Modeling and optimal control of human platform diving with somersaults and twists

The model-based investigation of fast dynamic motions of anthropomorphic systems is an interesting interdisciplinary field combining research efforts from applied mathematics, robotics, biomechanics, computer graphics and sports. Somersaults and twists of professional platform divers represent a particularly fascinating and extremely difficult type of motion. The purpose of this paper is to show how optimal control methods based on whole-body dynamic models of the diver can be very useful in generating natural platform diving motions. We present 3D somersaults with twists as well as pure somersaults in the sagittal plane for a variety of different take-off configurations and positions to be attained in the aerial phase that all have been produced by optimization of criteria related to energy input. By formulating the dive as a problem with several dynamic phases, we are able to treat contact and flight phase simultaneously, and also to split the flight phase in several sub-phases to correctly model requested positions in the air. Divers are modeled as multibody systems with actuators and damper elements at each joint. For the solution of the optimal control problem we use efficient direct multiple shooting methods based on the boundary value problem approach. The optimization results can be used to generate motions in computer graphics or robotics, but also provide useful insights into biological motion, including joint kinematics and the required torques and forces.