Analytical Inverse Kinematics for Franka Emika Panda – a Geometrical Solver for 7-DOF Manipulators with Unconventional Design

Abstract

This paper presents an analytical inverse kinematic solution for the 7-DOF Franka Emika Panda robot with joint offsets. Contrary to the common belief that this problem has been thoroughly studied, there is no published work that discusses the existence of multiple solutions from a pure geometrical perspective. By investigating the geometry of the robot, the proposed solution reveals 8 different joint configurations for a given end effector pose and fixed redundant parameter, and a non-iterative algorithm is designed to consistently obtain one of them during motion control without random switching. The solver is tested in terms of accuracy and computational speed, and data show that accurate results can be obtained within a few microseconds, making it highly preferable for online trajectory planning and optimisation. The presented methodology can be extended to other 7-DOF anthropomorphic manipulators.