  We present TrueRMA, a data-efficient, model-free method to learn
cost-optimized robot trajectories over a wide range of starting points and
endpoints. The key idea is to calculate trajectory waypoints in Cartesian space
by recursively predicting orthogonal adaptations relative to the midpoints of
straight lines. We generate a differentiable path by adding circular blends
around the waypoints, calculate the corresponding joint positions with an
inverse kinematics solver and calculate a time-optimal parameterization
considering velocity and acceleration limits. During training, the trajectory
is executed in a physics simulator and costs are assigned according to a
user-specified cost function which is not required to be differentiable. Given
a starting point and an endpoint as input, a neural network is trained to
predict midpoint adaptations that minimize the cost of the resulting trajectory
via reinforcement learning. We successfully train a KUKA iiwa robot to keep a
ball on a plate while moving between specified points and compare the
performance of TrueRMA against two baselines. The results show that our method
requires less training data to learn the task while generating shorter and
faster trajectories.
