A New Approach to the Solution of Robot Kinematics Based on Relative Transformation Matrices

In analyzing robot manipulator kinematics, we need to describe relative movement of adjacent linkages or joints in order to obtain the pose of end effector (both position and orientation) in reference coordinate frame. Denavit-Hartenberg established a method based on a 4×4 homogenous matrix so called “A” matrix. This method used by most of the authors for kinematics and dynamic analysis of the robot manipulators. Although it has many advantages, however, finding the elements of this matrix and link/joint’s parameters is sometimes complicated and confusing. By considering these difficulties, the authors proposed a new approach called ‘convenient approach’ that is developed based on “Relative Transformations Principle”. It provides a very simple and convenient way for the solution of robot kinematics compared to the conventional D-H representation. In order to clarify this point, the kinematics of the world known Stanford manipulator has been solved through D-H representation as well as convenient approach and the results are compared.

ROBUST MOSAICKING OF UAV IMAGES WITH NARROW OVERLAPS

This paper considers fast and robust mosaicking of UAV images under a circumstance that each UAV images have very narrow overlaps in-between. Image transformation for image mosaicking consists of two estimations: relative transformations and global transformations. For estimating relative transformations between adjacent images, projective transformation is widely considered. For estimating global transformations, panoramic constraint is widely used. While perspective transformation is a general transformation model in 2D-2D transformation, this may not be optimal with weak stereo geometry such as images with narrow overlaps. While panoramic constraint works for reliable conversion of global transformation for panoramic image generation, this constraint is not applicable to UAV images in linear motions. For these reasons, a robust approach is investigated to generate a high quality mosaicked image from narrowly overlapped UAV images. For relative transformations, several transformation models were considered to ensure robust estimation of relative transformation relationship. Among them were perspective transformation, affine transformation, coplanar relative orientation, and relative orientation with reduced adjustment parameters. Performance evaluation for each transformation model was carried out. The experiment results showed that affine transformation and adjusted coplanar relative orientation were superior to others in terms of stability and accuracy. For global transformation, we set initial approximation by converting each relative transformation to a common transformation with respect to a reference image. In future work, we will investigate constrained relative orientation for enhancing geometric accuracy of image mosaicking and bundle adjustments of each relative transformation model for optimal global transformation.

ROBUST MOSAICKING OF UAV IMAGES WITH NARROW OVERLAPS

This paper considers fast and robust mosaicking of UAV images under a circumstance that each UAV images have very narrow overlaps in-between. Image transformation for image mosaicking consists of two estimations: relative transformations and global transformations. For estimating relative transformations between adjacent images, projective transformation is widely considered. For estimating global transformations, panoramic constraint is widely used. While perspective transformation is a general transformation model in 2D-2D transformation, this may not be optimal with weak stereo geometry such as images with narrow overlaps. While panoramic constraint works for reliable conversion of global transformation for panoramic image generation, this constraint is not applicable to UAV images in linear motions. For these reasons, a robust approach is investigated to generate a high quality mosaicked image from narrowly overlapped UAV images. For relative transformations, several transformation models were considered to ensure robust estimation of relative transformation relationship. Among them were perspective transformation, affine transformation, coplanar relative orientation, and relative orientation with reduced adjustment parameters. Performance evaluation for each transformation model was carried out. The experiment results showed that affine transformation and adjusted coplanar relative orientation were superior to others in terms of stability and accuracy. For global transformation, we set initial approximation by converting each relative transformation to a common transformation with respect to a reference image. In future work, we will investigate constrained relative orientation for enhancing geometric accuracy of image mosaicking and bundle adjustments of each relative transformation model for optimal global transformation.