This paper is concerned with optimal motion planning for vibration reducing of free-floating flexible redundant manipulators. Firstly, dynamic model of the system is established based on Lagrange method, and the motion planning model for vibration reducing is proposed. Secondly, a hybrid optimization approach employing Gauss pseudospectral method （GPM） and direct shooting method （DSM）, is proposed to solve the motion planning problem. In this approach, the motion planning problem is transformed into a non-linear parameter optimization problem using GPM, and genetic algorithm （GA） is employed to locate the approximate solution. Subsequently, an optimization model is formulated based on DSM, and sequential quadratic programming （SQP） algorithm is used to obtain the accurate solution, with the approximate solution as an initial reference solution. Finally, several numerical simulations are investigated, and the global vibration or residual vibration of flexible link is obviously reduced by the joint trajectory which is obtained by the hybrid optimization approach. The numerical simulation results indicate that the approach is effective and stable to the motion planning problem of vibration reducing.
For the low-earth-orbit （LEO） long-duration multi-spacecraft rendezvous mission, a mixed integer nonlinear programming （MINLP） model is built with consideration of the , perturbation and the time window constraints based on lighting condition. A two-level hybrid optimization approach is proposed. The up-level problem uses the visiting sequence, the orbital transfer duration and the service time after each rendezvous as design variables, and employs the mix-coded genetic algorithm to search the optimal solution; the low-level problem uses the maneuver time and impulses in each rendezvous as design vari- ables, and employs the downhill simplex method to search the optimal solution. To improve the solving efficiency of the low-level problem, a linear dynamic model with J~ perturbation is derived, and the approximate strategy of the low-level prob- lem is then proposed. The proposed method has been applied to several numerical problems. The results lead to three major conclusions： （1） The MINLP model for LEO long-duration multi-spacecraft rendezvous mission is effective, and the proposed hybrid optimization strategy can obtain good solutions that satisfy time window constraints; （2） The derived linear dynamic equations are good first-order approximation to the long-duration rendezvous trajectory under ,J2 perturbation; （3） Under J2 perturbation, the long-duration rendezvous problem has multiple local minimums either in the duration of multiple orbits or in a single orbit, and it agrees with the problem＇s characteristic to use the mix-coded genetic algorithm.
A circumlunar free return orbit design model that satisfies manned lunar mission constraints is established. By combining analytical method with numerical method,a serial orbit design strategy from initial value design to precision solution is proposed. A simulation example is given,and the conclusion indicates that the method has excellent convergence performance and precision. According to a great deal of simulation results solved by the method,the free return orbit characters such as accessible moon orbit parameters,return orbit parameters,transfer delta velocity,etc. are analyzed,which can supply references to constitute manned lunar mission orbit scheme.
