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...

For uncalibrated visual servoing for image-based dynamic control of robot manipulators, acquiring an image Jacobian matrix (interaction matrix) or its inverse matrix is necessary and difficult. In this paper, a new controller of uncalibrated visual sevro using pseudo inverse of image Jacobian matrix is presented, which based on dynamics of robot manipulators. In this method, camera’s intrinsic ...

By using the Hadamard matrix product concept, this paper introduces two generalized matrix formulation forms of numerical analogue of nonlinear differential operators. The SJT matrix-vector product approach is found to be a simple, efficient and accurate technique in the calculation of the Jacobian matrix of the nonlinear discretization by finite difference, finite volume, collocation, dual rec...

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when...

The mapping between the Cartesian space and joint space of robot manipulators has long been a difficult task for redundant robots. Two main methods are used in the classical approach. One is by using direct kinematic inversion in the position regime; the other is to use Jacobian Transformation in the velocity regime. However, for a redundant robot, a non-squared Jacobian matrix is resulted when...

Problems arising when kinematically redundant manipulators are controlled using the Jacobian pseudoinverse are related to the non-integrability of the standard pseudo-inverse. This paper presents a class of generalized inverses which have the property of being integrable within any simply connected, nonsingular region of the workspace. Integrability is obtained by deriving the equations which d...

A pseudo-Euclidean space, or Smarandache space is a pair (Rn, ω|− → O ). In this paper, considering the time scale concept on Smarandache space with ω|− → O (u) = 0 for ∀u ∈ E, i.e., the Euclidean space, we introduce the tangent vector and some properties according to directional derivative, the delta differentiable vector fields on regular curve parameterized by time scales and the Jacobian ma...

A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The motivated by the effectiveness local nonlinear smoothers at overcoming strong transients. In limit a small pseudo-time step, method reduces to smoothing technique, while in large steps, an exact recovered along with its quadratic properties. formulation re...

These supplementary notes are provided in an educational spirit. Section 2 shows how the cross-product formula for computing columns of the Jacobian emerges from direct calculus. Section 5 extends to arbitrary Euler angles. Our work is not limited to homogeneous coordinates or Euler angles. However, these representations are well known and chosen merely to present to a wider audience. In fact o...