Mathematical modeling of industrial robots based on Hamiltonian mechanics

The paper deals with an advanced mathematical modeling for robot motion control. The explanation focuses on a composition of suitable mathematical models of robot dynamics intended for control design. Instead of usual Lagrangian formulation of dynamics, this paper presents robot dynamics by Hamiltonian formulation that leads to different physical descriptive quantities considered for control design. In the case of Hamiltonian formulation, a momentum is such physical quantity. In the paper, as representative control approaches, PD control with gravity compensation and model-oriented Lyapunov-based control are considered. The control approaches considering Hamiltonian formulation are demonstrated for simplicity on two-mass robot-arm system. However, the presented results are generally applicable e.g. to usual articulated multi-purpose industrial robots-manipulators.