Tension planner for cable-driven suspended robots with unbounded upper cable tension and two degrees of redundancy

Cable-driven parallel manipulator hanging in a suspended configuration are not fully constrained mechanisms due to the constant weight of the end effector. This force maintains tension in cables and it imposes a maximum limit on the tension in the cables. This study aims to analyze the maximum tension value as well as the maximum wrenches that the end effector can exert without losing control. The relation between the maximum wrench at the end effector and the tension values is useful for sizing the actuators. To exert the desired maximum wrench in any direction of the space, the regions of the workspace, where the wrench can be applied, are also calculated. The process of exerting the maximum wrench from the equilibrium state is defined using the null space of the robot's structure matrix to accomplish rapid path planning. The tension planner developed below is relevant to applications like pressing, hammering or drilling at different locations over a large workspace. This article develops the mathematical background to plan fast and agile motion for two-degree redundant suspended manipulator, calculates several examples of path plans, and then validates those calculations with multibody dynamics simulations.Spanish Government [DPI2014-57220-C2-1-P ; PGC2018-095939-B-I00]; RoboCity2030 DIH-CM Madrid Robotics Digital Innovation Hub [S2018/NMT-4331]; Programas Actividades I+D en la Comunidad de Madrid; Structural Funds of the EU.Peer reviewe