Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space. However, due to disadvantages of most widely used mathematical constructs for description of orientation such as Euler angles and rotational matrices, a need for unambiguous, compact, singularity free, computationally efficient method for representing rotational information is imposed. As a solution, unit quaternions are proposed and kinematic modeling in dual quaternion space arose. In this paper, an overview of spatial descriptions and transformations that can be applied together within these spaces in order to solve kinematic problems is presented. Special emphasis is on a different mathematical formalisms used to represent attitude of a rigid body such as rotation matrix, Euler angles, axis-angle representation, unit quaternions, and their mutual relation. Benefits of kinematic modeling in quaternion space are presented. New direct kinematics algorithm in dual quaternion space pertaining to a particular manipulator is given. These constructs and algorithms are demonstrated on the human centrifuge as 3 DoF robot manipulator.

Aircrew of a modern combat aircraft is exposed to hazardous effects of high G-forces and high angular velocities. In order to protect human lives and to avoid material losses, High-G training in human centrifuge is used to artificially increase accelerative force under controlled conditions. In this paper, centrifuge is modeled as 3 DoF revolute robot manipulator with planetary, roll and pitch axis. Pilot seat is controlled as last unit of robot manipulator. Control system is obtained by adding new functionalities for flight simulation in control unit for robot programming previously developed and by implementing solutions for the kinematics and dynamics of this robot. Standard open-loop flight simulations imply predefined profiles of absolute acceleration in the gondola of the centrifuge. It is necessary to develop algorithms for controlling this acceleration. An algorithm for calculating the angular velocity of main arm of human centrifuge which provides predefined profile of absolute acceleration in gondola of centrifuge, where the onset rate of absolute acceleration is constant, is developed. As a solution of nonlinear differential equation, Jacobi elliptic function appears. Results obtained by developed algorithm are compared with results obtained by simulation in Simulink.