# Inverse optimal control

**Katja Mombaur** - IWR**Jean-Paul Laumond** - LAAS-CNRS, Toulouse

It is a very common assumption in bionics and biomechanics that natural structures and processes are optimal due to evolution and individual development of the respective humans, animals, or plants. This is also true for many forms of human and animal motion such as locomotion. However, the specific optimization criterion applied to a particular motion is very often not known.But is is possible to observe the results of this natural optimization process by measurements, such as motion capture, EMG etc.
The study of these optimal processes in nature can therefore be formulated as an inverse optimal control problem, which results in determining the optimal control model â and in particular the objective function - that has produced a given (or partly given) solution. Inverse optimal control problems represent the opposite of classical (forward) optimal control problems for which the full problem formulation is given and the optimal trajectories are sought for. Inverse optimal control problems are much more difficult than standard identification problems since optimization and data fitting have to be handled simultaneously. | |

We propose a bilevel approach to solve inverse optimal control problems which efficiently combines a direct multiple shooting technique for the optimal control problem solution with a derivative free trust region optimization technique to guarantee the match between optimal control problem solution and measurements. We have applied inverse optimal control to various different examples, e.g. to determine optimality principles of human locomotion path generation to given target positions and orientations, using motion capture data of human subjects. |

**References:**

K. Mombaur, A. Truong, J.-P. Laumond: *From Human to Humanoid Locomotion - An inverse optimal control approach, *Autonomous Robots, Volume 28, Number 3 / April 2010 , published online 31 Dec. 2009

K. Mombaur, J.P. Laumond, A. Truong: *An inverse optimal control approach to human motion modeling*, ISRR 2009 (14^{th} International Symposium of Robotics Research), Lucerne, Switzerland, Aug./Sept. 2009, to appear in Springer STAR series

K. Mombaur, M. Sreenivasa , *Inverse optimal control as a tool to understand human yoyo playing*, to appear in Proceeedings of ICNAAM 2010, Rhodes, Greece, Sept. 2010