The application area of mobile robots is large and still growing, with
applications in making life easier for humans or in doing work that
otherwise would be dangerous or impossible to do due to hazardous or
unreachable environments. Most mobile robots, as is also the case of
most mechanical systems, are nonholonomic. Nonholonomic systems are
typically completely controllable but instantaneously they cannot move
in certain directions. These systems cannot move in certain directions
since at a certain time or state there are constraints imposed on the
motion. Model Predictive Control (MPC) is an optimization-based
control technique that has received an increasing research interest and
has been widely applied in industry. The main idea of the MPC technique
is to construct a feedback law by solving on-line a sequence of
open-loop optimal control problems, each of these problems using the
currently measured state of the plant as its initial state. Similarly to
optimal control, MPC has an inherent ability to deal naturally with
constraints both on the inputs and on the state. Since the controls are
obtained by optimizing some criterion, the method possesses some
desirable performance properties. In this seminar we discuss the use
of MPC to address the problem of path-following of nonholonomic systems.
We argue that MPC can solve this problem in a effective and relatively
easy way, and has several advantages relative to alternative approaches.
We address the pathfollowing problem by converting it into a
trajectory-tracking problem and determine the speed profile at which the
path is followed inside the optimization problems solved in the MPC
algorithm. We discuss also a control scheme for a set of vehicles
moving in a formation. There are two intrinsically different control
problems: one is the trajectory control problem, to devise a trajectory,
and corresponding actuator signals, for the formation as a whole; and
the other is to maintain the formation, the change of the actuator
signals in each vehicle to compensate for small changes around a nominal
trajectory and maintain the relative position between vehicles. So the
control methodology is a two-layer control scheme where each layer is
based on MPC. |