For redundant robot kinematics we construct an extended Jacobian inverse that approximates the Jacobian pseudo-inverse. Our construction relies on the approximation of codistributions associated with the Jacobian pseudo-inverse by an integrable codistribution, spanned by differentials of certain functions that serve as components of the augmenting kinematics map in the extended Jacobian inverse...

This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Exampl...

This paper is aimed at presenting a study on the kinematics of the Tricept robot, which comprises a three-degree-offreedom (dof) parallel structure having a radial link of variable length. The robot workspace is characterized and the inverse kinematics equation is obtained by using spherical coordinates. The inverse differential kinematics and statics are derived in terms of both an analytical ...

We study Jacobian inverse kinematics algorithms for mobile manipulators composed of a nonholonomic mobile platform and a holonomic onboard manipulator. In general, the Jacobian algorithms converge locally, often producing weird end effector and platform trajectories. In the paper we use the existing theory of Newton algorithms in order to improve the quality of convergence of the Jacobian algor...

The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. Both forward and inverse kinematics solutions for the TR 4000 educational robot arm are presented. The closed form solution of the inverse kinematics problem is of utmost importance in controlling robotic manipulator. In this paper, a closed form solution to the inverse kinematics...

In this paper the problem of matching Forward Kinematics (FK) motion of a 3 Dimensional (3D) joint chain to the Inverse Kinematics (IK) movement and vice versa has been addressed. The problem lies at the heart of animating a 3D character having controller and manipulator based rig for animation within any 3D modeling and animation software. The seamless matching has been achieved through the us...

The subject of this paper is a special class of parallel manipulators. First, we analyze a family of threedegree-of-freedom manipulators. Two Jacobian matrices appear in the kinematic relations between the jointrate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The singular configurations of these matrices are studied. The is...

This paper presents an image-based visual servo controller for an industrial robot. The simple structure controller is based on a transposed Jacobian which feeds back directly the image feature errors and the joint velocities. Under these hypotheses, the control algorithm does not need to use the inverse kinematics and the inverse jacobian matrix. Experimental results in two different industria...

The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, w...