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Details of the research

Computer numerical control (CNC) machines are widely used to manufacture complex components that are required to be very precise to comply with the rising demand. In order to achieve the desired manufacturing quality, motion trajectories must be traversable without violating systems’ constraints such as a permissible acceleration and jerk. Generally, the trajectories have to be at least second order differentiable in order to achieve a continuous velocity and acceleration. Linearly interpolated trajectories have been used for decades due to their simplicity in design and implementation. However, these linear trajectories cause undesired performance, such as stops between trajectories’ segments, unnecessary time and energy consumptions and wear on the system parts.

For improvement of motion trajectories, many methods have been proposed in the literature and most of them focus on smoothing the linear interpolated tool-path points using curve fitting techniques. For densely tool-path points, curve fitting techniques exhibit oscillations in the trajectory because high-order spline curves are numerically unstable. On the other hand, cubic parametric spline curves are used to smoothly interpolate the linear tool-path points. They are infinitely differentiable when used as a single curve, however, their differentiability is limited to first-order when two or more curves are connected.

In this study, a method for generating smooth motion trajectories using quintic Bézier curves and smooth velocity profiles based on the altered bang-bang approach was proposed. The altered bang-bang approach allows for smooth velocity transitions between the spline curves, such that low-velocity values can be used during the motion start and end, and in all areas with high curvatures. Since it is well known that mechanical systems cannot instantly accelerate to high velocities and that the velocity is inversely proportional to the curvature, smooth reference velocity ensures that the motion acceleration and jerk are within the permissible range.

In addition to the velocity profile matter, mechanical systems experience friction forces which vary nonlinearly with velocities. Therefore, on implementing a smooth velocity profile, a contouring controller with a feed forward friction compensator was applied in order to smoothly track the designed trajectory by canceling out the effect of friction forces. Experimental verification was conducted and results showed that the proposed method is effective for improving the performance of CNC systems.

Behind-the-scenes story

We had previously successfully developed a method to automatically generate smooth trajectories for mobile robots based on the assigned via-points. In addition, other members of our laboratory studied and developed a nonlinear motion controller with "a" friction compensator for feed drive systems. The performance of the designed controller was found dependent on the nature of the applied trajectory. Tracking performance was much better if the trajectory is smooth enough to be traversed by the system. On the other hand, poor performance was observed when traversing trajectories with high curvatures. It was in this light that we studied the method previously used for mobile robots and modified it for application to feed drive systems.

Future Research

The research team of this study believe that the proposed method will be adopted for industrial applications to enhance manufacturing performance. In addition, this study can be applied to other motion systems, such as autonomous mobile robots and driverless cars.

This study is partly sponsored by the Japan Society for the Promotion of Science (JSPS).