Six-DOF trajectory optimization for reusable launch vehicles via Gauss pseudospectral method

To be close to the practical flight process and increase the precision of optimal trajectory, a six-degree-offreedom（6-DOF） trajectory is optimized for the reusable launch vehicle（RLV） using the Gauss pseudospectral method（GPM）. Different from the traditional trajectory optimization problem which generally considers the RLV as a point mass, the coupling between translational dynamics and rotational dynamics is taken into account. An optimization problem is formulated to minimize a performance index subject to 6-DOF equations of motion, including translational and rotational dynamics. A two-step optimal strategy is then introduced to reduce the large calculations caused by multiple variables and convergence confinement in 6-DOF trajectory optimization. The simulation results demonstrate that the 6-DOF trajectory optimal strategy for RLV is feasible.

Reentry trajectory rapid optimization for hypersonic vehicle satisfying waypoint and no-fly zone constraints

To rapidly generate a reentry trajectory for hypersonic vehicle satisfying waypoint and no-fly zone constraints, a novel optimization method, which combines the improved particle swarm optimization （PSO） algorithm with the improved Gauss pseudospectral method （GPM）, is proposed. The improved PSO algorithm is used to generate a good initial value in a short time, and the mission of the improved GPM is to find the final solution with a high precision. In the improved PSO algorithm, by controlling the entropy of the swarm in each dimension, the typical PSO algorithm＇s weakness of being easy to fall into a local optimum can be overcome. In the improved GPM, two kinds of breaks are introduced to divide the trajectory into multiple segments, and the distribution of the Legendre-Gauss （LG） nodes can be altered, so that all the constraints can be satisfied strictly. Thereby the advan- tages of both the intelligent optimization algorithm and the direct method are combined. Simulation results demonstrate that the proposed method is insensitive to initial values, and it has more rapid convergence and higher precision than traditional ones.

Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy

The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method（GPM） and direct shooting method（DSM） is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions.The results indicate that the method is effective with good robustness.

Reentry trajectory optimization for hypersonic vehicle satisfying complex constraints

The reentry trajectory optimization for hypersonic vehicle（HV）is a current problem of great interest.Some complex constraints,such as waypoints for reconnaissance and no-fly zones for threat avoidance,are inevitably involved in a global strike mission.Of the many direct methods,Gauss pseudospectral method（GPM）has been demonstrated as an effective tool to solve the trajectory optimization problem with typical constraints.However,a series of diffculties arises for complex constraints,such as the uncertainty of passage time for waypoints and the inaccuracy of approximate trajectory near no-fly zones.The research herein proposes a multi-phase technique based on the GPM to generate an optimal reentry trajectory for HV satisfying waypoint and nofly zone constraints.Three kinds of specifc breaks are introduced to divide the full trajectory into multiple phases.The continuity conditions are presented to ensure a smooth connection between each pair of phases.Numerical examples for reentry trajectory optimization in free-space flight and with complex constraints are used to demonstrate the proposed technique.Simulation results show the feasible application of multi-phase technique in reentry trajectory optimization with waypoint and no-fly zone constraints.