倍四元数在6R串联机器人逆解中的应用

摘要

在研究了四元数性质的基础上,采用倍四元数求解6R串联机器人的逆运动学问题.将三维空间的位移表示成四维空间的双旋转,建立了倍四元数形式的机器人运动学方程,再通过消元,构造Dixon结式.最终通过求解Dixon结式求解出机器人16组解析解.最后,使用Matlab Robotics进行仿真,新方法能够求出机器人逆运动学全部解析解,而且速度比D-H方法提升了10%左右.%The inverse kinematics of a general 6R serial robots has much difficulty to be solved and amount of computations. Also, it exists singular solution. We uses double quaternion to deal with the problem. The displacement in three dimensions can be converted to double rotation, we can build kinematics equation of robots in the form of double quaternion, then eliminate and build Dixon resultant matrix and finally we get the all the 16 closed-form solutions. At last, we verify our new means using math robotics toolbox. We get all the solutions correctly and improve about ten percent comparing to d-h means in speed.