# Real-Time Tension Distribution Design for Cable-Driven Parallel Robot
## 1 Introduction  
A cable-driven parallel robot is a type of parallel robot that utilizes cables in place of the conventional rigid links to drive the end-effector of the robot. Within the framework of this system, the end-effector is linked to a number of cables that are driven by rotary motors. The cable-driven mechanism utilized by these types of robots is advantageous for a variety of reasons: it is lightweight, provides a large workspace, and is easy to transport and reconfigure. Due to these advantages, cable-driven robots are well-suited for use in a wide variety of applications, including rehabilitation robots, camera systems, multiple cooperative cranes, and more. Nevertheless, in order to properly design either the controller or the structure of such a robot, two aspects of the cable-driven robot system need to be taken into consideration. One is that the tension of the cable must be maintained at a positive value, as the cable can only pull the end-effector of the robot and cannot be used to push it. In addition, the tension of the cable ought to be limited at a maximum value in order to accommodate the saturation of the motor and the tensile strength of the cable. The other is the requisite redundancy design implemented in such robot systems. Although there have been are various categories proposed for cable-driven robots based on the number of cables and the robot's degrees of freedom, in practice, cable-driven robots can be divided into fully constrained, over-constrained, and under-constrained robots, denoted as \(m=n,m>n,m<n\), respectively, where \(n\) denotes the degree of freedom of the robot and \(m\) represents the number of cables. In practice, analysis and control design are challenging due cable-driven robots' lack of pushing capabilities. In addition to requiring that the saturation problem be factored into the control strategy, this impacts the feasible workspace of the robot. In [1], the authors classified the SEW (static equilibrium workspace) as the set of poses attained statically considering the gravity. In the research of [2;3], the WCW (wrench closure workspace) is defined as the set of poses in which cable tensions can sustain an arbitrary external wrench. In other scenarios, such as [4;5], the workspace where cable tensions can produce any bounded wrench in the required set is referred to as the WFW (wrench feasible workspace). In addition to the analysis of the feasible workspace of robots, many studies have concentrated on the control problem, that is, how to produce feasible tension to accomplish the control objective. The primary difficulty stems from the tension limits in combination with the issue of necessary redundancy in the over-constrained cable-robot configuration. In [6], an optimal tension distribution law for a computed PD control input from the viewpoint of workspace conditions was proposed. In [7], a feedback tracking control method based on the Control Lyapunov Function for cable suspended robots was presented. However, these approaches fail at other control aims, such as force control. In [8], an LP (Linear Programming) and QP (Quadratic Programming) solver was used to calculate the positive tension for a computed wrench. In [9], an LP solver for the optimal positive solution of the tension was able to provide rapid calculation. [PERSON] [10] developed an optimization algorithm for cable robots that minimizes the p-norm objective function, especially for high values of p. The LP and QP methods utilized in these investigations can achieve an optimal selection of positive tension distributions. However, the programming method used in these studies can cause a discontinuity in the cable tension, which renders the robot's control unstable. Furthermore, such programming methods can require an excessive amount of time to search for a feasible distribution in each step, making it difficult to realize the desired real-time calculation [11].