Bezier Curve Based Programmed Trajectory for Coordinated Motion of Two Robots in Cartesian Space

Abstract

Coordinated motion of two robots in Cartesian space is considered in the paper. The goal is to generate trajectories for which change of distance between points on trajectories during motion is minimal. To minimize relative position errors along trajectories an idea of corrective motion is introduced. Trajectory coordinates are calculated as the sum of programmed and corrective motions. To calculate the speed vector of the programmed motion at the current position, the speed at the closest point on the programmed trajectory is used. The closest point is defined as the one to which the distance from the current position is minimal or the programmed position at given time. In order to attract the generated trajectory to the programmed one a modification of the programmed speed vector is proposed. The described approach is verified in simulation. For simulation experiments programmed trajectories defined by Bezier curve segments are used. Simulations for different shapes of programmed trajectories and different programmed velocity rates are presented.