Abstract

Trajectory optimization is an essential tool for motion
planning under multiple constraints of robotic manipulators.
Optimization-based methods can explicitly optimize a trajectory
by leveraging prior knowledge of the system and have been used
in various applications such as collision avoidance. However, these
methods often require a hand-coded cost function in order to
achieve the desired behavior. Specifying such cost function for
a complex desired behavior, e.g., disentangling a rope, is a nontrivial
task that is often even infeasible. Learning from demonstration
(LfD) methods offer an alternative way to program robot
motion. LfD methods are less dependent on analytical models
and instead learn the behavior of experts implicitly from the
demonstrated trajectories. However, the problem of adapting the
demonstrations to new situations, e.g., avoiding newly introduced
obstacles, has not been fully investigated in the literature. In this
paper, we present a motion planning framework that combines
the advantages of optimization-based and demonstration-based
methods. We learn a distribution of trajectories demonstrated by
human experts and use it to guide the trajectory optimization
process. The resulting trajectory maintains the demonstrated
behaviors, which are essential to performing the task successfully,
while adapting the trajectory to avoid obstacles. In simulated
experiments and with a real robotic system, we verify that our
approach optimizes the trajectory to avoid obstacles and encodes
the demonstrated behavior in the resulting trajectory