CONTROL DESIGN FOR DIFFERENTIAL
STEERED MOBILE ROBOT: A POLYNOMIAL
APPROACH
L. Bruyere, A. Tsourdos, B. A. White,
J. T. Economou, P. C. K. Luk,
 Dept. of Aerospace, Power & Sensors, Craneld
University, Shrivenham, Swindon SN6 8LA, U.K.
a.tsourdos@cranfield.ac.uk
KEYWORDS
Polynomial eigenstructure assignment, mobile robot, quasi-linear, MIMO.
ABSTRACT
This paper describes a polynomial approach for the design of a dierential steered
mobile robot. Polynomial eigenstructure assignment can be seen as a dynamic
inversion approach suitable for mobile robots and vehicle models. The theory
of polynomial eigenstructure assignment is described for linear time invariant
systems. The approach is then applied to a quasi-linear MIMO mobile robot to
design a controller of specic structure. Simulations results show good tracking of
both velocity and rate meeting the design objectives for fast responses.
1. INTRODUCTION
One of the most popular methods for applying
linear time-invariant (LTI) control theory to time-
varying and/or nonlinear systems is gain schedul-
ing [Rugh 1993]. This strategy involves obtaining
Taylor linearised models for the plant at nitely
many equilibrium (\set points"), designing an
LTI control law (\point design") to satisfy local
performance objectives for each point, and then
adjusting (\scheduling") the controller gains in
real time as the operating conditions vary. This
approach has been applied successfully for many
years [Nichols et al. 1993, Hyde and Glover 1993].
Despite past success of gain scheduling in prac-
tice, until recently little has been known about it
theoretically as a time-varying and/or nonlinear
control technique. Also, determining the actual
scheduling routine is more of an art than a science.
While ad hoc approaches such as linear inter-
polation and curve tting may be sucient for
simple static-gain controllers, doing the same for
dynamic multivariable controllers can be a rather
tedious process.
During the 1980's, Rugh and his colleagues devel-
oped an analytical framework for gain scheduling
using extended linearisation [Baumann and Rugh
1986, Rugh 1993, Wang and Rugh 1987]. Also,
Shamma and Athans [Shamma and Athans 1990,
Shamma and Athans 1991, Shamma and Athans
1992] introduced linear parameter-varying (LPV)
systems as a tool for quantifying such heuristic
design rules as \the resulting parameter must
vary slowly" and \the scheduling parameter must
capture the nonlinearities of the plant". Shahruz
and Behtash [Shahruz and Behtash 1992] sug-
gested using LPV systems for synthesising gain-
scheduled controllers, and Shamma and Cloutier
[Shamma and Cloutier 1993] have used LPV plant
models with -synthesis [Packard and Doyle 1993]
for designing autopilots.
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