Optimization of Trajectories for Machine Learning Training in Robot Accuracy Modeling

TL;DR

This work addresses 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 and confirms that Nearest Neighbor heuristic searching produces significantly better trajectories than random sampling in this application.

Abstract

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.

Figures (16)

• Figure 1: 2D, 3x3 searches, rectangular grid. a,b: Suboptimal paths, found by heuristic search (using only 4 starting points). Starting point is enlarged green circle. Red arrows show sequence of points, blue curves are the solved trajectories (Section \ref{['TrajectorySolved']}, Fig. \ref{['basicTraj']}). c,d: Globally optimal path on 3x3 grid found by exhaustive searches. Hash codes identify pertinent data files.
• Figure 2: Comparing distributions of 10% heuristic (nearest-neighbor) paths (red) with 10% random search (blue, all 9 starting points) through the 2-D grid ($N=3$) by total time (Top) and total path energy use (Bottom).
• Figure 3: 4 NN searches at each of 9 starting points in a 9-point random grid produced these paths. Path time cost (Top) and energy cost (Bottom). Grid points used (8abb9a56).
• Figure 4: Globally optimum paths on the same random 9 point grid as Figure \ref{['3x3RandGridNN']}, resulting from exhaustive search. Minimum time cost path (Top) and minimum energy cost path (Bottom). Grid points used (8abb9a56).
• Figure 5: Distribution of one million randomly generated paths through the 2-D phase space (rectangular grid, $N=4$) by total time (Top) and total path energy use (Bottom).