Planning of dynamically feasible trajectories for translational, planar, and underconstrained cable-driven robots

Extensively studied since the early nineties, cable-driven robots have attracted the growing interest of the industrial and scientific community due to their desirable and peculiar attributes. In particular, underconstrained and planar cable robots can find application in several fields, and specifically, in the packaging industry. The planning of dynamically feasible trajectories (i.e., trajectories along which cable slackness and excessive tensions are avoided) is particularly challenging when dealing with such a topology of cable robots, which rely on gravity to maintain their cables in tension. This paper, after stressing the current relevance of cable robots, presents an extension and a generalization of a model-based method developed to translate typical cable tension bilateral bounds into intuitive limits on the velocity and acceleration of the robot end effector along a prescribed path. Such a new formulation of the method is based on a parametric expression of cable tensions. The computed kinematic limits can then be incorporated into any trajectory planning algorithm. The method is developed with reference to a hybrid multi-body cable robot topology which can be functionally advantageous but worsen the problem of keeping feasible tensions in the cables both in static and dynamic conditions. The definition of statically feasible workspace is also introduced to identify the positions where static equilibrium can be maintained with feasible tensions. Finally, some aspects related to the practical implementation of the method are discussed.