An attitude C3 reference trajectory construction of the spacecraft

In this paper, we solve the problem of determining the reference trajectory passing through the fixed values of the orientation quaternion at given time points. Additionally, two sets of boundary conditions are considered. In the first case, in addition to the quaternion, the angular velocity is set at the node, and in the second case, the angular velocity, angular acceleration, and its jerk are set simultaneously. The proposed method of constructing the quaternion reference trajectory is based on the idea of representing angular motion as a sequence of elementary rotations. Due to the presented approach, the normalization condition is satisfied and the third degree of smoothness of the reference trajectory is provided over the entire period of motion. The last condition ensures the smoothness of the control function. It is assumed that this will prevent the excitation of vibrations in the flexible elements of the spacecraft, which is of great importance in applications. In this paper, auxiliary quaternions and interpolation polynomials are obtained for different sets of nodal conditions that allow the reference trajectory to pass through the specified points. Also, the angular velocity and acceleration are found as functions of time, which is necessary for constructing the control as a solution to the inverse problem of dynamics.