned online in the presence of disturbances
using the current observed information. We model
the robot as a stochastic control-affine system with unknown
dynamics impacted by a Gaussian process, and the task as
a continuous Markov Decision Process. Replacing a traditional
greedy policy, LSAPA works for high-dimensional control-affine
systems impacted by stochastic disturbances and is linear in
the input dimensionality. We verify the method for Swing-free
Aerial Cargo Delivery and Rendezvous tasks. Results show
that LSAPA selects an input an order of magnitude faster
than comparative methods, rejecting a range of stochastic
disturbances. Further, experiments on a quadrotor demonstrate
that LSAPA trajectories that are suitable for physical systems.