  This paper proposes a new sampling-based kinodynamic motion planning
algorithm, called FMT*PFF, for nonlinear systems. It exploits the novel idea of
dimensionality reduction using partial-final-state-free (PFF) optimal
controllers.With the proposed dimensionality reduction heuristic, the search
space is restricted within a subspace, thus faster convergence is achieved
compared to a regular kinodynamic FMT*. The dimensionality reduction heuristic
can be viewed as a sampling strategy and asymptotic optimality is preserved
when combined with uniform full-state sampling. Another feature of FMT*PFF is
the ability to deal with a steering function with inexact steering, which is
vital when using learning-based steering functions. Learning-based methods
allow us to solve the steering problem for nonlinear systems efficiently.
However, learning-based methods often fail to reach the exact goal state. For
nonlinear systems, we train a neural network controller using supervised
learning to generate the steering commands. We show that FMT*PFF with a
learning-based steering function is efficient and generates dynamically
feasible motion plans. We compare our algorithm with previous algorithms and
show superior performance in various simulations.
