Tracking control for underactuated non-minimum phase multibody systems

TL;DR

This paper develops a novel control strategy for underactuated multibody systems with complex constraints, combining feedforward and funnel feedback control, demonstrated through simulation of a robotic manipulator.

Contribution

It introduces a new procedure to derive internal dynamics and a feasible coordinate set, simplifying control design for complex multibody systems.

Findings

Control strategy effectively manages underactuated multibody systems.

Simulation shows successful tracking in a nonlinear robotic manipulator.

New internal dynamics derivation simplifies control design process.

Abstract

We consider tracking control for multibody systems which are modelled using holonomic and nonholonomic constraints. Furthermore, the systems may be underactuated and contain kinematic loops and are thus described by a set of differential-algebraic equations that cannot be reformulated as ordinary differential equations in general. We propose a control strategy which combines a feedforward controller based on the servo-constraints approach with a feedback controller based on a recent funnel control design. As an important tool for both approaches we present a new procedure to derive the internal dynamics of a multibody system. Furthermore, we present a feasible set of coordinates for the internal dynamics avoiding the effort involved with the computation of the Byrnes-Isidori form. The control design is demonstrated by a simulation for a nonlinear non-minimum phase multi-input, multi-output robotic manipulator with kinematic loop.