论文
arXiv
SpatialIntelligence
Trajectory
Mobility
GeoSimulation
中文标题
具有棱锥形接近角约束的最优动力下降制导
English Title
Optimal Powered Descent Guidance with Pyramid-Shaped Approach-Angle Constraints
Revital Frenkel, Vitaly Shaferman
发布时间
2026/6/16 04:42:17
来源类型
preprint
语言
en
摘要
中文对照

本文解析推导了一种新型带不等式接近角路径约束的最优软着陆制导律。该制导律通过将最优轨迹约束在以着陆点为顶点的凸倒置棱锥体内,避免地面碰撞并实现接近角控制。采用常重力场下的三维质点线性运动学模型,并以控制能量的二次型代价函数及终端位置与速度约束为优化目标。利用庞特里亚金最小值原理及无约束弧段与约束弧段切换处的最优性条件,解析求得开环解、闭环解及最优终端时间。进一步证明:当路径约束起作用时,最优终端时间减小。所得制导律在闭环下连续、关于时间分段线性、关于状态非线性;当某一约束起作用时,控制器抵消垂直于该约束面的重力分量,使轨迹沿约束曲面演化。通过多种初始条件下的仿真验证,该制导律展现出精确的着陆性能,并始终满足路径约束。

English Original

In this paper, a novel optimal soft-landing guidance law with inequality approach-angle path constraints is analytically derived. The proposed guidance law prevents ground collision and enables approach-angle control by constraining the optimal trajectory to remain within a convex inverted pyramid originating at the landing point. A 3D point-mass linear kinematic model in a constant gravitational field is employed, together with a quadratic control-effort cost and terminal constraints on position and velocity. Analytical open-loop and closed-loop solutions, together with the optimal final time, are derived using Pontryagin's Minimum Principle and the optimality conditions at the transitions between unconstrained and constrained arcs. It is additionally shown that the optimal final time decreases when the path constraints become active. The resulting guidance law is continuous, piecewise linear in time, and nonlinear in the states in closed-loop. When a constraint becomes active, the controller cancels the gravitational component normal to the constraint, causing the trajectory to evolve along the constraint surface. The proposed guidance law is evaluated in simulations under various initial conditions, demonstrating accurate landing performance and consistent satisfaction of the path constraints.

元数据
arXiv2606.17280v1
来源arXiv
类型论文
抽取状态raw
关键词
SpatialIntelligence
Trajectory
Mobility
GeoSimulation
eess.SY
math.OC