Application of the Theory of Kinematic Motion Control of a Rigid Body

摘要

The theory of the kinematic control of the rotational (angular) motion of a rigid body and the spatial motion of a free rigid body used in the article is based on the quaternion and biquaternion kinematic models of the rigid body motion. In this theory, the kinematic equations of the rotational and (or) translational motion of a body are considered as the mathematical models of a rigid body motion, and the vectors of the angular and (or) translational velocities of a body or kinematic screws are used as the controls. The goal of the kinematic control is transfer of a rigid body from its assigned initial position to the desired final position by applying the required (program) angular and (or) linear velocities to the body. Also, the goal of the kinematic control can transfer a rigid body from its given initial position to any selected program path and, further, to an asymptotically stable motion along the program path with the required program angular and linear velocities by applying the required stabilizing angular and linear velocities to the body. In the article the authors present a review of the papers dedicated to the following applications of the theory of the kinematic control of a rigid body motion in the mechanics of a space flight, inertial navigation and mechanics of the robot manipulators: two-circuit control of the rotational motion of a rigid body (spacecraft) using a strapdown inertial navigation system; adjustable strapdown systems for orientation and navigation of the moving objects; TSP-Argus motion control platform complex for Mars-94 space project; optimal reorientation of the orbit, of the orbital plane and correction of the angular elements of the orbit of the spacecraft by means of a reactive acceleration, orthogonal to the plane of the orbit of the spacecraft; solving of the inverse problems of the kinematics of the robot manipulators using the biquaternion theory of the kinematic control; kinematic control for the mechanics of the robotic manipulators (independent program motion speed control).