Model Predictive Control of Robot Swarms

This paper presents a method to design a controller for a swarm of robots based on the principle of model predictive control. The controller for each robot is obtained by minimizing a receding-horizon cost function that involves a prediction of its own motion and the motion of its neighbors. Communication between robots is needed to supply the needed information for each robot to determine its next move so that the control objectives (intercepting fixed targets, tracking moving targets, avoiding collision between robots and between robots and obstacles, group formation) are achieved as a group. Two solutions are presented: (1) for a small group of robots where each robot communicates with every other robot in the group, and (2) for a large group of robots where each robot only communicates with its nearest neighbors. Simulation examples are used to illustrate the controller design method. The objective of the work described here was to derive controllers that produce swarm behavior based on the simplest possible understanding of robot motion and in the simplest possible constraints on that motion. Unlike much of existing work in the literature, we will derive these controllers by employing appropriate cost functions to be minimized in order to produce "classical" dynamic output feedback control laws. For each robot, the control input to be used at the current time step is a function of its past input and output data, and the data received from its neighbors. We intentionally avoid the use of heuristics to derive these controllers, and instead build the heuristics into the cost functions from which the controller gains are derived. For the problem at hand we consider a group of mobile robots deployed over a large area. These robots are semi- autonomous in that they periodically receive general instruction about their mission, but their movement is not dictated moment by moment by a centralized controller. The movement of such a group of robots must be coordinated among themselves. Each robot only uses the knowledge of its current state and the state of its neighbors to determine its next move. Collectively, however, group behavior emerges. As a group they succeed in their mission of mapping, tracking, or intercepting targets. Designing controllers for coordinated robot motion is the focus of this research topic. We will use predictive control theory to design these controllers. Using the principle of predictive control, a robot makes its current move based on a prediction of its own position at some time step in the future in relation to its environment. This concept has been successfully implemented in a single robot system. We now extend this controller design concept to the multiple robot environment, where a prediction of the positions of the neighboring robots is also taken into account to determine the robot's own motion. In this manner the group moves together in a coordinated fashion. The group collectively is capable of avoiding obstacles while carrying out its mission which could be intercepting fixed targets, tracking moving targets, avoiding collision between robots and between robots and obstacles, and group formation.