Synergistic Potential Functions for Constrained Attitude Control of Rigid Spacecraft
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摘要: 提出一种考虑航天器姿态约束的协同势函数设计方法, 在姿态全局收敛的同时, 保证姿态在机动过程中始终满足姿态约束. 首先, 建立航天器姿态指向约束模型, 并针对每一个指向约束设计软约束区域; 然后, 基于“角度扰动”方法设计协同势函数族; 接着, 通过设计协同势函数族内函数切换规律, 在软约束区域内构建满足姿态约束的势函数, 并给出区域内势函数临界点分布的调整方法; 最后, 将所得的势函数用于航天器的避障控制, 以比例−微分控制为例, 通过数值仿真, 验证该方法的有效性.Abstract: A synergistic potential functions design method considering attitude constraints is proposed to ensure the global convergence of attitude while always satisfying attitude constraints during the attitude maneuver. First, an attitude pointing constraint model is developed, and a soft constraint region is designed for each pointing constraint. Then, a family of synergistic potential functions is designed based on the “angular warping”. Next, using the common fractional and logarithmic forms of repulsive potential functions, a potential function considering the attitude constraint is designed in the soft constraint region by using the synergistic potential functions and a method to adjust the distribution of critical points in the soft constraint region by controlling the parameters of this potential function is given. Finally, the designed potential function is used in the controller design. The effectiveness of the proposed method is verified by numerical simulations using proportional-derivative control as an example.
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图 2 使用协同势函数族的姿态控制示意图
Fig. 2 Illustration of attitude control by means of synergistic potential functions
图 3 $k{P_{{{{\boldsymbol{A}}}}}}\left( {\boldsymbol{R}} \right)$取值范围随$\Phi_{{{\boldsymbol R}}}$的变化曲线
Fig. 3 The change curve of the range of$k{P_{{{{\boldsymbol{A}}}}}}\left( {\boldsymbol{R}} \right)$with$\Phi_{{{\boldsymbol R}}}$
图 6 避障切换下姿态机动仿真
Fig. 6 Attitude maneuver simulation when avoiding attitude constraints
表 1 惯性系下姿态限制
Table 1 Attitude constraints in the inertial frame
序号 指向${\boldsymbol{v}}$ 角度$\alpha \ (^ \circ) $ CZ1 $\left[ {0.5237,0.7208,0.4540} \right]^{\rm{T}}$ 20 CZ2 $\left[ {-0.5530,0.7612,-0.3387} \right]^{\rm{T}}$ 15 CZ3 $\left[ {-0.1488,-0.9393,0.3090} \right]^{\rm{T}}$ 25 
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