  Trajectory optimization for motion planning requires good initial guesses to
obtain good performance. In our proposed approach, we build a memory of motion
based on a database of robot paths to provide good initial guesses. The memory
of motion relies on function approximators and dimensionality reduction
techniques to learn the mapping between the tasks and the robot paths. Three
function approximators are compared: $k$-Nearest Neighbor, Gaussian Process
Regression, and Bayesian Gaussian Mixture Regression. In addition, we show that
the memory can be used as a metric to choose between several possible goals,
and using an ensemble method to combine different function approximators
results in a significantly improved warm-starting performance. We demonstrate
the proposed approach with motion planning examples on the dual-arm robot PR2
and the humanoid robot Atlas.
