Network Modelling and Simulation of Robots with Flexible Links. a Port-Based Approach

In this paper, the port Hamiltonian model of a manipulator is presented as the result of the power-conserving interconnection of a set of main components (rigid bodies, flexible links and kinematic pairs). The flexible link model we propose is different from classical approaches because it takes into account the infinite dimensional nature of elasticity, since it does not rely on any finite dimensional approximation (e.g. modal approximation) and, differently from Euler-Bernoulli or Timoshenko theory, it is able to describe large deflections in 3-D space. Once the flexible link model has been presented, a finite dimensional approximation is discussed in order to be able to simulate the infinite dimensional dynamics. Since energy and energy-related properties are crucial in port Hamiltonian systems, the spatial discretization technique is based on physical considerations so that, by exploiting the geometric structure of an infinite dimensional port Hamiltonian system, a finite dimensional approximation still in port Hamiltonian form can be obtained. Since rigid bodies and flexible links are described within the port Hamiltonian formalism, their interconnection is possible once a proper relation between the power conjugated port variables is deduced. These relations are the analogous of the Kirchoff laws of circuit theory. The final model is a mixed port Hamiltonian system because of the presence of a finite dimensional subsystem modelling the rigid bodies and of an infinite dimensional one describing the flexible links. The intrinsic modularity of the approach simplifies the model deduction and simulation, while the Hamiltonian description suggests the development of energybased controllers. In order to demonstrate the dynamical properties of the model and how complex mechanisms can be obtained by port interconnection, simulations of 1-dof and 2-dof serial manipulators are presented. Keywords— flexible robots, modelling, finite elements methods, simulation, port Hamiltonian systems