面向控制的3-RRR球面并联机构正运动学实时解法

以经典牛顿法为基础 ,针对 3 - RRR球面并联机构的机构学特点及控制中的特殊要求 ,提出了面向控制的高效迭代算法。利用机构运动连续性条件划分不同的控制阶段 ,当机构处于连续运动状态时 ,迭代结构中使用固定雅可比矩阵进行运算 ,缩短了单步迭代时间 ;当机构处于非连续运动状态时 ,使用变步长策略 ,引入调整量系数 ,抑制了大偏置初值带来的求解振荡。给出的算例证明 ,应用上述策略的正运动学求解算法兼顾了较大范围的收敛性与局部求解的快速性 ,运算速度满足控制过程的实时性要求。该方法同样适用于其它少自由度并联机构的正运动学求解。

Control Oriented Real Time Direct Kinematics Algorithm of 3-RRR Spherical Parallel Mechanism

A real time algorithm was proposed in this paper to solve the direct kinematics problem of 3-RRR spherical parallel mechanism(SPM). Considering the mechanical characteristics and special controlling requirements, a control orientated irritation algorithm based on the classical Newton method is concise, canonical and efficient. The control process is divided into various stages according to the kinetic continuity condition. In continuous motion state, the utilization of fixed Jacobian matrix in the irritation procedure reduces single step computation time. In noncontinuous motion state, the adjustment coefficient is leaded into the iretation scheme to restrain the solution vibration. A computation example at the end of the paper indicates that the algorithm applying the above strategy guarantees both large-scale and high-speed convergence, which is fast enough to fulfill real time requirement of the control process. The method in this paper could be easily expanded to solve the direct kinematics problem of other type of less DOF parallel mechanism.