Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

Abstract

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Tekil konumlardan geçen paralel robotlar için hareket planlamasında optimizasyon

“…Ancak bu çerçevede birden çok seçim alternatifi mevcuttur ve yapılacak kötü seçimler robotun uç noktasının yörünge üzerinde ileri-geri hareket etmesine yol açar [15]. Bir sonraki bölümde bu problemi önlemeye yönelik bir teorem geliştirilmiş ve ispatlanmıştır.…”

“…Paralel robotların Tip 2 tekil konumlardan kontrollü bir şekilde geçerek çalışma uzaylarının tamamını kullanabilmelerini sağlamak için, hareketli platformun hız ve ivmesi, hareket denklemleri geçilmek istenen tekil konumda tutarlı olacak şekilde planlanmalıdır [15,16]. Jui ve Sun [17] bu prensibe dayanan ve eyleyici limitlerini de göz önüne alan bir algoritma üzerinde çalışmışlardır.…”

A switching inverse dynamics controller for parallel manipulators around drive singular configurations

“…Ider [5,6] showed that a parallel manipulator can pass through its drive singular configurations while the * Correspondence: mozdemir@metu.edu.tr required actuator forces remain finite if the trajectory is planned such that its dynamic equations of motion are consistent at these singularities. He further showed that the dynamic equations can be modified to avoid ill-conditioning in their neighborhood.…”

A Study on Motion Planning of Four-Bar Mechanisms in the Presence of Singularities

“…However, non-redundancy offers improvements in terms of cost and complexity. One of the solutions in this regard is the planning of the motion in order to ensure the consistency of the dynamic model even at the singular position [9][10][11][12][13]. This motion planning technique has been also adapted to rigid-link flexible-joint and flexible parallel robots [14,15].…”