基于点触任务的可变形臂逆运动学求解

Inverse Kinematics Solution of Deformable Manipulator for Point Touching Task

为了更好地适应家庭环境下的人机交互,设计了一款可根据任务需求相应调整连杆形状的四关节可变形操作臂.与传统刚性臂相比,可变形臂具有灵巧度高、成本低和本质安全等优势,但臂形的任意性也会给操作臂运动学逆解带来额外的困难.针对可变形臂的空间点触任务,本文通过引入"点触角"这一概念放松了末端执行器的姿态约束,从而使原本欠驱动的运动学逆解问题转化为了在满足点触位置约束下,以点触角最小为优化目标的冗余臂逆解优化问题.针对该问题的求解耗时和点触精度,在旋量模型的基础上分别提出了改进的序列二次规划法(SQP)和粒子群优化(PSO)与Paden-Kahan(PSO-PK)子问题混合算法.SQP方法直接在位置层面进行非线性最优化问题求解,实验结果显示该方法在臂形由特殊变为任意时求解耗时几乎不会增加,求解效率高,对可变形臂的在线实时控制具有一定意义;同时利用分层搜索法进行初值设定可以降低该算法陷入局部极值的概率.PSO-PK算法利用Paden-Kahan子问题法的解析逆解对粒子群优化算法进行降维,实验结果表明,该算法能够在保证点触位置无误差的情况下获得稳定的最小点触角,从而使点触性能得到提高.

For the human-robot interaction in home environment, a 4-joint deformable manipulator is designed, whose links can deform to perform specific tasks. Compared with traditional rigid ones, the deformable manipulator is more dexterous, lower-cost and intrinsically safe. However, the arbitrary arm-shape brings extra difficulties into the manipulator inverse kinematics solution. For the the spatial touching task of the deformable manipulator, the concept of 'touching angle' is introduced to relax the orientation constraint of end-effector. Therefore the original inverse kinematics problem with the underactuation constraint is converted into an inverse optimization problem of redundant manipulator to minimizes the touching angle under the constraint of the touching position. For the solving time and touching accuracy of the problem, an improved sequential quadratic programming(SQP) and the particle swarm optimization and Paden-Kahan subproblems(PSO-PK) hybrid algorithm are proposed respectively based on the screw model. The SQP algorithm solves the nonlinear optimization problem directly at position level, and the results show that the time consumption won't increase as the arm-shape changes from a special one to an arbitrary one. It's suitable for online real-time control due to its high solving efficiency. The layered search method is used to decrease the possibility of local minimum through initial value setting. In the PSO-PK algorithm, the analytical inverse solution of Paden-Kahan subproblems is utilized to reduce the dimension of particle swarm optimization(PSO) algorithm. The experiment results demonstrate that the method can obtain the stable minimum touching angle without error in touching position and improve the touching performance.