Ruprecht-Karls-Universität Heidelberg
Optimization in Robotics and Biomechanics

Modeling and optimal control of human-like running

Katja Mombaur - IWR
Gerrit Schultz
- previously IWR, now at Freiburg
Joachim Knöthig - previously IWR

Designing and controlling an anthropomorphic mechatronic system that is able to perform a dynamic running motion is a challenging task. One difficulty is that the fundamental principles of natural human running motions are not yet fully understood. The purpose of our research is to show that mathematical optimization is a helpful tool to gain this insight into fast and complex motions.

We present physics-based running motions for complex models of human-like running which have been generated by optimization. Running is modeled as a multiphase periodic motion with discontinuities, based on multibody system models of the locomotor system with torque actuators and spring-damper elements at each joint. We use a 3D model of the human body with 12 bodies (2-segment torso, upper legs, lower legs, feet, upper arms, lower arms) and 25 DOF as well as a 2D version describing running in the sagittal plane with 9 bodies and 11 DOF.

The problem of generating gaits is formulated as offline optimal control problem and solved by an efficient direct multiple shooting method. We optimize energy-related criteria and show that the results have a close resemblance to running motions of humans. The results provide information about the internal forces and torques required to produce natural human running, as well as on the resulting kinematics.


Earlier research with a simple 2D model with 5 bodies (torso, upper and lower legs) has shown that articulated feet as well as arms are necessary to generate truly dynamic human-like running.


G. Schultz, K. Mombaur: Modeling and Optimal Control of Human-Like Running, IEEE/ASME Transactions on Mechatronics, Vol. 15, No. 5, Oct. 2010

G. Schultz, Optimal Control of Human Running, Diploma Thesis, IWR, University of Heidelberg, 2007

J. Knöthig: Modeling and Optimal Control of Human-like Gaits with Flight Phases, Diploma Thesis, IWR, University of Heidelberg, 20


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