Michel Basset

This paper addresses the problem of the distributed Formation Control (FC) of holonomic ground robots based on graph-rigidity theory. This framework enables the design of powerful formation control strategies but doesn't implicitly account for system constraints. While this limitation can be addressed using a Model Predictive Controller (MPC), the underlying regulation of inter-robot distances requires the use of non-linear models which are difficult to design and lead to complex non-linear optimization problems. To reduce the control strategy complexity, this paper derives a linearized prediction model of the distance error dynamics, which allows the Distributed MPC (DMPC) controller to be formulated as a Quadratic Programming (QP) optimization problem. As the mapping between the physical inputs and the virtual optimized inputs is non-bijective due to the overdetermined nature of the graph-rigidity framework, the mapping is directly integrated in the optimization problem, enabling both constraint handling and model inversion. A comparative study with a non-linear MPC controller is performed in a high-fidelity Gazebo simulation environment where robots are modelled as mecanum-drive. This demonstrates the performance of the strategy for leader-follower formation tracking and highlights the real-time performance gains over its non-linear counterpart.