X-ACTA eXtended Analytic Center Tension distribution Algorithm for Fixed and Mobile Cable-Driven Parallel Robot

Q: What problem does the extended Analytic Center method address?

It selects cable tensions for steering CDPRs beyond the Wrench-Feasible Workspace while keeping differentiability and supporting nonlinear constraints.

Q: How does the proposed method improve tension profile smoothness compared with common p-norm objectives?

It maintains continuous and differentiable tension profiles, avoiding discontinuities that can arise from 1-norm or ∞-norm minimization over feasible polyhedra.

Q: What accuracy behavior does the method achieve inside the WFW?

Unlike slack-based formulations that can introduce wrench errors, the method relegates wrench errors to a negligible area within the WFW while operating beyond it.

Jul 16, 2026

Upload by Theodora

Steering Cable-Driven Parallel Robots (CDPRs) require cable tensions beyond their Wrench-Feasible Workspace (WFW) for aggressive maneuvers and after cable failures. While tension determination has been extensively studied, few methods address these out-of-WFW conditions with smooth, real-time behavior. This work extends the Analytic Center method to select differentiable tension sets using barrier-based optimization with nonlinear constraints. Results provide continuous tension profiles, fast convergence to a unique solution, and negligible wrench errors within the WFW, validated by Pareto dominance and numerical experiments.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages10

Reading Time25 min

Introduction

Cable-Driven Parallel Robots and Tension Distribution Algorithms

Limitations of p-norm and slack-based methods

Motivation and contributions of the proposed approach

X-ACTA: eXtended Analytic Center Tension distribution Algorithm for ﬁxed and mobile cable-driven-parallel-robot Domenico Dona’, Vincenzo Di Paola, Alberto Trevisani and Matteo Zoppi arXiv :2607 .08265v 1 [ cs .RO] 9 Jul 2026 Abstract—Steering Cable-Driven Parallel Robots (CDPRs) beyond their Wrench-Feasible Workspace (WFW) augments their capabilities in challenging scenarios such as during aggressive maneuvers or following a cable failure. In this context, although the determination of cable tensions is a well-studied topic, only a few approaches address these scenarios. Therefore, this paper introduces an extended version of the Analytic Center method as a criterion for selecting cable tensions outside the WFW while maintaining differentiability and including non-linear constraints. Notably, the proposed method maintains continuous and differentiable tension proﬁles, ensures fast real-time convergence to a unique solution, and, in contrast to other slack-based formulations, relegates wrench errors to a negligible area of the WFW. Its superiority in terms of smoothness and wrench error is conﬁrmed via Pareto dominance with respect to the leading state-of-the-art method. Lastly, the effectiveness of the method is demonstrated through numerical experiments. Index Terms—Parallel, Cable Robots, Wrench Feasible Workspace, Tension Distribution Algorithm, Analytic Center, Continuous, Differentiable, Non-linear Constraints. I. INTRODUCTION Cable-Driven Parallel Robots (CDPRs) are typically composed of a moving platform, namely a rigid body, actuated by cables exerting forces on it. The selection of cable tensions in CDPRs has been a core research topic since their birth [1] . In particular, overconstrained CDPRs, where the number of cables exceeds the payload’s Degrees of Freedom (DoFs), require the selection of a tension set among inﬁnitely many feasible ones. This choice is typically made by solving an optimization problem known as the Tension Distribution Algorithm (TDA) . The existing approaches differ in the choice of optimization objective, constraints, and solution method, typically tailored to the task requirements [2] . Generally, p-norm-based metrics have been widely adopted as objectives for TDAs [3] . The 1-norm, for example, is key to several studies [4]–[6] . Such problems are typically solved using Linear Programming (LP) approaches due to fast convergence; however, the jump between the vertices of the feasible polyhedron, resulting from the 1−norm minimization, often results in discontinuous tension proﬁles. Similarly, discontinuities can occur when using the ∞-norm [3] . Because Domenico Dona’ is with the Faculty of Engineering, Free University of Bozen-Bolzano, Via Bruno Buozzi 1, Bozen 39100, Italy (e-mail: [domenico.dona@unibz.it](domenico.dona@unibz.it)) . Vincenzo Di Paola and Matteo Zoppi are with Department of Mechanical, Energy, Management and Transportation Engineering (DIME), University of Genova, Via alla Opera Pia 15, Genova 16143, Italy (e-mail: vin[cenzo.dipaola@edu.unige.it](cenzo.dipaola@edu.unige.it); [matteo.zoppi@unige.it](matteo.zoppi@unige.it)). Alberto Trevisani is with the Department of Management and Engineering (DTG), University of Padua, Stradella San Nicola 3, Vicenza 36100, Italy (e-mail: [alberto.trevisani@unipd.it](alberto.trevisani@unipd.it)). Corresponding author: Domenico Dona’ Fig. 1. Scheme of a generic cable-driven parallel robot. continuity is a must to ensure precision while executing tasks, the criteria have been reformulated employing p-norms where 1 < p < ∞ [7] . Consequently, a widely adopted objective is the 2-norm of the tension vector [8]–[10] or its distance with respect toa reference tension, usually taken as the mean between the minimum and maximum ones [3], [11], [12] . The popularity of these methods relies on the possibility of efﬁciently solving the associated optimization problem, using either closed-form solutions [9], [11] or speciali

FAQs

What problem does the extended Analytic Center method address?

It selects cable tensions for steering CDPRs beyond the Wrench-Feasible Workspace while keeping differentiability and supporting nonlinear constraints.

How does the proposed method improve tension profile smoothness compared with common p-norm objectives?

It maintains continuous and differentiable tension profiles, avoiding discontinuities that can arise from 1-norm or ∞-norm minimization over feasible polyhedra.

What accuracy behavior does the method achieve inside the WFW?

Unlike slack-based formulations that can introduce wrench errors, the method relegates wrench errors to a negligible area within the WFW while operating beyond it.

Jul 16, 2026

Upload by Theodora