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Model Predictive Control for Nonholonomic Vehicles

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.
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