Hamiltonian path planning in constrained workspace

Abstract

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

Singularity Avoidance for Cart-Mounted Hand-Guided Collaborative Robots: A Variational Approach

“…The above considerations allow us to conclude that the singularity avoidance can be achieved by establishing a proper motion law of the cart, which in turn amounts to finding a curve from x C (t j ) to x C (t j+1 ) that does not intersect with the non-admissible region. Such a problem can be interpreted as constrained (the constraint is due to the fact that the trajectory cannot go backward in time) path planning with obstacle avoidance, which can be solved with many tools [33,34]. In the following, we employ a variational approach.…”