  Recently, machine learning (ML) methods have been developed for increasing
the accuracy of robot mechanisms. Complex mechanical issues such as non-linear
friction, backlash, flexibility of structure transmission elements can cause
these errors and they are hard to model. ML requires training data and the
above mechanical phenomena are highly dependent on position of the robot in the
workspace and also on its velocity, especially near zero velocity in both
directions where non-linearities such as Streibek and Coulomb friction are most
pronounced. It is well known that success of ML methods depends on amount of
training data and it is expensive/time consuming to collect data from physical
robot motion. We therefore address the problem of searching for trajectories in
the 6D space of positions and velocities which collect the most information in
the least amount of time. This reduces to a special case of the
traveling-salesman problem in that the robot must be programmed to visit
sampled points in the position-velocity phase space most efficiently. Two goals
of this work are 1) Computationally study the difficulty of the TSP in this
application by applying it to X, Y, Z motion in 3D space (6D phase space) and
2) assess the effectiveness of an extremely simple Nearest Neighbor search
algorithm compared to random sampling of the search space. Results confirm that
Nearest Neighbor heuristic searching produces significantly better trajectories
than random sampling in this application.
