Rapid Swing-Free Transport of Nonlinear Payloads Using Dynamic Programming

Residual vibration suppression in freely suspended payload transports has been the focus of extensive work in the past. Many methods have been used to address this problem, including both open-loop motion planning and closed-loop control techniques. However, to be effective, most of these methods require linearization of the system and, in turn, have been restricted in their maneuver speeds. The inherent nonlinearity of suspended payload systems suggests the need for a more rigorous method, where the complete dynamic description can be retained throughout the optimization. Dynamic programming (DP) is such a method. This paper will outline the development of the DP algorithm for a discrete time system as well as its application to the rapid transport of a doubly suspended payload, a nonlinear system. The system consists of a long slender payload, suspended by a cable at each end. The two cables are each held by an independent robot manipulator. We will show that DP is effective at reducing residual oscillations for nonlinear systems, as demonstrated by both simulations and experimental validation. Residual oscillations were suppressed to less than 5% of their original magnitudes.