Speed regulation of a self-balancing robot by energy shaping

The self-balancing robot is a mobile platform extensively utilised in the formulation of control algorithms targeting position regulation. Contrary to the aforementioned control objective, this paper presents an energy shaping control strategy designed to drive the self-balancing robot at a predetermined velocity while ensuring the pendulum remains in an upright vertical position. This work introduces a novel strategy that allows to simplify and solve the matching equations, resulting from a Genuine-Hamiltonian energy shaping position/velocity regulation controller, applied to a self balancing robot, which has a non–constant inertia matrix and that can not be transformed into a constant one via partial linearisation. This novel technique allows to solve in an algebraic form some of the matching equations, which in general, are described by partial differential equations (PDEs), simplifying their solutions. Comparative real-time experimental results illustrate the satisfactory performance of the proposed controller in comparison with other controllers already in the literature.