Dynamic Models of Spherical Parallel Robots for Model-Based Control Schemes

Abstract

In this paper, derivation of different forms of dynamic formulation of spherical parallel robots (SPRs) is investigated. These formulations include the explicit dynamic forms, linear regressor, and Slotine-Li (S-L) regressor, which are required for the design and implementation of the vast majority of model-based controllers and dynamic parameters identification schemes. To this end, the implicit dynamic of SPRs is first formulated using the principle of virtual work in task-space, and then by using an extension, their explicit dynamic formulation is derived. The dynamic equation is then analytically reformulated into linear and S-L regression form with respect to the inertial parameters, and by using the Gauss-Jordan procedure, it is reduced to a unique and closed-form structure. Finally, to illustrate the effectiveness of the proposed method, two different SPRs, namely, the ARAS-Diamond, and the 3-RRR, are examined as the case studies. The obtained results are verified by using the MSC-ADAMS ® software, and are shared to interested audience for public access.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

“…However, the problem of dynamic analysis of RSPMs has been addressed in various works using Newton-Euler, the Lagrange method [37], the recursive matrix method [38], the principle of virtual work [39,40], and the D'Alembert principle approach [41]. A Newton-Euler approach based on screw theory has been proposed to obtain actuator torques and constraint wrenches [42]. In ref.…”

“…In the first step, z 2 can be used as control input for the system presented in Eq. (42). So, z 2 is defined as a function of z 1 as follows:…”