Control of multibody systems in DAE form applied to a cable robot
Journal of the Brazilian Society of Mechanical Sciences and Engineering (2019)
Certain types of multibody systems cannot be conveniently modelled using minimal coordinates. Then, redundant coordinates can be chosen to represent the system kinematics. This results in the equations of motion being described by differential-algebraic equations (DAEs). Control of systems described by DAEs is not straight-forward in practical applications. In this paper, application and implementation of a linear quadratic regulator is shown for underactuated systems in DAE form. Therefore, the equations of motion are linearised around the desired state trajectory and transformed into ordinary differential equations using Maggi’s formulation with application of the QR decomposition. For implementation of the state feedback controller, measurements or estimates of the full state vector are required. For observer design, an unscented Kalman filter is proposed which is able to account for measurements of the algebraic coordinates. Application of the controller in a two-degree of freedom control structure is shown in simulations and experiments on an underactuated cable robot.