Jean-Paul Laumond

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R/sup 2//spl times/S/sup 1/ of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning. >

Position referencing and consistent world modeling for mobile robots

In order to understand its environment, a mobile robot should be able to model consistently this environment, and to locate itself correctly. One major difficulty to be solved is the inaccuracies introduced by the sensors. The approach proposed in this paper to cope with this problem relies on 1) defining general principles to deal with uncertainties : the use of a multisensory system, favo ring of the data collected by the more accurate sensor in a given situation, averaging of different but consistent measurements of the same entity weighted with their associated uncertainties, and 2) a methodology enabling a mobile robot to define its own reference landmarks while exploring its environment. These ideas are presented together with an example of their application on the mobile robot HILARE.

Visibility-based probabilistic roadmaps for motion planning

This paper presents a variant of probabilistic roadmap methods (PRM) that recently appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps, called visibility roadmaps. Our algorithm integrates an original termination condition related to the volume of the free space covered by the roadmap. The planner has been implemented within a software platform allowing us to address a large class of mechanical systems. Experiments show the efficiency of the approach, in particular for capturing narrow passages of collision-free configuration spaces.

Stabilization of trajectories for systems with nonholonomic constraints

A new technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. In this note, we suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired (nominal) feasible trajectory, the note gives an explicit control law which will locally exponentially stabilize the system to the desired trajectory. The theory is applied to several examples, including a car-like robot. >

Shortest paths synthesis for a car-like robot

This paper deals with the complete characterization of the shortest paths for a car-like robot. Previous works have shown that the search for a shortest path may be limited to a simple family of trajectories. Our work completes this study by providing a way to select inside this family an optimal path to link any two configurations. We combine the necessary conditions given by Pontryagins maximum principle with a geometric reasoning. This approach enables us to complete the local information with a global analysis of different wave fronts. We construct a partition of the configuration space in regions where the same kind of path is optimal to reach the origin. In other words, we determine a shortest path synthesis by providing, at each point, an optimal control law to steer the robot to the origin.

From human to humanoid locomotion--an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.

Controllability of a multibody mobile robot

Presents a proof of controllability for multibody mobile robots. An instance of such systems correspond to a car pulling and pushing trailers, like a luggage carrier in an airport. Three modeling levels are built: geometrical, differential and control models respectively. The authors shows that four different control systems correspond to a same differential model. The differential model is then used to give a same proof of controllability for four distinct multibody mobile robot systems.<<ETX>>

Manipulation Planning with Probabilistic Roadmaps

This paper deals with motion planning for robots manipulating movable objects among obstacles. We propose a general manipulation planning approach capable of addressing continuous sets for modeling both the possible grasps and the stable placements of the movable object, rather than discrete sets generally assumed by the previous approaches. The proposed algorithm relies on a topological property that characterizes the existence of solutions in the subspace of configurations where the robot grasps the object placed at a stable position. It allows us to devise a manipulation planner that captures in a probabilistic roadmap the connectivity of sub-dimensional manifolds of the composite configuration space. Experiments conducted with the planner in simulated environments demonstrate its efficacy to solve complex manipulation problems.

An Optimality Principle Governing Human Walking

In this paper, we investigate different possible strategies underlying the formation of human locomotor trajectories in goal-directed walking. Seven subjects were asked to walk within a motion capture facility from a fixed starting point and direction, and to cross over distant porches for which both position and direction in the room were changed over trials. Stereotyped trajectories were observed in the different subjects. The underlying idea to attack this question has been to relate this problem to an optimal control scheme: the trajectory is chosen according to some optimization principle. This is our basic starting assumption. The subject being viewed as a controlled system, we tried to identify several criteria that could be optimized. Is it the time to perform the trajectory? The length of the path? The minimum jerk along the path? We found that the variation (time derivative) of the curvature of the locomotor paths is minimized. Moreover, we show that the human locomotor trajectories are well approximated by the geodesics of a differential system minimizing the norm of the control. Such geodesics are made of arcs of clothoids. The clothoid or Cornu spiral is a curve, whose curvature grows with the distance from the origin.

Visibility based probabilistic roadmaps

Presents a variant of probabilistic roadmap algorithms that appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps. The algorithm has been implemented within a software platform allowing us to address a large class of mechanical systems. Experiments show the efficiency of the approach in capturing narrow passages of collision-free configuration spaces.