Extremum-Seeking Gain-Scheduled Adaptive Input Shaping Applied to Flexible-Link Robot

Abstract

Input shaping was used to design a finite impulse response (FIR) prefilter. This filter, when convoluted with a reference input, produces a shaped reference input that avoids resonance, resulting in significantly less residual vibration. A flexible system that follows this shaped reference input is able to move from point to point faster due to less settling time. The problem with traditional input shaping is that the filter requires knowledge of the system’s natural frequencies and damping ratios and hence its performance deteriorates when the system is time varying. This paper proposed a novel adaptive input shaping algorithm. The system’s natural frequencies and damping ratios were gain-scheduled based on system-measured states and were simultaneously adjusted by extremum seeking for minimum residual vibration. The proposed algorithm was applied to the point-to-point movement of a one-link, flexible-link robot manipulator whose payload varied with time. The experimental results confirmed the effectiveness of the proposed algorithm, compared with the unadaptive case.