Inverse kinematics of robot manipulators with offset wrist

Abstract

Ahstract-The inverse kinematics for a robot manipulator with offset wrist is formulated as a minimization problem in this paper to reduce its complexity and accelerate the computation speed. A specific type of robot such as Yaskawa MA1400, which has an offset between the last two axes, is chosen for analysis.Given an initial guess angle of last joint, all the 6 joint angles can be easily found through analytical solution. The output value is compared with the initial guess. An error function with only one variable is then defined and Newton-Raphson method is applied to search for the solution where the error goes to zero.To check the validity of the algorithm, forward kinematics is first computed and the position and orientation of end-effector are then applied in the inverse kinematics to solve the joint angles back. The computation converges within 5 iterations in cases when the angle 85 is far away from zero and the accuracy is within 10. 10 degree. When 85 approaches zero, searching direction is slightly modified to achieve convergence for the algorithm. The number of iterations increases for the same accuracy. The results show that the approach presented in this paper greatly reduces the computation time and is suitable for real time application.

Optimal path crossing the orientation exclusion zone of a robot with offset wrist

“…The methods of Milenkovic and Huang [25] as well as Aboaf and Paul [26] effectively fix combined angle θ 6 = 0 without attempting to minimize θ 7 . Furthermore, joints 5, 7 and 8 have axis directions ω 5 = ω 7 × ω 6 , ω 7 and ω 8 that are nearly separated by 90 • when tool deviation θ 7 is kept well under 90 • (see inset to Fig. 3).…”

“…Fig. 1(b) shows the MA1400 in the posture illustrated by Wu et al [7] showing the wrist offset. The dimensions of the MA1400 are from that source.…”

“…06 (1999) [5] Definition 3.40 states that a robot singularity is a "condition caused by collinear alignment of two or more robot axes resulting in unpredictable robot motion and velocities." The assertion that a robot with an offset wrist does not have a wrist singularity [6,7] is correct inasmuch as the type of offset in question allows the critical pair of joint axes to be parallel but not collinear. For this assertion to be made without qualification, however, further suggests that the path reversal occurring near where those joint axes become parallel is indeed not heretofore known.…”

A novel closed-form solution for the inverse kinematics of redundant manipulators through workspace analysis

“…For un-resoluble manipulators, different geometric approaches have been developed in literature. One interesting technique, based on the works presented in [54,55,56,57,58,59], considers a variation of the original manipulator with three joint axes intersecting at a single point. Then, Pieper closed-form method can be employed for solving the inverse kinematics of that modified manipulator.…”

Análisis Cinemático de Robots Manipuladores Redundantes: Aplicación a los Robots Kuka LWR 4+ y ABB Yumi

“…Para manipuladores no redundantes, en (Lin and Min, 2015) se utiliza un método geométrico para hallar las tres primeras articulaciones y un método analítico para las tresúltimas. Por otro lado, en (Kucuck and Bingul, 2005) se resuelve el problema para manipuladores concretos mediante distintos métodos puramente numéricos o puramente analíticos mientras que en (Wu et al, 2015) se resuelve dando un valor a q 6 que luego se corrige mediante un método iterativo. Finalmente, en (Pan et al, 2012) se utiliza un método mixto en el que se combinan las soluciones analíticas con las soluciones numéricas.…”