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.
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