Analysis of Panda's Elbow Motion in Null Space and a Combined Analytical-Numerical IK with Intuitive Redundancy Resolution

The kinematic structure of Franka Emika's redundant cobot Panda features two translational offsets that prevent three of the six pairs of adjacent joints from intersecting each other. These offsets make Panda's elbow motion in null space hard to predict with respect to existing redundancy parameters. The null space motion analysis of Panda's elbow presented in this work leads to the definition of a redundancy parameter that can be used intuitively. The semi-analytical approach applied in this work induces a fast inverse kinematics algorithm that offers a redundancy resolution which does not affect the reachability of the given end effector pose. Even libfranka, Franka Emika's supplied library, does not offer such a Cartesian approach of keeping control of Panda's secondary motion while fulfilling primary manipulation tasks.