Stiffness-based Analytic Centre Method for Cable-Driven Parallel Robots

TL;DR

The paper addresses the tension distribution problem in Cable-Driven Parallel Robots (CDPRs) with a focus on stiffness-aware control. It proposes the Analytic Center with Stiffness (ACS), a barrier-based optimization that tunes active stiffness through cable tensions while satisfying the wrench balance $\mathbf{W}\boldsymbol{\tau}+\boldsymbol{w}_e=0$ and tension bounds. Compared with the Adaptive Preload Control (APC) approach across planar and spatial CDPRs, ACS provides smoother tension profiles, safer operation without frequent limit saturation, and competitive computation time. The findings indicate that ACS is a practical method for real-time stiffness adaptation in CDPRs, with future work exploring experimental validation and nonlinear effects.

Abstract

Nowadays, being fast and precise are key requirements in Robotics. This work introduces a novel methodology to tune the stiffness of Cable-Driven Parallel Robots (CDPRs) while simultaneously addressing the tension distribution problem. In particular, the approach relies on the Analytic-Centre method. Indeed, weighting the barrier functions makes natural the stiffness adaptation. The intrinsic ability to adjust the stiffness during the execution of the task enables the CDPRs to effectively meet above-mentioned requirements. The capabilities of the method are demonstrated through simulations by comparing it with the existing approach.

Figures (8)

• Figure 3: Level curves of Linear Programming (LP), Quadratic Programming (QP), and Analytic Center (AC). The objectives are normalized to have the same scale. Different example solutions are depicted in black, blue, and green. Refer to Table \ref{['tab:models']} for the data used.
• Figure 4: Level curves of Analyitc Center with Stiffness (ACS) and Adaptive Preload Control (APC) for two representative values of the preload parameter $\eta_c$. The objectives are normalized to have the same scale.
• Figure 7: Cable tension results for the Adaptive Preload Control (APC) and Analytic Center with Stiffness algorithms for the planar four cables robot.
• Figure 8: Cable tension results for the Adaptive Preload Control (APC) and Analytic Center with Stiffness algorithms for the spatial eight cables robot.
• Figure 9: Sum of tensions and preload parameter evolution for the four cables robot; it is worth noting that the ACS algorithm is smoother.