Globally Optimal Online Redundancy Resolution for Serial 7-DOF Kinematics Along SE(3) Trajectories

Redundant robots offer the possibility of improving agility, compared to their non-redundant counterparts, by exploiting the additional kinematic DOFs to increase a measure called manipulability. While it is common to maximize the manipulability measure during redundancy resolution locally, global optimization of a full trajectory is usually computationally too expensive and thus only considered for offline procedures in current literature. However, local maximization is prone to be sub-optimal and at times even fails at preserving agility of a robot that ought to be reactive. In this work we build upon our previous contributions on online trajectory generation on SE(3) and closed-form task space manipulability of a 7-DOF serial robot, and combine it with graph search techniques for global optimization. This enables, for the first time, online trajectory generation with globally optimal redundancy resolution regarding manipulability, to maintain agility in reactive robot behavior.