Available Wrench Set for Planar Mobile Cable-Driven Parallel Robots

Abstract

Cable-Driven Parallel Robots (CDPRs) have several advantages over conventional parallel manipulators most notably a large workspace. CDPRs whose workspace can be further increased by modification of the geometric architecture are known as Reconfigurable Cable Driven Parallel Robots(RCDPRs). A novel concept of RCDPRs, known as Mobile CDPR (MCDPR) that consists of a CDPR carried by multiple mobile bases, is studied in this paper. The system is capable of autonomously navigating to a desired location then deploying to a standard CDPR. In this paper, we analyze the Static equilibrium (SE) of the mobile bases when the system is fully deployed. In contrast to classical CDPRs we show that the workspace of the MCDPR depends, not only on the tension limits, but on the SE constraints as well. We demonstrate how to construct the Available Wrench Set (AWS) for a planar MCDPR wih a point-mass end-effector using both the convex hull and Hyperplane shifting methods. The obtained results are validated in simulation and on an experimental platform consisting of two mobile bases and a CDPR with four cables.

Wrench-Feasible Workspace of Mobile Cable-Driven Parallel Robots

“…For MCDPRs, AWS takes the form of a convex polytope and is the image of the tension space under the linear mapping of the wrench matrix W [?, 25,35]. Thus V -representation defines the AWS of MCDPRs by finding the set of vertices forming the boundary of the convex polytope.…”

“…The classical HSM used to characterize the AWS of the CDPRs is explained in [?, 25]. However, due to the additional static equilibrium conditions, the classical HSM is not sufficient to fully characterize the AWS of MCDPRs [35]. As a consequence, this section introduces an improved version of HSM while taking into account the static equilibrium conditions of the MCDPR mobile bases in addition to the cable tension limits.…”

“…For a given pose, the set of wrenches a mechanism can generate is defined as Available Wrench Set (AWS) [35]. For classical CDPRs, AWS A CDPR depends uniquely on the robot's geometric architecture and the cable tension limits [?, 25], expressed as:…”

“…By adding the additional conditions associated with the static equilibrium of the mobile bases, A is no longer a zonotope, but a convex polytope [35]. The two widely used approaches to characterize such convex polytopes are V -representation, known as the Convex Hull approach, and H -representation, known as the Hyperplane Shifting Method (HSM) [26].…”

FASTKIT: A Mobile Cable-Driven Parallel Robot for Logistics

“…The AWS for CDPRs only takes into account the Static Equilibrium (SE) of the moving-platform. In contrast, for FASTKIT to be in SE, both mobile bases and the moving-platform should be in SE [31]. Its a necessary and a sufficient condition for the FASTKIT to be in SE.…”