针对具有冗余机械臂的自由漂浮空间机器人（Free Floating Space Robot， FFSR）点到点避免奇异性规划和控制问题，提出了一种冗余FFSR的点到点避免奇异控制方法。首先，该方法基于离散状态依赖李卡提方程（DSDRE）控制器设计方法，利用FFSR的动力学和运动学方程实现了FFSR系统方程的伪线性重构；然后，基于伪线性重构系统及DSDRE状态调节器设计方法实现了FFSR的关节角速度和末端位姿的同时跟踪控制；其次，根据跟踪控制器对FFSR广义雅克比矩阵（GJM）行满秩的设计要求，定义FFSR的奇异性判别依据，构造了避奇异约束函数；再次，由于冗余FFSR系统具有多逆运动学解特点，考虑关节角及关节角速度约束，结合避奇异约束函数设计了FFSR的期望轨迹在线规划器，进一步将设计的跟踪控制器与规划器相结合提出了冗余FFSR末端点到点避奇异运动控制方法。最后，为验证所提方法的有效性同时考虑简化计算，采用平面4连杆FFSR模型进行数值仿真，仿真结果表明所提点到点避奇异运动控制方法能够有效实现冗余FFSR系统的点到点避奇异运动。
A point-to-point singularity avoidance control method for the Free Floating Space Robot (FFSR) with the redundant manipulator is proposed in this paper. According to the Discrete State Dependent Riccati Equation (DSDRE) based controller design method, pseudo linear reconstruction of the FFSR system equation is realized by using the dynamic and kinematic equations for FFSR. Then, based on the pseudo linear equations and DSDRE state regulator design method, the tracking control of the joint angular velocity and effector's trajectory is realized. According to the requirements for full row rank of the Generalized Jacobian Matrix (GJM) in controller design, the singularity discrimination basis of FFSR is defined and the singular constraint function is constructed. Due to the characteristic of multi-inverse kinematics solutions for redundant FFSR systems, considering the constraints of joint angle and angular velocity, an online planner for FFSR's desired trajectory is designed with the constraint functions for singularity avoidance. A control method for point-to-point singularity avoidance is finally proposed by combining the designed tracking controller with the planner. To verify the effectiveness of the proposed method and simplify the computation, the planar 4-link FFSR model is used for numerical simulation. The simulation results show that the proposed method for point-to-point avoidance singularity control can effectively realize the avoidance of point-to-point singularity of redundant FFSR systems.
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