Recursive second-order inverse dynamics for serial manipulators

Various model-based control schemes, e.g. feedback-linearizing control of robotic manipulators with series elastic actuators require time derivatives of the control forces, i.e. of the equations of motion. This is referred to as the higher-order inverse dynamics problem. As this must be evaluated on the controller hardware, computationally efficient formulations are crucial. While recursive O (n) inverse dynamics algorithms are well-established, such for the higherorder inverse dynamics are relatively new. O (n) algorithms for the latter problem were published recently building upon the known recursive inverse dynamics algorithms in terms of Denavit-Hartenber (DH) parameters. The DH convention is restrictive, however. Also the higher-order formulations are naturally very complex. Both issues are addresses in this paper with concepts from screw and Lie group theory. An O (n) algorithm for determining the first and second time derivative of the inverse dynamics solution is presented. The Lie group approach provides a high level of compactness while ensuring the computational efficiency. Being frame invariant this formulation allows for using representations in different frame. Two formulations are presented, one using the body-fixed and the other the so-called hybrid representation of twists. The latter is deemed to be computationally more efficient that the classical body-fixed version. Results are shown for a 6-DOF industrial manipulator.