Formation control is one of the salient features of multi-agent robotics. The main
goal of this field is to develop distributed control methods for interconnected multi-robot systems so that robots will move with respect to each other in order to keep a
formation throughout their joint mission. Numerous advantages and vast engineering
applications have drawn a great deal of attention to the research in this field.
Dynamic game theory is a powerful method to study dynamic interactions among
intelligent, rational, and self-interested agents. Differential game is among the most
important sub-classes of dynamic games, because many important problems in engineering
can be modeled as differential games.
The underlying goal of this research is to develop a reliable formation control
algorithm for multi-robot systems based on differential games. The main idea is to benefit from powerful machinery provided by dynamic games, and design an improved
formation control scheme with careful attention to practical control design requirements,
namely state feedback, and computation costs associated to implementation.
In this work, results from algebraic graph theory is used to develop a quasi-static optimal
control for heterogeneous leader{follower formation problem. The simulations
are provided to study capabilities as well as limitations associated to this approach.
Based on the obtained results, a finite horizon open-loop Nash differential game is
developed as adaptation of differential games methodology to formation control problems
in multi-robot systems. The practical control design requirements dictate state-feedback;
therefore, proposed controller is complimented by adding receding horizon
approach to its algorithm. It leads to a closed loop state-feedback formation control.
The simulation results are presented to show the effectiveness of proposed control
scheme.