Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots

Abstract

International audienceThis paper deals with the wrench-feasible workspace (WFW) of n-degree-of-freedom parallel robots driven by n or more than n cables. The WFW is the set of mobile platform poses for which the cables can balance any wrench of a given set of wrenches, such that the tension in each cable remains within a prescribed range. Requirements of nonnegative cable tensions, as well as maximum admissible tensions, are thus satisfied. The determination of the WFW is an important issue since its size and shape are highly dependent on the geometry of the robot and on the ranges of allowed cable tensions. The approach proposed in this paper is mainly based on interval analysis. Two sufficient conditions are presented, namely, a sufficient condition for a box of poses to be fully inside the WFW and a sufficient condition for a box of poses to be fully outside the WFW. These sufficient conditions are relevant since they can be tested, with the means to test them being discussed in the paper. Used within usual branch-and-prune algorithms, these tests enable WFW determinations in which full-dimensional sets of poses (volumes) are found to lie within or, on the contrary, to lie outside the WFW. This provides a useful alternative to a basic discretization, the latter consisting of testing a discrete (zero-dimensional) finite set of poses. In order to improve the efficiency of the computations, a means to mitigate the undesirable effects of the so-called wrapping effect is introduced. The paper also illustrates how the proposed approach is capable of dealing with small uncertainties on the geometric design parameters of a parallel cable-driven robot

A cable-driven robot for architectural constructions: a visual-guided approach for motion control and path-planning

“…Cables are controlled usually by a positioning system (Borgstrom et al 2008) that actuates in motors for rolling and unrolling cables. These robots are capable of performing many manipulation tasks and they have several conveniences over typical robotic manipulators (German et al 2001): a smaller number of moving parts, a lower level of visual intrusion (Gouttefarde et al 2011), a larger working area and a higher payload ratio relative to the robot's weight. On the other hand, cable interferences, inaccuracies at the end-effector due to cable stretch, and the limited force in the downward directions are some the disadvantages of cable-driven robot (Usher et al 2005).…”

“…These problems led to some approaches (Oh and Agrawal 2006;Gouttefarde et al 2011;German et al 2001) that usually define the controllable workspace of cable-driven robots using a force-feasible methodology. The kinematics model is obtained by the distribution of cable forces (Borgstrom et al 2009): fully-constrained and under-constrained.…”

An Optimization Approach for the Inverse Kinematics of a Highly Redundant Robot

“…Cables are controlled usually by a positioning system that actuates in motors for rolling and unrolling cables. These robots are capable of performing many manipulation tasks and they have several conveniences over typical robotic manipulators [5]: a smaller number of moving parts, a lower level of visual intrusion [6], a larger working area and a higher payload ratio relative to the robots weight. On the other hand, cable interferences, inaccuracies at the end-effector due to cable stretch, and the limited force in the downward directions are some the disadvantages of cable-driven robot [20].…”

Wire Robot Suspension Systems for Wind Tunnels

“…Discretization approaches are also proposed in Hay & Snyman (2004;2005). Advanced approaches base on the continuous analysis and verification of the workspace as described in Bruckmann et al (2007a); Gouttefarde et al (2011;. The application of those methods is subject to future work.…”