@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"
}