The singularities of a 3R robot are usually determined, in terms of its joint angles, from the determinant of its Jacobian which can then be mapped onto the robot’s workspace through its forward kinematics. The presence of cusps in these singularity plots permits to change robot’s posture without meeting a singularity and hence their relevance. This paper shows how, using Distance Geometry, the...

This paper briefly discusses two of the well-known position/force control schemes used for industrial manipulators: Admittance Control and Hybrid Position/Force Control. In order to eliminate the instability problem that may occur in the customary versions of these schemes for large position errors, a modification is proposed, which is based on determining the joint-space position errors using ...

In this paper, a dual system consisting of two 5 DOF (RRRRR) robot manipulators is considered as a cooperative robotic system used to manipulate a rigid payload on a desired trajectory between two desired initial and end positions/orientations. The forward and inverse kinematic problems are first solved for the dual arm system. Then, dynamics of the system and the relations between forces/momen...

A class of trust-region algorithms is developed and analyzed for the solution of optimization problems with nonlinear equality and inequality constraints. Based on composite-step trust region methods and a filter approach, the resulting algorithm also does not require the computation of exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices. As demonstr...

All methods for solving linear or nonlinear systems of equations require the evaluation of residual vectors, most algorithms are based on Jacobian-vector products and many schemes involve vector-Jacobian products. Moreover, while only exact Newton methods form and factor the Jacobian explicitly, some information about the size of its elements or the structure of its spectrum appears to be indes...

Averaging diffeomorphisms is a challenging problem, and it has great applications in areas like medical image atlases. The simple Euclidean average can neither guarantee the averaged transformation is a diffeomorphism, nor get reasonable result when there is a local rotation. The goal of this paper is to propose a new approach to averaging diffeomorphisms based on the Jacobian determinant and t...

Newton-Krylov methods, combination of Newton-like methods and Krylov subspace methods for solving the Newton equations, often need adequate preconditioning in order to be successful. Approximations of the Jacobian matrices are required to form preconditioners and this step is very often the dominant cost of Newton-Krylov methods. Therefore, working with preconditioners destroys in principle the...

A parametric, continuous-time Markov model for digraph panel data is considered. The parameter is estimated by the method of moments. A convenient method for estimating the variance–covariance matrix of the moment estimator relies on the delta method, requiring the Jacobian matrix—that is, the matrix of partial derivatives—of the estimating function. The Jacobian matrix was estimated hitherto b...

The computation of solution paths for continuation problems requires the solution of a sequence of nonlinear systems of equations. Each nonlinear system can be solved by computing the solution of a succession of linear systems of equations determined by Jacobian matrices associated with the nonlinear system of equations. Points on the solution path where the Jacobian matrix is singular are refe...