# Natural locomotion trajectories for humans and humanoid robots

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

**, AIST, Tsukuba, Japan**

Eiichi Yoshida

Eiichi Yoshida

If a human being is asked to move from a given start point to a given target in an empty room, he will usually choose, out of all possible paths, a very specific one. Obviously this natural path depends on the properties of the individual human being, but there also seem to be some general ``path generation criteria'' that always remain valid. The figure gives two example locomotion scenarios and the expected natural (red) as well as undesired (blue) behaviors.

In our research, we explore the underlying principles of natural locomotion path generation of human beings. By ``locomotion path'' we denote the motion of a subject as a whole in the plane - i.e. the development of his overall position and orientation -, and not the relative joint motions at his internal degrees of freedom.

This project is thus more concerned with the cognitive aspects of motion planning than with the biomechanics of locomotion.

The knowledge of these principles is not only useful to gain more insights into human motion, but will ultimately also serve to implement biologically inspired path planning algorithms on a humanoid robot.

The key of our approach is to formulate the path planning problem as optimal control problem. We propose a single dynamic model valid for all situations, which includes both nonholonomic and holonomic modes of locomotion.

Human locomotion in many cases is nonholonomic, i.e. there is a differential coupling between the direction of motion and the body orientation: humans in most cases prefer forward walking over sideward or diagonal steps. However, in certain situations such an orthogonal component in the translational velocity (i.e. a holonomic mode of locomotion) seems perfectly natural, e.g. to avoid obstacles or to quickly reach close-by targets that do not lie in the current direction of body orientation. In our formulation, the choice between holonomic and nonholonomic behavior is not accomplished by a switching model, but it appears in a smooth way, along with the optimal path, as result of the optimization by efficient numerical techniques.

A crucial element in our model is the objective function that generates the natural locomotion paths, and which is generally a weighted combination of several individual criteria.

In the early stage of our research, we started to manually tune the components of the objective function, such that the behavior for several test cases for the humanoid robot model is qualitatively good. Later, we managed to truly identify the cost function of human locomotion from motion capture data by means of inverse optimal control techniques. It can be shown that human behavior can be reproduced to a very good accuracy by a combined criterion that minimized total time , squared accelerations in forward, sideward and rotational direction, as well as the angular difference between actual orientation and orientation towards the goal.

The resulting model can be transferred to humanoid robots such as HRP-2 to enable them to autonomously generate locomotion paths.

Current extensions of this research include the avoidance of fixed obstacles and other moving subjects during locomotion.

**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, Springer Tracts in Advanced Robotics (STAR), May 2011

K. Mombaur, J.P. Laumond, E. Yoshida: *An Optimal Control Based Formulation to Determine Natural Locomotor Paths for Humanoid Robots*, Advanced Robotics, Vol. 24, No. 4, March 2010