Directed Formation Control Using Distance and Angle in Local Coordinate Frameworks

The formation control of multiagent systems is widely recognized to be challenged due to ambiguity. Solving this challenge solely by introducing extra control variables may lead to the emergence of additional undesired equilibria. In this work, we mitigate this potential issue by introducing constraints on the angles, in conjunction with distance and angle variables. Specifically, we propose a novel 2-D formation control scheme for acyclic triangulated directed graphs, ensuring strong congruency between the actual and desired formations. By introducing state-dependent time-varying control gains, the proposed scheme avoids the drawback of existing methods that require repetitive adjustment of control parameters based on the desired formation pattern. Moreover, for n nonpoint single-integrator agent models, the maintenance of connectivity and collision avoidance among neighboring agents is effectively addressed through a novel distance transformation. Lastly, the stability and convergence of the system are analyzed theoretically, the simulation study and practical experiments are conducted to validate the effectiveness of the proposed method.