Planning of optimal free paths of robotic manipulators with bounds on dynamic forces

The dynamic optimization of robot arm motion is carried out along free paths joining two given end points. The goal is to obtain soft functioning while performing transfer at a fast rate compatible with bounds set on actuators, joint lateral loads, dynamic forces acting on the payload or on the manipulator base. Such constraints are efficiently dealt with by applying the Pontryagin maximum principle, provided that the dynamic forces to be bounded are expressed as explicit linear functions of the actuating inputs. The dynamic model is formulated in terms of Hamiltonian phase variables which have proved their reliability when dealing with dynamic optimization. The results of numerical simulation of two-link and three-link arms are presented