基于伪谱法的自由漂浮柔性空间机器人姿态运动规划与反馈控制

姚其家,戈新生

振动与冲击 ›› 2019, Vol. 38 ›› Issue (7) : 20-27.

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PDF(923 KB)
振动与冲击 ›› 2019, Vol. 38 ›› Issue (7) : 20-27.
论文

基于伪谱法的自由漂浮柔性空间机器人姿态运动规划与反馈控制

  • 姚其家,戈新生
作者信息 +

Attitude motion planning and feedback control for a free-floating flexible space robot based on pseudo-spectral method

  • YAO Qijia,GE Xinsheng
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摘要

研究自由漂浮柔性空间机器人的动力学建模与姿态控制问题。针对初始状态不确定性对系统姿态造成的影响,提出一种基于伪谱法的运动规划与反馈控制相结合的姿态控制策略。首先,利用假设模态法近似描述柔性臂杆的弹性变形,并利用Lagrange方法建立空间机器人系统的动力学模型。在运动规划方法的设计中,利用Legendre伪谱法将空间机械臂非完整运动规划问题转化为非线性规划问题,再利用序列二次规划算法求解此非线性规划问题得到系统的优化运动轨迹和最优控制输入。在反馈控制方法的设计中,将状态方程在已知的参考轨迹上线性化处理,利用Pontryagin极大值原理将对参考轨迹的跟踪问题转化为两点边值问题,再利用Legendre伪谱法离散此两点边值问题,将其转化为线性代数方程组进行求解,该过程无需任何积分计算,具有很好的实时性。最后,通过数值仿真验证了本文提出的姿态控制策略的有效性和鲁棒性。

Abstract

Dynamic modeling and attitude control of a free-floating flexible space robot were investigated. In order to deal with effects of initial state uncertainties on the system attitude,an attitude control strategy combining motion planning and feedback control based on the pseudo-spectral method was proposed. Firstly,the elastic deformation of the flexible arm was described approximately with the assumed mode method,and the dynamic model of the space robot system was established using Lagrange method. In design of motion planning,Legendre pseudo-spectral method (LPM) was used to convert the space mechanical arm’s non-holonomic motion planning problem into a nonlinear programming one. Then the sequential quadratic programming algorithm was employed to solve the nonlinear programming problem to obtain the system’s optimized motion trajectory and the optimal control inputs. In design of feedback control,the state equation was linearized on the known reference trajectory. The problem of tracking reference trajectory was converted into a two-point boundary value problem based on Pontryagin’s maximum principle. Then LPM was used to discretize the two-point boundary value problem and convert it into a set of linear algebraic equations to be solved. This process didn’t need any integration calculations and had good real-time performance. Finally,numerical simulations verified the effectiveness and robustness of the proposed attitude control strategy.

关键词

运动规划 / 空间机器人 / 最优控制 / 反馈控制 / Legendre伪谱法

Key words

motion planning / space robot / optimal control / feedback control / Legendre pseudospectral method

引用本文

导出引用
姚其家,戈新生. 基于伪谱法的自由漂浮柔性空间机器人姿态运动规划与反馈控制[J]. 振动与冲击, 2019, 38(7): 20-27
YAO Qijia,GE Xinsheng. Attitude motion planning and feedback control for a free-floating flexible space robot based on pseudo-spectral method[J]. Journal of Vibration and Shock, 2019, 38(7): 20-27

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