New Hamiltonian Formulation and Control of Robotic Systems

In this paper, a novel constructive method is presented to provide a new Hamiltonian formulation with dissipation for both fully actuated and underactuated robotic systems. Firstly, a high-order partial derivative operator, unified partial derivative operator (UPDO) is introduced, and its properties are investigated, which play essential and instrumental roles in the results presented in the paper. Secondly, Hamiltonian formulation is investigated for the first time by choosing the sum of kinetic energy and virtual potential energy, rather than the physical potential energy, as the Hamiltonian function. With the help of UPDO, we give one new property of robotic systems, which is fundamental to the Hamiltonian formulation, and at the same time we can show that the Hamiltonian formulation has a very appealing structure and some nice properties for further analysis. It is shown that in the new formulation, the matching conditions become a set of algebraic equations which are much easier to solve in comparison with solving a set of partial differential equations. Finally, robust adaptive control is studied for robotic systems by augmenting the new Hamiltonian formulation introduced in the paper