Numerical Stability of Iterative Solvers for Inverse Kinematics
نویسنده
چکیده
In its basic formulation, the inverse kinematics (IK) problem seeks to compute a set of joint angles such that the end of a given joint chain coincides with a certain position in space. Further constraints, such as orientation, velocity, and preferences for curvature, are possible, but beyond the scope of this project. In this report, we describe the basic forward and inverse kinematics problems, describe mathematical techniques for solving them, and present results from our implementations. In particular, we study the Jacobian Pseudoinverse and Damped Least Squares methods. They can be numerically unstable, so we focus on cases when such problems arise. We conclude that Damped Least Squares performs better for our benchmarks, and given mathematical intuition as to why this is the case.
منابع مشابه
From Inverse Kinematics to Optimal Control
Numerical optimal control (the approximation of an optimal trajectory using numerical iterative algorithms) is a promising approach to compute the control of complex dynamical systems whose instantaneous linearization is not meaningful. Aside from the problems of computation cost, these methods raise several conceptual problems, like stability, robustness, or simply understanding of the nature ...
متن کاملStability of the Parareal Time Discretization for Parabolic Inverse Problem
The practical aspect in the parareal algorithm that it consist of using two solvers over different time stepping, the coarse and fine solvers to produce a rapid convergent iterative method for multi processors computations. The coarse solver solve the equation sequentially on the coarse time step while the fine solver use the information from the coarse solution to solve, in parallel, over the ...
متن کاملA stable iteration to the matrix inversion
The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...
متن کاملA hybrid numerical method for solving the inverse kinematics of a class of spatial flexible manipulators
This paper proposes a hybrid numerical method (HNM) to solve the inverse kinematics of a class of spatial flexible manipulators modeled b y mass/spring (mass-lumped stations and masslessspring fields) modeling method. HNM includes two parts: one is an implicit recursive numerical method (IRNM) which is used to f ind a better approximate solution to the inverse problem, the other is a global ite...
متن کاملAn iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...
متن کامل