Dynamic Stability Measurement and Grey Relational Stability Sensitivity Analysis Methods for High-Speed Long-Span 4-1 Cable Robots

High-speed long-span 4-1 cable robots (4-1HSLSCRs) have the characteristics of a simple structure, superior performance and easy control, and they can be used comprehensively in coal quality sampling, water quality monitoring, aerial panoramic photographing, etc. However, because of the high-speed movement of the end-effector and the unidirectional constraint property and nonlinear characteristics of the long-span cables, the dynamic stability of the 4-1HSLSCRs presents severe challenges. This paper, as a result, focuses on the two special problems of carrying out dynamic stability measurement and a stability sensitivity analysis for the 4-1HSLSCRs. First, a systematic approach that combines the cable tension, position and velocity of the end-platform based on both the dynamic model and the determinations of the cable tension is proposed for the high-speed robot, in which two cable tension and two position influencing factors are developed, respectively, whereas a velocity function is constructed, which represents the influence of the end-effector velocity on the dynamic stability of the 4-1HSLSCRs. Second, a grey relational analysis method for analyzing the dynamic stability of the 4-1HSLSCRs is developed, where the relationship between the dynamic stability of the 4-1HSLSCRs and the influencing factors (the position and velocity of the end-effector, as well as the cable tension) is investigated in detail. Finally, the measure approach and sensitivity analysis method for dynamic stability of 4-1HSLSCRs, namely, a camera robot with a high speed and long-span cables, is verified through simulation results. The results show that the large-span cable sags have significant effects on both the cable tensions and the dynamic stability of the camera robot, whereas the stability sensitivity evaluation results indicate that the effect of the stability sensitivity of the cable tensions on the dynamic stability of the camera robot is the greatest, followed by the velocity of the end-effector, and last is the position of the end-effector.