Smallest Maximum Cable Tension Determination for Cable-Driven Parallel Robots

Abstract

The maximum cable tension is a crucial parameter in the design of a cable-driven parallel robot (CDPR) since the various mechanical components of the CDPR must be designed to safely withstand the loads induced by this maximum tension. For CDPRs having a number of cables at least equal to its number of DOFs, this paper deals with the determination of the smallest maximum cable tension vectors allowing a required wrench set to be feasible. The problem is formulated as the minimization of the maximum cable tension infinity norm under linear inequality constraints which include the wrench-feasibility constraints. The solution to this minimization problem is not unique, and the solution set is shown to be a convex polytope in the maximum tension space. Hence, various smallest maximum tension vectors generally exist and the computations of two different solution vectors are introduced. The first vector has all its components equal to the minimum infinity norm which can be directly obtained from the minimization problem inequality constraints. An algorithm is proposed to determine the second vector as the solution vector having the least possible value for each of its components. The computation of the smallest maximum tension vectors for general required wrench sets are then presented. The cases of particular wrench set definitions relevant to heavy payload manipulation applications are also introduced. Finally, these contributions are applied to the configuration (geometry) optimization of a large-dimension 6-DOF CDPR installed on a building facade to manipulate heavy payloads.

Dynamic Modeling, Workspace Analysis and Multi-Objective Structural Optimization of the Large-Span High-Speed Cable-Driven Parallel Camera Robot

“…According to Equation (12), it is a non-linear transcendental equation because J and F are associated with H. In this paper, we propose an iterative-based algorithm to determine H, which is different from the algorithm in our previous paper. The algorithm termination condition is when the difference of two sags obtained from adjacent steps is small enough, which could meet after several iterative steps.…”

“…Determining an optimal structure of a CDPM meeting a set of optimization objectives is generally challenging, which can be solved by formulating a constrained optimization problem. There has been plenty of prior work in the structural optimization of CDPMs, which employ various optimization objects, such as workspace size [9], condition number of Jacobian matrix [10], tension factor [11,12], stiffness [13][14][15], avoiding collision of cables [16,17], manipulability [18] and the maximum acceptable horizontal distance [19]. However, most of the above optimization methods belong to traditional optimization methods, such as the simplex method, interval analysis, Dynamic-Q, grouped coordinate descent and enumeration method, which are sensitive to initial values and easily fall into local optimums, leading to a failure to obtain a global optimal solution.…”

An Overview of Cable-Driven Parallel Robots: Workspace, Tension Distribution, and Cable Sagging

“…Ueland et al [78] analyze the problem of determining optimal cable tension distribution for over constraint CDPRs based on studies [58,70,77], thereby proposing a new optimal objective function that ensures the continuity of the cable tension. Hussein et al [79] provide a solution for determining the minimum value of the upper limits of cable tension for CDPRs with DORs equal to or greater than 1. e constraint condition of this issue is that the cable tension limits must satisfy a required wrench set.…”

Variable-Structure Cable-Driven Parallel Robots

“…[23] uses quadratic programming to find the distribution that minimizes the Euclidean norm of τ and reduce the required actuator sizes for a given CDPR. In [24], the authors use the infinity norm to minimize the maximum tension in any one cable. In other studies, such as [25,26], the optimization has been designed to maximize the manipulator stiffness.…”