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针对非轴对称欠驱动航天器提出了一种新的基于微分平滑特性的时间最优轨迹规划算法。首先,在控制输入受限的约束条件下,对给定的初末姿态,选取航天器机动时间最短为待优化的性能指标。其次,在欠驱动航天器的非受控轴上引入虚拟控制输入,扩展系统的平滑特性,从而使得系统的姿态和控制输入变量均可由平滑输出函数及其各阶导数代数表征;同时为保证优化问题的等价性,引入虚拟控制输入始终为零的附加等式约束。进一步,利用伪谱法离散系统的平滑输出函数,将优化问题最终转化为一个低维的,仅含有代数约束的非线性规划问题,且无需积分求解系统的动态力学方程。仿真结果表明该算法不仅能够有效地减少优化所需的时间,而且运算精度较高。
A new time-optimal trajectory planning algorithm based on differential smoothing characteristics is proposed for non-axisymmetric under-actuated spacecraft. First of all, under the constraints of limited control inputs, the shortest maneuvering time of the spacecraft is selected as the performance index to be optimized for a given initial / final attitude. Secondly, the virtual control input is introduced into the unmanned spacecraft of under-driven spacecraft to extend the smoothing characteristics of the system so that both the attitude and control input variables of the system can be characterized by the smooth output function and its derivative algebra. At the same time, The equivalence of the problem, the introduction of virtual control input is always zero additional equations constraints. Further, by using the pseudo-spectral method to discretize the smooth output function of the system, the optimization problem is eventually transformed into a low-dimensional nonlinear programming problem that contains only algebraic constraints, without the integral solution of the dynamic mechanical equations of the system. Simulation results show that this algorithm not only can effectively reduce the time required for optimization, but also has higher computational accuracy.