We have been first interested in car like systems. For this type of systems we provided the first complete algorithm that consists in transforming any collision-free path into a sequence of admissible collision-free ones. This result is mainly based on the knowledge of the shortest paths (the so-called Reeds and Shepp curves). The combinatorial analysis of the path complexity is related to the study of the underlying nonholonomic metrics. We proved that the number of maneuvers to park a car varies as the inverse of the square of the size of the free space. Such a proof has been made possible via a complete synthesis of the Reeds and Shepp curves. The picture on the right below shows the domains of the configuration space (x,y,theta) reachable by shortest paths of a given length.

Selected Publications:

"A motion planner for nonholonomic mobile robots"    
J.P.LAUMOND , P.JACOBS , M.TAIX , R.MURRAY
IEEE Transactions on Robotics and Automation, 10(5), pp.577-593, October 1994

"Shortest path synthesis for a car-like robot"    
P. SOUÈRES and J.-P. LAUMOND,
IEEE Transaction on Automatic Control, 41 (5), May 1996

"Obstacle distance for car-like robots"    
M.VENDITTELLI , J.P.LAUMOND and C.NISSOUX
IEEE Transactions on Robotics and Automation, 15(4), pp.678-691, August 1999

We have also worked a lot on tractor trailer systems with several contributions. We have studied the relations between local controllability and global completeness of path planning algorithms, by defining a property a local method needs to satisfy in order to be applicable in several global planning schemes. Based on these studies, we have proposed two types of local methods for differentially flat two input systems and accounting for local controllability (click on top picture to see a movie).

Selected Publications:

"Multi-level path planning for nonholonomic robots using semi-holonomic subsystems"
S.SEKHAVAT , P.SVESTKA , J.P.LAUMOND and M.H.OVERMARS
International Journal of Robotics Research, 17(8), pp.840-857, August 1998

"Topological property for collison-free nonholonomic motion planning: the case of sinusoidal inputs for chained form systems"
S. SEKHAVAT and J.-P. LAUMOND,
IEEE Transactions on Robotics and Automation, 14(5), pp.671-680, October 1998

"Flatness and small-time controllability of multibody mobile robots : application to motion planning"
F. LAMIRAUX and J.-P. LAUMOND
IEEE Transactions on Automatic Control, 45(10), October 2000

Besides path planning, we have worked in reactive trajectory deformation for nonholonomic systems. The goal was to design a method enabling a robot to cope with uncertainties in the map of the environment as well as with imprecision of the localization. These perturbations can make an initially collision-free planned trajectory in collision with real obstacles of the environment. The idea of our trajectory deformation method is to perturb the input function along the initial trajectory in order to get away from obstacles detected by the on-board sensors of the robot, keeping the nonholonomic constraints satisfied. (Click on top picture to see an animation)

See also the demo with mobile robot Hilare 2 towing a trailer

Selected Publications:

"Reactive Path Deformation for Nonholonomic Mobile Robots"
F. LAMIRAUX, D. BONNAFOUS and O. LEFEBVRE
to appear in the IEEE Transactions on Robotics