Motion planning for manipulators in complex environments

Abstract

Difficulties we are faced with in order to solve the motion-planning problem for manipulators are twofold : 1) the practical difficulty of dealing with rotations in a three dimensional space, 2) the inherent exponential complexity of the Free Space construction with the number of degrees of freedom.

To answer the first point, we have given general tools to translate the control of critical distances between solids in Cartesian Space into constraints in Configuration Space. This results in building a local model of Free Space, that we use both to locally generate safe trajectories by minimization techniques, and to build global discretized models of Free Space.

To answer the second point, we have proposed to decouple the search for the global shape of the trajectory from the fine motion computations. The two levels operate with very distinct time-scales : a fast one for the computation of displacements from local information, a slow one for the learning of global strategies from execution of a path. This method can also be adapted to various applications, such as the exploration of an unknown, eventually changing, environment by a mobile robot.

In addition, we have extended the motion-planning problem to a broader class of examples, defined by the control of a set of measures on the system.