Optimal Control History Research Articles

Optimal continuous control for remote orbital capture

Optimal control histories are presented for the problem of detumbling (passivating) a satellite. It is proposed that this be done remotely by a robot spacecraft, sometimes referred to as a teleoperator or orbital maneuvering vehicle, in preparation for the return of both vehicles to low-Earth orbit. The dynamics of the coupled two-body system are described with equations of motion derived from an Eulerian formulation (the Hooker-Margulies equations). Two degrees of rotational freedom and one of translation are allowed at the joint that connects the orbital maneuvering vehicle and target spacecraft. The initial condition of the target satellite is free spin and precession. Representative masses and inertias are assumed for both bodies. Application of optimal control theory results in a nonsingular, two-point-boundary-value problem that is solved numerically for the controls, which are principally the external (thruster) and internal (joint) torques to be applied by the orbital maneuvering vehicle. Control histories and vehicle motion are found for both constrained and unconstrained fixed-time optimization. Constraint forces and torques at the joint are determined.

Point Control of a One-Link Flexible Manipulator

An alternative approach to the control of nonrigid, distributed parameter systems is presented. Transfer functions that relate the response of points on the system to a controlling force or torque are used in place of ordinary differential equations, which represent an approximation to the system dynamics. The implications of this “point control” approach are discussed with regard to plant modeling accuracy, uncontrolled regions, open-loop and closed-loop control strategies, system identification, and feedback estimation. Sample optimal control histories are illustrated for a single-link manipulator member with end load.

A New Approach to Onboard Real-Time Optimum Computations for Aerial Combat Games

HE following is a description of a technique designed to ultimately permit on-line real-time optimal control cal- culations for aerial combat maneuvering commands. One-on- one aerial combat as studied here consists of one aircraft under our direct control maneuvering to release weapons against a second aircraft flying unpredictable maneuvers. The nature of this situation is that time lags exist between evader action and pursuer reaction with imperfect information about the evader always being present. A realistic study of this type of aerial combat required the mathematical models developed to assume no knowledge of the opponents performance data, capabilities or intentions. Information available to the attack- ing aircraft concerning the evading aircraft has been restricted to that measurable by the onboard sensor/computer system, such as altitude, Mach number, and relative distance. Results demonstrating the applicability of this approach are presented, together with a preliminary assessment of the airborne computer requirements. Contents response of the pursuer, provided we make certain approxi- mations about the subsequent motion of the evader which is necessary for the use of optimal control theory. The approxi- mation employed here is that the evader will continue to fly a hypothetical straight line whose orientation is defined by this initial state vector. The resulting optimal control history, along with the pursuer and evader state vectors constitute an element of the library. The optimal control histories for all possible combinations of the pursuer and evader state vectors from their meshes are then computed on the ground and stored systematically to form the pursuer onboard library of optimal control commands. During the course of an actual aerial engagement, the sensors onboard the pursuer's aircraft will periodically record and transmit to the onboard computer, both the evader's and pursuer's state vectors. The library of optimal pursuer control commands is then interpolated using these state vectors to obtain the corresponding optimum response. This response or sequence of optimal commands is displayed to the pilot and/or fed directly to the control system, and are followed for a short interval of time. At this point, the pursuer's and evader's state vectors are automatically updated and new responses displayed. This process continues throughout the engagement. Because of the speed of the simple numerical interpolations, real time operations is no problem. The frequency of the updating will be primarily determined by the ability of the onboard sensors to track the evader. This concept has been tested numerically to determine the accuracy of the process. Results thus far obtained have shown that this chain of approximate maneuvers stays very near the optimum maneuver that would have resulted if the entire evader trajectory had been known a priori. Figures 1 and 2 compare the results obtained using the library concept with the optimum trajectory obtained by knowing the evader's complete escape path a priori. Even though the 10 sec time interval between updates is much larger than would actually be achieved in flight, assuming the defender is under continuous observation, the two results are