Deployment/Retrieval Control of Tethered Subsatellite Through an Optimal Path

Development of a feedback control law to follow an optimal path is presented concerning the deployment/retrieval phase of a subsatellite connected to the Shuttle through a tether. The optimal path to be tracked is obtained numerically by solving a two-point boundary-value problem with inequality constraints on tether tension that is the control force, with fixed boundary conditions, and with an unspecified terminal time. The feedback control algorithm is designed using a Lyapunov function to asymptotically reduce the deviation of the actual trajectory from the optimal path. The Lyapunov function is defined to be positive definite and to be zero when the trajectory coincides simultaneously with the optimal path. The present method of control is simulated numerically, and the results show excellent controlled response of the tethered subsatellite system. A comparison of the present approach with the neighboring optimum feedback control is also presented and shows the superior performance of the tracking-type control using the Lyapunov function for large initial variations from the optimal path.

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