Optimal Control Of Rapid Cooperative Spacecraft Rendezvous With Specific-direction Thrust

Orbital transfer under limited continuous thrust can be carried out rapidly with strong maneuver ability,and has been a hot topic in aerospace field research.Early research mostly employed impulsive thrust,and the trajectory optimization was a linear problem.Orbital transfer under high continuous thrust has much challenging problems,including strong non-linearity and multi-peak.So,the convergence of results is more difficult and amount of calculation become larger.In addition,most research of continuous thrust is based on the freely thrust direction,even if the optimal control can be achieved theoretically,it is still difficult to achieve it in real-world space operation.Therefore,there are still many problems to be solved to achieve orbit transfer under continuous thrust in real space operations.Focusing on the long-distance rapid cooperative rendezvous of two spacecraft under finite continuous thrust,this paper proposes a practical strategy for space operation using multiple specific-direction thrusts.Based on the orbital dynamic theory and Pontryagin's maximum principle,the dynamic equations and optimal control equations for radial,circumferential,and normal thrust are determined.The optimization method is a hybrid algorithm.By introducing configuration variables,the discontinuous switching control of the spacecraft engine has been smoothed.The optimal control problem is finally transformed into a high-dimensional parameter optimization problem,by integrating the differential equations of the maneuvering and gliding segments of the spacecraft.The cooperative rendezvous of two spacecraft in mission orbit under multiple specific-direction continuous thrust make the number of variables to be optimized increases.Therefore,quantum particle swarm optimization(QPSO)algorithm with strong global search capability is used firstly to search the optimization parameters.Then the result is modified by the sequential secondary programming algorithm(SQP),which has significant local search capability.At last,the convergent and accurate solution is obtained.Because the hybrid method needs to set the engine switching strategy in advance,the cases in this paper were researched using different sequences,such as two firing arcs and two not-firing arcs.At this time,the spacecraft cannot reach the mission orbit within the specified time;When we set six firing arcs and six not-firing arcs,the spacecraft can completed the rendezvous within the specified time,and consumed a reasonable amount of fuel;When we set six firing arcs and six not-firing arcs,a larger number of variables were introduced.It brought great difficulties to optimization and simulation,slowing down the computation speed sharply and even leading to nonconvergence.Therefore,too few firing arcs and not-firing arcs will cause the mission fail,and it is impractical to preset too many firing arcs and not-firing arcs.This is the reason why the control strategy was preset to four firing arcs and four not-firing arcs for the cases designed in this paperFor the selection of orbital dynamics models,the classical orbital elements having a clear physical meaning.In the orbital rendezvous task designated in this paper,the constraints can be clearly given.However,the classical orbital elements dynamics model has some singularities when the eccentricity and the orbit inclination is zero.It will occur some problems when solving near-circular orbit transfer.The dynamical equations of orbital elements of modified vernal equinox without singular points is more suitable for the situation of near-circular orbit transfer or problems of small orbit inclination.Numerical simulation calculations and comparative analysis of different mission orbits are obtained by using the two dynamic equations.The results show that only orbital element of modified vernal equinox dynamic model is suitable for near-circle orbits.For the elliptical orbit transfer problem,there is little difference between the two dynamic models.In order to verify that spacecraft with multiple specific-direction thrusts can complete the rendezvous mission,coplanar and non-coplanar mission orbital rendezvous are simulated and optimized.For the coplanar mission orbit,since the normal thrust has no effect on the shape of the orbit,we only set the radial and t circumferential thrust.We only configure the thrust system in the circumferential and normal directions to solve the non-coplanar problem,because the radial thrust was relatively small and the number of optimization variables will reduced.The result shows that the two spacecraft with multiple specific-direction thrusts completed the rendezvous task in the mission orbit.In addition,it can be known from the spacecraft trajectory picture that the normal thrust only appears near the orbit intersection.Therefore,the normal thrust can be used to solve the out-of-plane in-plane problem first and then the in-plane motions are controlled by circumferential thrust.For the cases in this paper,continuously variable direction thrust and specific-direction thrust are used respectively for numerical calculation,and the results are analyzed and compared.By comparing the optimization results of the two thrust models in the in-plane problem,the fuel consumption and flight time were found to be almost the same.The non-coplanar rendezvous results indicate that the flight time under multiple specific-direction thrusts is almost the same as the flight time using the continuously variable direction thrust model,although the fuel consumption is somewhat higher.But the direction of the continuously variable direction thrust model in burning sections presents a complex curve change,which is hard to accomplish in the actual operation process.After analyzing and comparing the simulation results in this paper,it is found that the multiple specific-direction thrusts can reach the mission orbit within a limited time,and it is more convenient than the continuously variable thrust in actual operation.