The Robotics Toolbox is a software package that allows a MATLAB user to readily create and manipulate datatypes fundamental to robotics such as homogeneous transformations, quaternions and trajectories. Functions provided, for arbitrary serial-link manipulators, include forward and inverse kinematics, Jacobians, and forward and inverse dynamics. This article introduces the Toolbox in tutorial form, with examples chosen to demonstrate a range of capabilities. The complete Toolbox and documentation is freely available via anonymous ftp.

A robotics toolbox for MATLAB

To relate measurements made by a sensor mounted on a mechanical link to the robot’s coordinate frame, we must first estimate the transformation between these two frames. Many algorithms have been p...

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Hand-Eye Calibration Using Dual Quaternions

Mathematics of three-dimensional eye rotations.

The authors have developed "augmented reality" technology, consisting of a see-through head-mounted display, a robust, accurate position/orientation sensor, and their supporting electronics and software. Their primary goal is to apply this technology to touch labor manufacturing processes, enabling a factory worker to view index markings or instructions as if they were painted on the surface of a workpiece. In order to accurately project graphics onto specific points of a workpiece, it is necessary to have the coordinates of the workpiece, the display's virtual screen, the position sensor, and the user's eyes in the same coordinate system. The linear transformation and projection of each point to be displayed from world coordinates to virtual screen coordinates are described, and the experimental procedures for determining the correct values of the calibration parameters are characterized. >

Calibration of head-mounted displays for augmented reality applications

The design of strapdown inertial navigation system (INS) algorithms based on dual quaternions is addressed. Dual quaternion is a most concise and efficient mathematical tool to represent rotation and translation simultaneously, i.e., the general displacement of a rigid body. The principle of strapdown inertial navigation is represented using the tool of dual quaternion. It is shown that the principle can be expressed by three continuous kinematic equations in dual quaternion. These equations take the same form as the attitude quaternion rate equation. Subsequently, one new numerical integration algorithm is structured to solve the three kinematic equations, utilizing the traditional two-speed approach originally developed in attitude integration. The duality between the coning and sculling corrections, raised in the recent literature, can be essentially explained by splitting the new algorithm into the corresponding rotational and translational parts. The superiority of the new algorithm over conventional ones in accuracy is analytically derived. A variety of simulations are carried out to support the analytic results. The numerical results agree well with the analyses. The new algorithm turns out to be a better choice than any conventional algorithm for high-precision navigation systems and high-maneuver applications. Several guidelines in choosing a suitable navigation algorithm are also provided.

Strapdown inertial navigation system algorithms based on dual quaternions

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion-vector pairs as spatial operators, is compared with homogeneous transforms in terms of computational efficiency and storage economy. The conclusion drawn is that quaternion-vector pairs are as efficient as, more compact than, and more elegant than their matrix counterparts. A robust algorithm for converting rotational matrices into equivalent unit quaternions is described, and an efficient quaternion-based inverse kinematics solution for the Puma 560 robot arm is presented. >

On homogeneous transforms, quaternions, and computational efficiency

A computational analysis and a comparison of line-oriented representations of general (ie rotational and translational) spatial displacements of rigid bodies are presented Four mathematical formalisms for effecting a general spatial screw displacement are discussed and analyzed in terms of computational efficiency in performing common operations needed in kinematic analysis of multilinked spatial mechanisms The corresponding algorithms are analyzed in terms of both sequential and parallel execution It is concluded that the dual-unit quaternion representation offers the most compact and most efficient screw transformation formalism but that line-oriented methods in general are not well suited for efficient kinematic computations or real-time control applications Owing to line-based geometry, underlying its definition, screw calculus represents a set of valuable tools in theoretical kinematics However, the mathematical redundancy inherent in Plucker coordinate space representation makes the screw calculus computationally less attractive than the corresponding point-oriented formalisms >

A computational analysis of screw transformations in robotics

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion/vector pairs as spatial operators, is discussed and analyzed. Sequential and parallel algorithms for some of the common spatial operations are given for both homogeneous transforms and quaternion/vector pairs and compared in terms of computational efficiency. The two approaches are shown to be essentially equivalent in the absence of the need for frequent renormalization of rotational operators. >

J. Funda

Papers

On homogeneous transforms, quaternions, and computational efficiency

A computational analysis of screw transformations in robotics

A comparison of transforms and quaternions in robotics