A formulation for path planning of manipulators in complex environments by using adjacent configurations

Abstract

The problem of robot path planning among obstacles has been approached by formulating robot configurations by means of a suitable fully Cartesian coordinate description. Thus, an analytical expression has been found for adjacent configurations, which is useful in deducing an optimization formulation for the collision-free path problem. An algorithm is proposed to solve the problem of finding a feasible path to be followed to an end point by a robot between given start and end points in space. In the procedure a map of feasible robot configurations is obtained by using a suitable nonlinear programming technique; then a weighted graph is associated to the map and finally a search algorithm is used to obtain a sequence of free-of-collision robot configurations between two previously selected points. The algorithm has been successfully applied to redundant planar robotic manipulators with rotational and prismatic joints, and three-dimensional robotic manipulators. Some numerical examples are reported in the paper.