Stabilization of a 2D-SpiderCrane Mechanism Using Damping Assignment Passivity-based Control

Cable-operated manipulators, also termed cable robots, possess a number of unique properties which make them suitable for tasks involving high payloads, large workspaces, and interacting with dangerous materials. But the fact that cables can only pull the end effector but not push it, makes their feedback control law more challenging than their counterpart, the rigid robots. In this paper, we present a modeling and control strategy for a cable suspended structure called the \lq{SpiderCrane}\rq. By avoiding heavy mobile components, the design of this crane makes it particularly useful for work requiring high speeds. The modeling of such a multiple cable mechanism is challenging due to the number of constraints arising from cable interactions. From a control theoretical point of view, such mechanical systems are underactuated, which gives rise to challenging control issues. In this paper, we consider a 2-dimensional version of SpiderCrane that captures most of its control-related aspects. We employ a novel approach, by which we separate the cable and pulley dynamics from the payload dynamics for the ease of controller design. This enables us to view the payload as a pendulum suspended from a cable whose suspension point lies on a mass that moves in a two-dimensional space. We apply interconnection and damping assignment passivity-based control to both shape the potential energy and change the interconnection structure for swing minimization. Damping is injected to ensure (asymptotic) stabilization.