A methodology to plan the trajectories of robots that move in an n-dimensional Euclidean space, have to reach a target avoiding obstacles and are constrained to move in a region of the space is described. It is shown that if the positions of the obstacles are known then a Hamiltonian function can be constructed and used to define a collision-free trajectory. It is also shown that the method can be extended to the case in which the target or the obstacles (or both) move. Results of simulations for a pair of planar robots and a three degrees-of-freedom manipulator are finally reported.
