Optimal positioning of robots: feasibility of continuous trajectories among obstacles

The authors present a general method for the automatic positioning of a robot in the workcell. The criterion for the optimization routine is a function of the trajectory feasibility, given the static or moving obstacles as well as the joint limits. The authors mathematically define a property of trajectory feasibility and describe a numerical method to calculate it. The optimization problem, the criterion, and the constraints are formalized. A numerical solution, and the results of two test cases are included