Minimum-time S-curve commands for vibration-free transportation of an overhead crane with actuator limits

S-curve commands are ubiquitous in servo drives owing to their simplicity and smoothness. Nevertheless, they need to be adapted for use in flexible systems, where the problem of residual vibration must be addressed. This paper proposes a simple motion planning method for the vibration-free transfer process of an overhead crane using S-curve commands. Based on a position baseline S-curve, which is generated from a bang-off-bang acceleration profile, two approaches are proposed to build the vibration suppression capability. One is an embedding method that injects the essential terminal conditions for vibration-free transportation into the baseline S-curve command without altering its original form. The other is a shaping method inspired from the input shaping technique. In both schemes, the baseline S-curve is parameterized to establish minimum-time optimization problems, in which maximum velocity and maximum acceleration of the actuator are explicitly taken into consideration. The minimum-time solutions are successfully obtained by solving constrained (discrete) nonlinear programs. An online trajectory generation can be realized using the proposed approach. Both simulation and experimental results are given to verify the effectiveness of the proposed method.