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UBC Theses and Dissertations

Trajectory generation, control, and geometric error compensation for a 9-axis micromachining center Yuen, Alexander


This thesis presents a trajectory generation algorithm, a control strategy, and a geometric error compensation methodology for a novel 9-axis micromachining center which combines a 3 axis micromill with a 6 degree of freedom magnetically levitated rotary table. The proposed trajectory generation algorithm resolves redundant degrees of freedom by numerically solving for axes positions from desired tool positions and orientations. Differential axes positions are found while ensuring the stroke limits of the drives are respected and singularities are avoided. The differential solution is numerically integrated to obtain the axes positions with respect to displacement. The axes commands are then scheduled in time, while respecting the velocity, acceleration, and jerk limits of each of the drives, and traversing the toolpath as fast as possible. The experiments showed trajectories that resolved redundancies, avoided singularities, and respected all physical limits of the drives. A control strategy which combines the capabilities of the micromill and the rotary table is introduced. A sliding mode controller with a LuGre friction compensator is designed to control the position of the micromill, based on identified physical parameters. A lead-lag position controller with an integrator and a notch filter is designed to control the rotary table. Since the translational axes of the micromill and rotary table are in parallel, the tracking error of the micromill is sent as a reference command to the rotary table, compensating the tracking errors of the micromill with the higher bandwidth of the rotary table. In experiments, the dual stage control law improved tracking error over the micromill alone. The geometric errors of the 3-axis micromill is compensated by using the precision motion of the 6 degree of freedom rotary table. The geometric errors of the 3-axis micromill are mea sured with a laser interferometer, fit to quintic polynomials, and incorporated into the forward kinematic model. The tooltip deviation is found by subtracting the ideal tooltip position from the tooltip position affected by geometric errors. Rotary table commands, from all 6 axes, that compensate for these deviations are found using a gradient descent algorithm. Experiments showed reductions in end effector deviations.

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