Approximate algorithms for Space Station Maneuver Optimization

Abstract

The general problem of large spacecraft rotational raphics. maneuvers while in a circular orbit is considered. Near-minimum time attitude maneuvers for ISS stage 41-E is analyzed. Both small and large attitude maneuvers constitute the main topic of this thesis. The formulation assumes three orthogonal sets of thrusters oriented with respect to the spacecraft body axes. Euler parameters or quadrillions are used as the primary attitude coordinates. The equations of motion are solved using an inverse dynamics approach. Bang-bang torque profiles are used. The usual instantaneous switches of bang-bang control are replaced by the inverse tangent function. The switch function is designed as a function of the non-dimensional time differences between the current maneuver time and parameter (switch time). In this manner, the discontinuity of the sign function for near-minimum time maneuvers was avoided. Two switches per control are considered in this study for sub-optimal near-near minimum time maneuvers. Torque smoothing is used to avoid discontinuous jumps in the control which would excite vibrational modes in the structure. The switch times, maximum thrust magnitudes, and optimal final maneuver times are determined using the MATLAB built-in function "CONSTR". This algorithm optimizes a control parameter set for the given maneuver. This is an iterative parameter optimization method that requires a "sufficiently close'' initial guess of the control parameters. Results showing attitude and angular velocity histories, and thruster moments are presented for six-switch small and large attitude maneuvers. The results obtained are theoretical solutions intended to illustrate the methodology, and to study practical aspects of the approach taken. These solutions have not been experimentally or analytically verified at the present moment. While global convergence cannot be claimed, several families of converged solutions are obtained. An approach is established whereby such families of representative maneuvers could be established by a priori computation. This "external field map'' could be accessed to interpolate good starting estimates for near-real-time initiation of the optimization algorithm.