A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of Parallel Kinematic Manipulators
Andreas Müller, Shivesh Kumar, Thomas Kordik
In IEEE Robotics and Automation Letters, IEEE, volume 8, pages 1-8, Apr/2023.
Series elastic actuators (SEA) were introduced for
serial robotic arms. Their model-based trajectory tracking control
requires the second time derivatives of the inverse dynamics
solution, for which algorithms were proposed. Trajectory control
of parallel kinematics manipulators (PKM) equipped with SEAs
has not yet been pursued. Key element for this is the computationally
efficient evaluation of the second time derivative of the
inverse dynamics solution. This has not been presented in the
literature, and is addressed in the present paper for the first time.
The special topology of PKM is exploited reusing the recursive
algorithms for evaluating the inverse dynamics of serial robots.
A Lie group formulation is used and all relations are derived
within this framework. Numerical results are presented for a 6-
DOF Gough-Stewart platform (as part of an exoskeleton), and for
a planar PKM when a flatness-based control scheme is applied.