Embedded control synthesis using one-step methods in discrete mechanics

Low bandwidth control and estimation for nonlinear systems presents a challenging problem that is often encountered when dealing with implementation on an embedded platform. Discrete mechanics techniques for system modeling are well-suited to low-bandwidth applications because they possess desirable numerical properties over a large range of timesteps including exact constraint conservation, and excellent Hamiltonian and momentum behaviors. We present an overview of a variational integrator based discrete mechanics system representation and corresponding state choice that allows the discrete flow to be expressed as a one-step map as required by classical digital control design tools. This modeling paradigm is used to experimentally control an underactuated, nonlinear system with low frequency control. Simulations of the experimental system demonstrate significantly better extended Kalman filter performance using the present framework over a traditional one-step Euler approximation.