Redundancy Parameterization of the ABB YuMi Robot Arm

The ABB YuMi is a 7-DOF collaborative robot arm with a complex, redundant kinematic structure. Path planning for the YuMi is challenging, especially with joint limits considered. The redundant degree of freedom is parameterized by the Shoulder-Elbow-Wrist (SEW) angle, called the arm angle by ABB, but the exact definition must be known for path planning outside the RobotStudio simulator. We provide the first complete and validated definition of the SEW angle used for the YuMi. It follows the conventional SEW angle formulation with the shoulder-elbow direction chosen to be the direction of the fourth joint axis. Our definition also specifies the shoulder location, making it compatible with any choice of reference vector. A previous attempt to define the SEW angle exists in the literature, but it is incomplete and deviates from the behavior observed in RobotStudio. Because our formulation fits within the general SEW angle framework, we also obtain the expression for the SEW angle Jacobian and complete numerical conditions for all algorithmic singularities. Finally, we demonstrate using IK-Geo, our inverse kinematics (IK) solver based on subproblem decomposition, to find all IK solutions using 2D search. Code examples are available in a publicly accessible repository.