Fast Trajectory Planning for VGT Manipulator via Convex Optimization

Yongsheng Yang,Shiqiang Hu,Bosen Jiang

doi:10.5772/60506

Abstract

Variable-geometry truss (VGT) can be used as joints in a large, lightweight, high load-bearing manipulator for many industrial applications. This paper introduces the modelling process of a multisection three-degree-freedom double octahedral VGT manipulator and proposes a new point-to-point trajectory planning algorithm for a VGT manipulator with a nonlinear convex optimization approach. The trajectory planning problem is converted to a quadratic convex optimization problem, and if some parameters are appropriately chosen the proposed algorithm is proved to be of global convergence and to have a super-linear convergence rate. The effectiveness of the proposed algorithm is illustrated by numerical simulation.

Highlights

Variable-geometry truss (VGT) manipulator is a kind of hyper-redundant manipulator with a very large degree of kinematic redundancy
Koryo Miura proposed the concept of VGT in 1984 [1] and several papers discussed the design of different structures for a VGT manipulator, such as Rafael AvileHs’s paper in 2000 [2], K
Remark 2: Because of the particularity of the VGT trajectory planning problem, the original problem is converted to a quadratic convex optimization problem, and in Algorithm 1 the Hessian matrix of subproblem (31) is W (Xk, λk), which can be written in simple form

Summary

Introduction

Variable-geometry truss (VGT) manipulator is a kind of hyper-redundant manipulator with a very large degree of kinematic redundancy. We use l0 to represent the lengths of the rods in bottom plane and top plane and use l and Regina Sun-Kyung Lee in 2000 [9] These papers are all focused on the forward and inverse prob‐. The three actuators compose a plane, which is lems, and there are few papers discussing the trajectory planning of VGT manipulator with multiple modules. Nonozhkin’s paper in 2006 [11] and Chien-Chou Lin’s paper in 2012 [12] These papers are only focused on the trajectory planning problem in the two-dimensional plane of the manipulators. Le kinematic problems in the remaining2.2pFaorwtaordfkSineemcattiioc pnro2ble.m for single VGT module. By using (1-4), the forward kinematic problem for the single VGT module is solved

Inverse kinematic problem for single VGT module

Trajectory planning algorithm

Convergence and convergence rate analysis

Simulation

Conclusions