High scientific value areas on celestial bodies such as the Moon and Mars are often located in hazardous terrains. To achieve safe landing exploration, a novel planning method is proposed, which can ensure that the planned trajectory maintains a user-specified distance from obstacles, thus reducing potential collision risk induced by factors such as the body size and model uncertainties. Firstly, the basic model of the trajectory optimization problem and its convexification version is given. The obstacles are modeled as polynomial functions, based on which the “if-then” obstacle avoidance logic explicitly considering the safe distance, is described as a sum of squares constraint. This constraint formulation applies to any obstacle described by a finite number of polynomials, independent of the specific expression of the polynomials (reflecting the shape of the obstacle). Subsequently, the convexification process for the obstacle avoidance constraint is given. Finally, the sequential sum of squares programming problem for the obstacle avoidance trajectory is established, which boils down to a series of semidefinite programming problems. Simulation results show that the closest distance between the planned trajectory and obstacles strictly satisfies the specified distance constraint, and the trajectory could avoid non-convex obstacles. With the promising convergence properties of underlying convex optimization algorithms, advanced autonomous obstacle avoidance guidance schemes are expected to be formed based on the proposed trajectory planning method.

中文翻译：

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定量考虑障碍物安全距离的动力下降轨迹规划方法


月球和火星等天体上的高科学价值区域往往位于危险地形。为了实现安全着陆探索，提出了一种新颖的规划方法，该方法可以确保规划的轨迹与障碍物保持用户指定的距离，从而减少由于车身尺寸和模型不确定性等因素引起的潜在碰撞风险。首先，给出了轨迹优化问题的基本模型及其凸化版本。障碍物被建模为多项式函数，基于此，明确考虑安全距离的“if-then”避障逻辑被描述为平方和约束。该约束公式适用于由有限数量的多项式描述的任何障碍物，与多项式的具体表达式（反映障碍物的形状）无关。随后，给出了避障约束的凸化过程。最后，建立了避障轨迹的序贯平方和规划问题，将其归结为一系列半定规划问题。仿真结果表明，规划轨迹与障碍物的最近距离严格满足指定的距离约束，轨迹能够避开非凸障碍物。凭借底层凸优化算法的良好收敛特性，预计将基于所提出的轨迹规划方法形成先进的自主避障引导方案。