Rapid Computation of Optimally Safe Tension Distributions for Parallel Cable-Driven Robots

Abstract

Abstract-In this paper, we present a novel linear-program formulation that yields "optimally safe" (OS) tension distributions in parallel cable-driven robots by the introduction of a slack variable. The slack variable also enables explicit computation of a near-optimal, feasible starting point. This, in turn, enables rapid computation of the OS tension distributions. The formulation also contains a parameter that can be used to steer cable tensions toward desired regions of operation. We present static results from two simulated robotic systems that demonstrate the ability of our formulation to avoid tension limits. Simulated execution of highly dynamic trajectories on both systems demonstrates rapid-computation abilities. Furthermore, we present experimental results from a real robotic system that further validate the importance of safe tension distributions.Index Terms-Cable tension distributions, parallel cable-driven robots, parallel robots, redundant robots.

An Overview of the Development for Cable-Driven Parallel Manipulator

“…In [33,39,40], the authors, respectively, take advantage of convex method, variant of bland's pivot rule, and gradient projection to obtain the tension distribution. In the meanwhile, [41,42] address the same problem by using minimization of the Euclidean norm of the cable tensions and p-norm of the relative cable tensions to avoid the discontinuity of the cable tension in a continuous trajectory with linear-program formulation.…”

Tension distribution shaping via reconfigurable attachment in planar mobile cable robots

“…[18][19][20][21][22] In this paper we will focus our discussion on the analysis and optimization of the tension factor T F , which is defined by 23…”

Cable Force-Balancing Distribution of the Cable-Driven Parallel Mechanism for Actuator Saturation Avoidance

“…Thus, every cable tensile force of the CDPM should always be kept positive in order for the CDPM to be properly operational. Indeed, the optimization problem for the cable force distribution of the CDPM should be defined by an appropriate objective function subject to inequality conditions to secure that every cable force is kept within the range, between the minimum and maximum tensile cable forces [1][2][3][4][5]. Recently, the pseudoinverse solution equation for the redundantly actuated PM with one redundant actuation is interpreted as line equations.…”

“…The method is effective to avoid actuator saturation and can be summarized as follows. Force equation of the n DOF CDPM with nr  cables can be expressed as follows: (2) Note that the general equation for cable force solutions can be obtained by taking the pseudo-inverse of (1) as follows: Indeed, as shown in [6], the optimal solution for the cable actuation force can be found through the search for the intersection points or intersection lines between lines and/or planes. But differently from in [6], additional planes,   f at the current searching reference point is minimal compared with ones at other intersection points is met.…”