Matrix form of motion model for uniaxial wheeled measuring module

Аuthors

Chernomorskii A. I.^*, Maximov V. N.^**, Plekhanov V. E.^***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: chernomorsсky@yandex.ru
**e-mail: memsdsp@gmail.com
***e-mail: ve_plekhanov@rambler.ru

Abstract

The uniaxial wheeled module (UWM) presented in the paper is intended for automatization of measurements of runway detailed geometrical parameters (inclination angles, roughness, etc.). While measuring UMW should be balanced in such a way that allows its inverted pendulous platform to stay in horizontal plane when moving along a predetermined trajectory on the runway surface. This balancing is provided by accelerating UWM motion in the direction of platform inclination. The task of UWM trajectory motion guidance is being solved by forming required forward speed and track rate.
There is an effective approach to such control problems called partial feedback linearization. Certain elements of the system state vector are chosen and non-linear transformation is carried out so that in the new (transformed) system with non-linear state feedback chosen elements would linearly depend on new control inputs. This approach assumes that dynamic motion model of the system under control is represented in special matrix form.
In this paper authors present the derivation of the required motion model for the non-holonomic UWM with no wheel-surface friction taken into account. The method of Lagrange multipliers is used to derive the equations, while non-holonomic constraints which define subspace of valid velocities of the UWM are applied to get rid of unknown multipliers. Derived matrix-form model was tested by simulation together with partial feedback linearization control system, and it was shown that the accuracy of UWM balancing stabilization had been achieved of about 0.1 degree, what is quite enough to meet the measurement requirements.

Keywords:

uniaxial wheeled module, nonholonomic constraints, Lagrange multipliers, feedback linearization

References

1. Chernomorskii A.I., Maksimov V.N., Plekhanov V.E. Vestnik Moskovskogo aviatsionnogo instituta, 2011, vol. 18, no. 3, pp. 170-176.
2. Isidori A. Nonlinear Control Systems, New York, Springer, 1995, 564 p.
3. Maksimov V.N., Chernomorskii A.I., Plekhanov V.E. Izvestiya KBNTs RAN, 2011, no. 39, pp.181-186.
4. Dobronravov V.V. Osnovy mekhaniki negolonomnykh system (Mechanics of nonholonomic sytems), Moscow, Vysshaya Shkola, 1970.
5. Pathak K., Franch J., Agrawal S. 43rd IEEE Conference on Decision and Control, 2004, Bahamas, pp. 3962-3967.