Nonholonomic motion planning

Jean-Paul Laumond

LAAS-CNRS, Toulouse, France

This lecture introduces differential geometry tools (vector field Lie algebra) to address kinematic constraints (such as "rolling without sliding") into the general motion planning framework. The worked-out examples will be cars and mobile robots with trailers. Then we will present recent results showing that the human locomotion naturally obeys some nonholonomic constraints. This last example opens perspectives in motion planning for humanoid robots.

The lecture will include: - basic differential geometry concepts - the notion of small-time controllability - the vector field Lie algebra and the LARC theorem - effective methods to steer nonholonomic systems (and open problems) - a general scheme for nonholonomic motion planning - on the human locomotion and humanoid robotics.