Non-Minimal Modeling and Structure-Preserving Integration for Planar Elastically Coupled Systems

Kurzfassung

A generalized formulation of evolution equations, which contains gradient and Hamiltonian systems, has been recently discussed in the context of systematic energy-preserving spatial discretization and time integration using a Galerkin and Petrov-Galerkin ansatz, respectively. Among the examples from different physical domains, mechanical systems with holonomic constraints, described in terms of non-minimal configuration variables and velocities, fit into the formulation. The models feature only the derived constraints on velocity level, and they can be numerically integrated, preserving energy and constraints without drift-off. In this contribution, we set up this formulation for N-link planar manipulators with mono- or multi-articular elastic couplings in redundant Cartesian coordinates and velocities. Before sketching the recursive construction of the model, we recall the variational principle the model is derived from. A three-link configuration is used as a simulation example to display the numerical conservation of constraints and energy. Finally, we discuss the extension of the model by joint torque inputs and perspectives regarding control design.