Total energy-shaping control for mechanical systems via Control-by-Interconnection

TL;DR

This paper introduces a novel energy-shaping control method for under-actuated mechanical systems using a control-by-interconnection framework, simplifying the matching conditions and enabling numerical solutions for specific system classes.

Contribution

It reformulates energy-shaping control as a control-by-interconnection problem, providing alternative matching conditions and numerical solutions for certain under-actuated systems.

Findings

Controllers successfully applied to cart-pole and acrobot systems.

New matching conditions based on added energy constraints.

Numerical solutions for kinetic energy matching in specific systems.

Abstract

Application of IDA-PBC to mechanical systems has received much attention in recent decades, but its application is still limited by the solvability of the so-called matching conditions. In this work, it is shown that total energy-shaping control of under-actuated mechanical systems has a control-by-interconnection interpretation. Using this interpretation, alternate matching conditions are formulated that defines constraints on the added energy, rather then the total closed-loop energy. It is additionally shown that, for systems that are under-actuated degree one with the mass matrix depending on a single coordinate, the kinetic energy matching conditions resolve to ODEs which can be evaluated numerically. Using this approach controllers are proposed for the benchmark cart-pole and acrobot systems.