A Real-Time Capable Forward Kinematics Algorithm for Cable-Driven Parallel Robots Considering Pulley Kinematics

Abstract

A real-time capable Forward Kinematics (FK) algorithm for Cable-Driven Parallel Robots (CDPRs) considering the pulley kinematics is proposed. The algorithm applies iteratively QR decomposition to solve a linearized version of the least squares problem representing the FK. Differential kinematics delivers an analytical expression for the Jacobian matrix of CDPRs considering the pulley kinematics. This Jacobian matrix is used to construct the linearization of the FK problem. Experimental and numerical results address the convergence capabilities of the proposed algorithm.

Redundancy Resolution Integrated Model Predictive Control of CDPRs: Concept, Implementation and Experiments

“…The Forward Kinematic algorithm used in this work is slightly different from the state-of-the-art published methods. Indeed, QR decomposition are used to iteratively solve the linearized version of the Forward Kinematic problem as described in [35].…”

“…Consequently, the pose of the platform can be calculated as the vector x minimizing the difference between the lengths calculated from the motor angular positions and those consistent with the kinematic model. This method is presented in [35] and briefly discussed in the Appendix.…”

A Nonlinear Model Predictive Control for the Position Tracking of Cable-Driven Parallel Robots

“…Blocks (b) and (c) correspond to the kinematic modeling of the CDPR and can be implemented using well-known methods, e.g. [58]- [60]. Note that the NMPC in block (a) is independent of blocks (b), (c) and (d) and thus independent of cable properties (e.g.…”

Unsupervised Neural Network Based Forward Kinematics for Cable-Driven Parallel Robots with Elastic Cables

“…Various works have led to optimization problems for real-time analysis based on minimizing the potential energy [18], finding the lowest equilibrium pose [7] or minimizing cable tensions [14]. Iterative (usually, Levenberg-Marquadt) algorithms have found themselves useful in locally minimizing pose errors [18], using Hessian matrix to construct convex problem [17] and Jacobian matrix to solve the linearized approximation of the FK problem [21] at hand.…”