Near-time optimal feedrate planning for the NURBS curve considering interpolation error constraints

Abstract

Compared with general time-optimal robot feedrate planning, trajectory machining tasks require consideration of feedrate command constraints and the complexity of parameter spline curves. The interpolation error generated during the interpolation stage affects the command accuracy and contour accuracy of the trajectory. To ensure that the robot end-effector feedrate maintains consistency with the feedrate command and to improve the contour accuracy of the trajectory, this study proposes a two-stage method: near-time optimal feedrate planning for the NURBS curve considering interpolation error constraints. In the first stage, the end-effector velocity constraint under joint velocity constraint is calculated, and the feedrate command is corrected based on that constraint. Then, the corrected feedrate command is transformed into parameter form, and feedrate planning is carried out utilizing the direct transcription method. In the second stage, interpolation is carried out after feedrate planning, and interpolation error is calculated to detect any over-limit positions. If any over-limit positions are detected, the first over-limit position is recorded, and feedrate planning with reduced feedrate limit is carried out at that position. This process is repeated until the interpolation error constraint is satisfied. A series of simulations and experiments were conducted in this study. The simulation results show that the proposed method can consider feedrate command constraints and limit interpolation errors within specified constraints. The experimental results show that the proposed method can reduce contour errors, particularly at low feedrate command.