Application of Hamiltonian dynamics to manipulator control in constrained workspace

We describe a methodology to plan the trajectory of a robotic manipulator moving in an n-dimensional Euclidean space. The robot has to reach a target avoiding obstacles and is allowed to move in a constrained space. We show that if the position of the target and of the obstacles in known a priori, then a Hamiltonian function can be constructed and used to define the trajectory. A simulation concerning a real three-dimensional manipulator is finally reported.