STABILITY OF CONTROLLED MOTION IN DIVING SIMULATIONS

Abstract

The twisting somersault motion of a diver in free flight is simulated using a standard man model modelled by an anthropomorphic multibody system of rigid segments (MBS). That man model is originated by Saziorski [1]. The key point for this purpose is a Lyapunov-stable dynamic control of the MBS. This method is a generalization of the augmented PD control law known from nonlinear control theory in robotics, see [2]. Strategies how to find control laws are used such that an MBS with degree of freedom n is moving on an m-dimensional submanifold, 0<m£n. The nominal motion of the man model which has to be controlled results from a kinematic analysis of video sequences where the inverse kinematics is realized by dynamic tracking. That means, the man model is embedded in a set of marker points generated by video records. Force-coupling is used to approximate the marker points by corresponding model-fixed points. Then, integration of Lagrange‘s equations supplies the desired nominal motion of the intrinsic joint variables (but not the motion of the man model in the air, which takes place in free flight). In a second step (now without force-coupling) consistent initial velocities for the free flight are evaluated by nonlinear optimization in order to minimize the deviations of the model-fixed points from measurement data. So the total amount of angular momentum of the MBS which keeps constant during free flight is optimized. The conservation of the angular momentum defines a constrained manifold on which the diver model is moving, because it moves in free flight with the obtained initial velocities and with the control forces/moments in the joints. REFERENCES: [1] Aruin, A. S., Saziorski, W. M. 1989. Ergonomic Biomechanics, Moscow: Mechanical Engineering. [2] Murray, R. M., Li, X., Sastry, S. S. 1994. A Mathematical Introduction to Robotic Manipulation. Boca Raton, Ann Arbor, London, Tokyo: CRC Press.