A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of Parallel Kinematic Manipulators

Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of inverse dynamics solution, which algorithms proposed. Trajectory parallel kinematics manipulators (PKM) equipped with SEAs has not yet been pursued. Key element this is computationally efficient evaluation derivative solution. This presented in literature, and addressed present paper first time. The special topology PKM exploited reusing recursive evaluating robots. A Lie group formulation used all relations are derived within framework. Numerical results a 6- DOF Gough-Stewart platform (as part an exoskeleton), planar when flatness-based scheme applied.