Command Shaping Nonlinear Inputs Using Basis Functions

Manufacturing operations exist which require robotic repositioning of flexible payloads. Product quality or throughput can be adversely affected if payload vibration is not controlled. Using command shaped inputs can prevent excitation of payload dynamics, however, most of the literature has focused on linear, single input systems. General robotic repositioning typically involves simultaneous motion of multiple degrees of freedom resulting in the payload excitation function being a nonlinear combination of the robot input states. Under these conditions, removal of the individual input’s frequency content in the vicinity of the payload’s resonances does not guarantee that the nonlinear combination of the inputs will be free of detrimental frequency content. Presented in this paper is a method for trajectory design of point-to-point flexible payload maneuvers with multiple inputs nonlinearly driving payload dynamics. Simulation and experimental results are provided for the coordinated maneuver of a flexible beam. Using this trajectory generation approach, the residual oscillation is reduced by a factor of 20 as compared to the worst case maneuver, without a reduction in total maneuver time.