A Novel Solution to the Inverse Kinematics Problem of General 7R Robots

Abstract

Task and Motion Planning for a 7-DOF serial robot containing only revolute joints needs a fast and numerically stable inverse kinematics solution. The analytical methods are real-time, but they are robot dependent. Although the numerical methods based on inverse differential kinematics can solve the inverse kinematics problem (IKP) of 7R robots with arbitrary geometric parameters, their numerical stability is insufficient. Moreover, it is time-consuming for them to converge to a single solution that depends on the initial guess. The main innovation of this article is the development of a practical method for solving the IKP of general 7R robots. The proposed method can find multiple solutions and is also faster than the numerical method. It combines symbolic preprocessing, Sylvester dialytic elimination, and eigendecomposition. First, according to the Denavit-Hartenberg convention of geometric representation, a general kinematics model of a 7R manipulator is established. Secondly, the joint variables are separated by symbolic preprocessing, and then two symbolic matrices are obtained. After numerical substitution, a square matrix of polynomial coefficients is computed through Gaussian and Sylvester dialytic elimination. Finally, utilizing the eigendecomposition of the matrix restructured from the square matrix, the values of some variables are obtained, and then the remaining variables are solved by back-substitution. The simulation and experimental data are analyzed. The comparison results verify that the proposed method applies to solving the IKP of general 7R robots and is almost real-time, effective, and numerically stable.

Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets

“…IK solutions are often computed by solving a nonconvex mathematical program. The tools of algebraic geometry can be used to reformulate certain IK problems as systems of polynomial equations, which can be solved as eigenvalue problems [23], [24], [25]. While simpler than a nonconvex optimization problem, we require a closed-form solution for our desired parametrization.…”

An improved inverse kinematics solution method for the hyper‐redundant manipulator with end‐link pose constraint

“…Zaplana et al (2018) proposed a solution framework to obtain the closed-form solution by adding constraints on redundant degrees of freedom. Xie et al (2022) proposed an inverse kinematic solution method by combining the symbol processing method, Sylvester dialytic elimination, and eigendecomposition. Martín et al (2018) proposed the natural-CCD (Cyclic Coordinate Descent) algorithm.…”

Axis manipulation to solve Inverse Kinematics of Hyper-Redundant Robot in 3D Space

“…The algebraic strategy includes Jacobian, Grobner bases, the product of exponential [6], analytical inverse kinematics [7][8], conformal geometric algebra [9], and generalised analytical methods [10]. In the iterative approach, several strategies have been proposed, such as Artificial Neural Network [11] [12], iterative algorithm [13], genetics algorithm, ANFIS, Fuzzy Logic, evolution algorithm (EA) [14] [15], and iterative algorithm [16] [17]. The geometric approach offers a simpler calculation such as repetitive basic inverse kinematics of a two-link [18], the angular deflection of the upper platform concerning the lower platform [19], a non-iterative geometric approach for inverse kinematics [20], and a modified modal method [21] [22].…”