  Sampling-based kinodynamic planners, such as Rapidly-exploring Random Trees
(RRTs), pose two fundamental challenges: computing a reliable (pseudo-)metric
for the distance between two randomly sampled nodes, and computing a steering
input to connect the nodes. The core of these challenges is a Two Point
Boundary Value Problem, which is known to be NP-hard. Recently, the distance
metric has been approximated using supervised learning, reducing computation
time drastically. The previous work on such learning RRTs use direct optimal
control to generate the data for supervised learning. This paper proposes to
use indirect optimal control instead, because it provides two benefits: it
reduces the computational effort to generate the data, and it provides a low
dimensional parametrization of the action space. The latter allows us to learn
both the distance metric and the steering input to connect two nodes. This
eliminates the need for a local planner in learning RRTs. Experimental results
on a pendulum swing up show 10-fold speed-up in both the offline data
generation and the online planning time, leading to at least a 10-fold speed-up
in the overall planning time.
