Projecting a point using perpective projection involves finding where the line from the eye to the point intersects the viewplane . But i am finding it hard to relate this in terms of frame attachments of DH matrix as to why the perpectives are all zero. Please if anyone could explain me or suggest me good reads on this topic for explanation.
Dear Hirak,
I suggest you to see links and attached files in topic.
- Handbook Of Industrial Automation
https://books.google.dz/books?isbn=0203908589
- Forward Kinematics - Robotics@SNU
robotics.snu.ac.kr/edX/2014-1/lecturenotes/SNUx_Chapter_5.pdf
- Position and orientation of rigid bodies
https://homes.cs.washington.edu/~todorov/.../05_Kinematics.pdf
- Kinematic Modeling, Identification, and Control of Robotic Manipulators
https://books.google.dz/books?isbn=1461319994
- Kinematic Model of Robot Manipulators - LAR-DEIS - Unibo
www-lar.deis.unibo.it/people/cmelchiorri/Files.../FIR_04_Kinem.p...
Best regards
Hello Hirak,
Posture and orientation may be jointly and linearly handled by means of the homogeneous coordinates transforms. DH is only a specific homogeneous coordinates-based convention used in robotics to model the spatial transform from one articular join to the next one. By composing such multiple joint transformations, it is easily possible to determine both the 3D posture and the 3D orientation of the robot end effector relative to its base frame. By using its inverse transform, the coordinates of any 3D point in the workspace may be expressed relative to the end effector frame. Let us suppose now that a camera is attached to the end effector. The perspective transform as an intermediairy transform then allows to compute the coordinates of this 3D point relative to the camera viewplane frame. Doing that, you naturally switch from 3D homogeneous coordinates to 2D homogeneous coordinates.
Let us note that the perspective transform itself admits a linear representation according to the homogeneous coordinates formalism...
For more technical/mathematical details, I suggest that you check out both sections §5.2.1 and §5.2.2 pages 143-144 from:
- Horaud et al., " Vision par ordinateur: outils fondamentaux ", 1995 - https://hal.inria.fr/inria-00590049/document
The document is written in French language but this should not be an obstacle thanks to the available online language translators.
Hoping it will be helpful to you.
Regards
Dear
The advantage of the D-H representation is that it is a minimal representation, in the sense of requiring the smallest number of parameters to describe the robot’s kinematic structure.We begin by recalling the Chasles-Mozzi theorem: Any displacement of a rigid body can be expressed as a finite rotation about some fixed line in space (the screw axis), followed by a finite translation parallel to the fixed line. Since both the rotation and translation are taken about the same fixed line, reversing their order still results in the same displacement.
regards
- Badges
- Science topic
- Similar topics
- Engineering
- Modeling