IEEE Robotics & Automation Magazine - September 2023 - 46

while ensuring the robot's stability. The efficiency of both
methods are investigated through full-scale experiments using
different ranges of speeds as well as different types of ground
and trajectory shapes.
MOBILE ROBOT PATH TRACKING
ASSUMPTION AND KINEMATIC DESCRIPTION
The considered modeling is a bicycle representation of the
Ackermann-type mobile robot, where the control point is chosen
as the middle of the rear axle, and where only the front
axle is a steering axle. The extended kinematic model of the
robot (i.e., including sideslip angles) can then be defined in
Figure 1. As can be seen in the figure, the robot is viewed as a
bicycle model moving on a plane ground. Based on this
assumption, the control variables are the front Ackermann
angle Fd and the longitudinal velocity at the rear axle v. As
the objective of this article is to achieve accurate path tracking,
the motion of the robot is described with respect to the
followed trajectory (D). As a result, state variable X is composed
of curvilinear abscissas s (the distance achieved along
the trajectory), lateral error y, and angular deviation .iu
Because the article addresses off-road mobile robotic
control at relatively high speeds, the classical rolling without
sliding assumption cannot be satisfied. As a consequence, the
proposed model accounts for lateral perturbations due to sliding,
thanks to two sideslip angles, Fb and
bR , for the front and
rear axles, respectively. As detailed in [13], these two variables
may be estimated online using a nonlinear observer, which is
not detailed in this article. In the following section, these two
variables are assumed to be known.
CONTROL LAW EXPRESSION FOR
TRAJECTORY CONTROL
Based on this kinematic model, a predictive controller of the
front steering can be inferred [7], which regulates the lateral
error and angular deviation in the presence of sliding. This

IEEE Robotics & Automation Magazine - September 2023

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