Inverse Kinematics of 7-DOF Robots and Limbs by Decomposition and Approximation

Abstract

The paper proposes a novel method for extremely fast inverse kinematics computation suitable for fast-moving manipulators and their path planning and for the animation of anthropomorphic limbs. In a preprocessing phase, the workspace of the robot is decomposed into small cells, and data sets for joint angle vectors (configurations) and hand positions/orientations (postures) are generated randomly in each cell using the forward kinematics. Due to the existence of multiple solutions for a desired posture, data classification is utilized to identify various solutions. The generated and classified data are used to determine the parameters of a simple linear or quadratic model that closely approximates the inverse kinematics within a cell. These parameters are stored in a lookup file. During the online phase, given the desired posture, the index of the appropriate cell is found, the model parameters are retrieved, and the joint angle vectors are computed. The advantages of the proposed method over the existing approaches are discussed. Data resulting from many trial runs are compiled for a manipulator and an anthropomorphic arm to demonstrate the performance of the proposed method.

Real-time solution of the forward kinematics for a parallel haptic device using a numerical approach based on neural networks

“…Results show that the fourth order Taylor series approximation provides acceptable prediction accuracy. Tarokh proposed a fast-speed algorithm to compute the inverse kinematics of a 7-DOF robot through decomposition and approximation [9]. The workspace of the robot was decomposed into small cells, and a simple linear or quadratic model was used to approximate the inverse kinematics within a cell.…”

“…Various numerical approaches have been studied in Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] to obtain fast and efficient FKP solutions for parallel mechanisms. These approaches include iterative approaches, polynomial approximation approaches, optimization algorithmbased approaches, and neural network (NN)-based approaches.…”

Inverse kinematics solution for trajectory tracking using artificial neural networks for SCORBOT ER-4u

“…These are Algebraic, Geometric and Iterative methods to find the solutions for the IK problem. Similarly, agreed by [3] and [4] that for Algebraic method, there's no closed form of solution and specifically not suited for real (physical) robotic applications. As for Geometric method, suggested by [1] and [4] the IK solution is limited up to 3 DOF robots.…”

Novel inverse kinematic approaches for robot manipulators with Pieper-Criterion based geometry

“…Generally, analytical approaches, which yield complete, accurate and fast solutions, are preferable to numerical ones that are usually used to gain the approximate solutions by convergent iteration [9]. Different from the above commonly used methods, a mixed numerical-analytical approach is proposed in [10] to approximate the IK solutions, product-of-exponentials (PoE) formulas [11][12][13], vector dot product operations [14][15][16][17][18] and double quaternions [19,20] are involved to simplify the IK solving processes.…”