基于R~*(3,0,1)几何代数的6轴机器人位姿反解

Inverse Kinematic of Six-Axis Robots Based on R~*(3,0,1) Geometric Algebra

R~*(3,0,1)几何代数模型结合了对偶四元数和共形几何的优势,即对偶四元数计算效率高,共形几何对点、面具有统一的坐标变换算子,能计算点、面之间的有向距离.本研究基于R~*(3,0,1)几何代数模型提出了6轴机器人位姿反解新算法,即在6轴机器人运动学反解过程中,根据关节到3种奇异形位参考面有向距离不同的属性,基于R~*(3,0,1)几何代数能确定唯一的运动学位姿反解,省去了传统反解中通过"最短行程"的准则来择优的步骤.该算法具有能检测关节与奇异面距离、算法简单、使反解问题的描述更为直观、能确定唯一解等优点,能很好地应用于实际的机器人运动控制中.将该算法在PUMA 560型机器人上进行了数值验证.

The geometric algebra model R^*(3,0,1)combines the benefits of dual quaternions and conformal geometric algebra,i.e.,dual quaternions can compute faster while comformal geometric algebra have the same translation algorithm for points and planes as well as have algorithm to compute sign distance between points and planes.A new inverse kinematic of industrial robots algorithm is proposed on the basis of R^*(3,0,1)model,i.e.,the unique solution of inverse kinematic of industrial robots is determined by the sign distances between joints and three singular planes,and the sign distances can be computed by R^*(3,0,1)model.This new algorithm can find unique solution without comparing a preferred one which is widely applied in general inverse kinematic solution.This new algorithm has advantages,such as being able to compute the sign distance to the singular planes,being simple,highly speedy to compute unique inverse kinematic solution effectively when applied to practical robot motion control.This algorithm is numerically verified on PUMA 560.