Control of following Force in Gimbal Suspension by Programmed Transfer of Vehicle in the Class of Spiral-Screw Trajectories
DOI:
https://doi.org/10.14738/tmlai.86.8743Keywords:
gimbal system, hodograph, Rodrigues-Hamilton parameters, components of control forces, spiral-screw trajectory, natural trihedral, quaternion matrices.Abstract
The programmed transfer of the transport vehicle in space is carried out in the class of helical trajectories, using forcing (throttling) and deviation of the following driving force in the gimbal. The paper introduces the mathematical models of the transport vehicle kinetics in space in the terrestrial reference system and in the basis of the natural trihedral of the trajectory, using the quaternion form. The kinematics of the transport vehicle in the fixed and mobile reference systems, as well as the orientation of the natural trihedral in the inertial space, are represented by the hodograph of the program helix trajectory in vector and quaternion forms. The components of the controlling driving force in the basis of the natural trihedral are determined by the kinetostatics equations of the programmed transfer of the transport vehicle along a helical trajectory in the required speed mode. The authors proposed a structural scheme of the gimbal suspension, providing the required driving force components. The authors considered two possible sequences of rotations of the moving gimbal rings and demonstrated their equivalence. Laconic formulas are established for the control angles of rotation of the moving gimbal rings.
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