Optimal B-spline motion trajectory generation considering corner tolerances for industrial machines

Abstract

This paper presents a method to improve the motion performance of industrial machines. Their motion trajectories are optimized in B-spline representation, in which control points and knot vectors are adjusted mainly. Positions of control points should be optimized such that tolerances around corners are satisfied as constraints. The number of control points is reduced by assigning straight-line segments as target trajectories and constraining the range of control points around start and end position of each line segment. The control polygons can be explicitly set within a range of tolerances around corners. The proposed problem formulation can be successfully solved by a nonlinear programming technique. A trajectory generation example demonstrates the effectiveness of the proposed in which minimal-time and tolerance satisfaction are achieved.