Stability of Controlled Motion of a Gymnast in High-Speed Mid Air Maneuvers

Abstract

The twisting somersaults motion of a diver in free flight is simulated using a standard man model based on an anthropomorphic multibody system (MBS). The aim of the paper is to present a Lyapunov-stable dynamic control law of an MBS with n degrees of freedom moving along an m-dimensional submanifold (0<m≤n). The prescribed motion defining that submanifold results from a kinematic analysis of video sequences. The inverse kinematics is solved by dynamic tracking. Consistent initial velocities for the free flight are evaluated by nonlinear optimization minimizing the deviation of the body fixed marker points from the measurement data. So, the total amount of the angular momentum of the MBS which has to be constant during the free flight is optimized. The conservation of the angular momentum of the MBS defines an intrinsic constraint manifold on which the diver is moving. This conservation law can also be used for nonholonomic motion planning. The approach essentially uses differential-geometric concepts and methods well-known from the Lagrangian Multibody Dynamics.