Optimizing  motions in biomechanics and robotics by means of 
the direct boundary value problem approach
 
Katja Mombaur


Gaining insight into the fundamental principles of human walking and 
running motions  is crucial for researchers in robotics, biomechanics, 
rehabilitation and sports science. 
In this talk, we show that mathematical models and numerical optimization are
very helpful tools to gain that knowledge. 
We show in particular the usefulness of the direct boundary value problem
approach developed by Bock to solve this class of problems. 
Motions in biomechanics and robotics result in multi-phase models of highly
nonlinear ODEs or
DAEs with state variable discontinuities and complex constraints.  
Relevant objective functions such as the stability, robustness or 
energy consumption may give rise to additional discontinuities. 
We present walking, running and artistic  
motions for complex human-like configurations 
in the sagittal plane and in three dimensions which have been
generated by optimization. We give results for different objective functions
 some of which lead to remarkably natural motions.