On Global Trajectory Tracking Control for an Omnidirectional Mobile Robot with a Displaced Center of Mass
Received 17 September 2019; accepted 11 February 2020
2020, Vol. 16, no. 1, pp. 115-131
Author(s): Andreev A. S., Peregudova O. A.
This paper addresses the trajectory tracking control design of an omnidirectional mobile
robot with a center of mass displaced from the geometrical center of the robot platform. Due
to the high maneuverability provided by omniwheels, such robots are widely used in industry
to transport loads in narrow spaces. As a rule, the center of mass of the load does not coincide
with the geometric center of the robot platform. This makes the trajectory tracking control
problem of a robot with a displaced center of mass relevant. In this paper, two controllers
are constructed that solve the problem of global trajectory tracking control of the robot. The
controllers are designed based on the Lyapunov function method. The main difficulty in applying
the Lyapunov function method for the trajectory tracking control problem of the robot is that
the time derivative of the Lyapunov function is not definite negative, but only semidefinite
negative. Moreover, the LaSalle invariance principle is not applicable in this case since the
closed-loop system is a nonautonomous system of differential equations. In this paper, it is
shown that the quasi-invariance principle for nonautonomous systems of differential equations
is much convenient for the asymptotic stability analysis of the closed-loop system. Firstly,
we construct an unbounded state feedback controller such as proportional-derivative term plus
feedforward. As a result, the global uniform asymptotic stability property of the origin of
the closed-loop system has been proved. Secondly, we find that, if the damping forces of the
robot are large enough, then the saturated position output feedback controller solves the global
trajectory tracking control problem without velocity measurements. The effectiveness of the
proposed controllers has been verified through simulation tests. Namely, a comparative analysis
of the bounded controller obtained and the well-known “PD+” like control scheme is carried
out. It is shown that the approach proposed in this paper saves energy for control inputs.
Besides, a comparative analysis of the bounded controller and its analogue constructed earlier
in a cylindrical phase space is carried out. It is shown that the controller provides lower values
for the root mean square error of the position and velocity of the closed-loop system.
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