制导炮弹协同方案弹道快速规划

Cooperative scheme trajectory rapid trajectory programming for guided projectile

为求解复杂的多弹多阶段协同弹道规划问题,提出一种增广集中式-协同弹道规划算法(AC-CTPM)。首先根据制导炮弹飞行过程中各阶段特性建立5阶段弹道规划模型,之后将n_p发制导炮弹的5阶段弹道规划问题组合扩展为较为复杂的5n_p阶段最优控制问题,然后采用多阶段Radau伪谱法将无限维最优控制问题(OCP)离散为有限维非线性规划问题(NLP),最后调用成熟的NLP求解器SNOPT求解。为提高对复杂的5n_p阶段最优控制问题的求解效率,在AC-CTPM中提出一种将2D标称弹道转换为3D预测方案弹道的协同弹道规划问题初始值获取方法(IGVAM),每一发制导炮弹分别以各自发射点为原点建立新地面坐标系,在新地面坐标系内快速规划出2D方案弹道,之后通过扩展和坐标转换将新坐标系中规划的2D方案弹道转换成原地面坐标系中的3D方案弹道,这些3D方案弹道组合构成协同弹道规划问题的初始预测。采用AC-CTPM算法对单炮多发、多炮齐射同时弹着任务场景进行仿真求解,获得了满足炮弹自身约束以及协同约束的协同方案弹道,验证了AC-CTPM算法的有效性。与分布式协同弹道规划算法(D-CTPM)以及传统集中式协同弹道规划算法(TC-CTPM)进行仿真对比,结果表明:AC-CTPM算法规划的协同方案弹道的目标函数平均比TC-CTPM算法优5.07%,比D-CTPM算法优32.98%,而AC-CTPM算法的求解耗时却比TC-CTPM算法减少86.48%,比D-CTPM减少82.36%,验证了AC-CTPM算法的优越性。

To solve the complex problem of multi-projectile-multi-phase cooperative trajectory programming,an augmented centralized collaborative trajectory programming method(AC-CTPM)is proposed.Firstly,a five-phase trajectory programming model is established based on the characteristics of each phase in the flight process of guided projectiles.Then,the five-phase trajectory programming problems of np guided projectiles are combined and extended to a more complex 5np phases optimal control problem(OCP).The multi-phase Radau pseudo-spectral method is used to discretize the infinite-dimensional OCP into a finite-dimensional nonlinear programming problem(NLP),which is finally solved using the mature NLP solver SNOPT.To improve the efficiency of solving the complex 5np phases OCP,in AC-CTPM,we propose an initial guess value acquisition method(IGVAM)for converting 2D scheme trajectories into 3D predicted trajectories in cooperative trajectory programming problem.Each guided projectile establishes a new ground coordinate system with its own launch point as the origin.Within this new coordinate system,2D scheme trajectories of the projectile are rapidly programmed.Subsequently,by expanding and transforming the coordinates,the programmed 2D trajectories in the new coordinate system are transformed into the 3D scheme trajectory.The 3D scheme trajectories of each projectile are combined to form the initial prediction of the cooperative trajectory programming problem.By applying the AC-CTPM algorithm,we conducted simulation-based solving for the scenario of simultaneous impact tasks with single-gun multiple-firing and multiple-gun salvo.We obtained cooperative trajectory solutions that satisfy the projectile self-constraints and cooperative constraints,which verifies the effectiveness of AC-CTPM algorithm.Simulation comparisons with distributed collaborative trajectory programming algorithm(D-CTPM)and traditional centralized collaborative trajectory programming algorithm(TC-CTPM)shows that the objective function of the cooperative scheme trajectory programmed by AC-CTPM algorithm is on average 5.07%better than that of TC-CTPM algorithm and 32.98%better than that of D-CTPM algorithm on average,while the solution time of the AC-CTPM algorithm is reduced by 86.48%compared with TC-CTPM algorithm and by 82.36%compared with D-CTPM algorithm,which verifies the superiority of the AC-CTPM algorithm.