Application of Hamiltonian dynamics to manipulator control in constrained workspace

We describe a methodology to plan the trajectories of a robotic manipulator moving in an n-dimensional Euclidean space. The robot has to reach the target avoiding obstacles and is constrained to move in a region of the space. We show that if the positions of the target and of the obstacles are known a priori then a Hamiltonian function can be constructed and used to define a collision-free trajectory. A simulation concerning a real three-d.o.f. manipulator is reported.