@INPROCEEDINGS{L_Brodtmann2023-pa,
title = "Kinematics of Serial Robotics - Algorithms for simplified
calculation of Direct \& Inverse Kinematics in a Consistent
Coordinate Reference system",
booktitle = "Emerging Technologies and Future of Work",
author = "L. Brodtmann, Norbert and Schilberg, Daniel",
abstract = "A novel algorithm structure of direct and inverse kinematics
for the motion calculation of articulated robots is presented.
These algorithms are based on a 3D rotation matrix, which is
known in itself but not established in robotics, as well as the
principle of a normalized vector orientation, introduced here.
The algorithms can handle any number of rotation and telescop
axes, can be fully parameterized according to individual
hardware and are also much clearer than the established \&
classic Denavit-Hartenberg conventions.State of the art
According to current research (2022/23), the (published) robot
mathematics are still based on the classical Denavit-Hartenberg
conventions from 1955, which formalize the calculation of the
``Direct'' kinematics. For this purpose, they require a
separate Local Coordinate System (LCS) for each robot arm in
addition to the stationary (world) reference coordinate system.
On the one hand, the spatial position of individual links to
each other is therefore not directly comparable. On the other
hand, the movement of a single robot arm changes the spatial
point position of each following link in the kinematic chain
accordingly - which is not represented by the LCS.For decades,
the DH conventions have been considered state of the art for
forward and direct kinematics in science and technology.
Standard algorithms for backward and inverse kinematics,
however, have not been disclosed to the general public.
Companies that manufacture robots consider the computational
core of their own algorithms to be a ``trade secret''. Only the
operator level is published.Solution approachIn this paper, a
general inverse kinematics trajectory control algorithm for
serial robot systems (articulated arm and SCARA) is presented.
These algorithms systematically avoid the problem of
uncontrolled singularity of inverse kinematics. The combination
of similar rotation matrices working consistently in the
(world) reference coordinate system as well as the normalized
vector orientation -- introduced in this work -- offer a number
of advantages. They not only allow a doubtless parameter
assignment without danger of confusion of the two length
parameters required for each DH matrices. It becomes possible
to specify a generally valid algorithm of inverse kinematics
for trajectory control.The solution to be published here does
not require any additional location coordinates for each moving
robot element, it consistently references one and the same
(world) reference coordinate system. Any vector position and
its orientation in 3D-Space can be compared directly - an
essential prerequisite for the snapping algorithms of the
inverse kinematics also disclosed here and the additional
option of an integrated traversability of the robot on the
gantry system. The consistency of the coordinate system enables
perspective representation in imaging processes.The vector
input values required for this are directly available -- in the
(world) reference coordinate system (CRS) -- for each point of
the kinematic chain.For hardware control, kinematic angular
values of the robot arm movement are output via a motion
protocol. A specially developed simulation visualizes the
moving robot silhouette and the path to be traced in a freely
selectable perspective.",
publisher = "AHFE International",
year = 2023,
conference = "AHFE 2023 Hawaii Edition"
}