Ruprecht-Karls-Universität Heidelberg
Optimization in Robotics and Biomechanics

Modeling and optimal control of human platform diving

Katja Mombaur - IWR
Jens Koschorreck, Katja Roos
- former IWR members

Somersaults and twists of professional platform divers represent a particularly fascinating and extremely difficult type of motion.

During a very short and intense contact phase with the platform, the diver has to apply exactly the right forces and make its body attain the right take-off position and velocities that allow him a perfect execution of the jump and a perfect plunge in the water.

During flight, the diver's possibilities to modify the jump are limited since the motion of the overall center of mass can not be changed and invariably follows its parabolic trajectory. In addition the overall angular momentum about the center of mass remains constant at the value it had at take-off.

Relative motions of the segments of the anthropomorphic system are possible within these manifolds, and within the ranges of internal angle, angular velocity and torque limits.

The purpose of this research 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.



J. Koschorreck, K. Mombaur: Optimization of Somersaults and Twists in Platform Diving, Computer Methods in Biomechanics and Biomedical Engineering, Vol. 12, No. 2-1, 2009

Jens Koschorreck : Optimal Control of Somersaults with Twists, Diploma Thesis, IWR, University of Heidelberg, 2008

Katja Roos: Numerical Optimization of Platform Diving, Diploma Thesis, IWR, Univesity of Heidelberg, 2006

K. Mombaur,
Last Update: 19.10.2011 - 16:03

The photographs in the header of this webpage have been taken at the Musee de l'Automate in Souillac, France