半直接配点法在航天器追逃问题求解中的应用

Application of Semi-Direct Collocation Method for Solving Pursuit-Evasion Problems of Spacecraft

采用半直接配点法求解时间固定两航天器追逃问题,提出一种新的数值求解追逃双方最优控制策略的方式,避免了求解非线性两点边值问题。在两航天器均为连续小推力假设条件下,以终端距离为支付函数,给出了半直接配点法求解此追逃问题的过程。在此数值方法中,根据半直接转换将微分对策问题转化为一个最优控制问题,由Gauss-Lobbato配点法最终将此最优问题转化为非线性规划问题,继而通过序列二次规划方法求解。这种半直接配点法避免微分对策问题最优策略的必要条件(两点边值问题)求解,并且数值稳定性好。数值仿真给出了追逃双发的最优控制策略和相应的追逃轨迹。

The semi-direct collocation method is adopted for solving the pursuit-evasion problem with fixed timehorizon.A new numerical way to solve the optimal control strategies of the pursuit and evasion spacecraft is proposed such that a two-point boundary value problem is not necessary to be solved.Under the assumption of the continuous low-thrust,the procedure solving such a pursuit-evasion problem is given with the payoff of the terminal distance of two spacecraft.In such a numerical method,the differential game is reduced to an optimal control problem according to the semitransformation.Then,by the Gauss-Lobbato collocation method the optimal control problem is reduced to a nonlinear programming problem which is solved by the sequential quadratic programming method.Such a semi-direct collocation method does not need to solve the necessary condition(a two-point boundary value problem)for the optimal strategies of the differential games,and it is numerically stable.The numerical simulation result shows the optimal control strategies and the associated pursuit-evasion trajectory for a pursuit-evasion problem of spacecraft.