Distributed Variation Parameter Design for Dynamic Formation Maneuvers With Bearing Constraints

The aim of this study is to investigate the problem of cooperative multi-robot variation parameter design for dynamic formation maneuvers with bearing constraints. Notably, scaling and translation are relatively economical bearing-preserving motions in terms of formation changes. Typically, the variation parameters, i.e., the desired scaling size and translation vector, are designed offline a priori, and it is often challenging to dynamically generate the desired formation in response to a changing ambient environment. This paper proposes an online distributed design method to determine the variation parameters of an entire formation. First, local variation policies are generated by the proposed high-order control barrier functions based on received local excitations from the environment. Subsequently, using the distributed average tracking technique, consensus filters are employed to integrate various local variation policies in a weighted-average manner, which ensures that the bearing is maintained in dynamic formation maneuvers. Finally, numerical simulations and experiments are conducted to demonstrate the effectiveness of the proposed method. <italic>Note to Practitioners</italic>&#x2014;This paper is motivated by the neglect of the research on the automatic co-adjustment of the formation variation parameters in most existing formation control schemes, which rely on fixed and pre-defined desired variation parameters (scaling size and translation vector). To address this limitation, this paper suggests an online distributed design method to determine the variation parameters of an entire formation in dynamic ambient environments. The proposed method consists of three parts: 1) By considering received local excitations from the environment as perturbations to asymptotically stable virtual systems, unconstrained local variation policies are generated. 2) By employing high-order control barrier functions, we solve the bounded magnitude constraints for distributed average tracking (DAT) algorithms and the minimum scale constraint for collision avoidance, leading to the generation of constrained local variation policies. 3) By using DAT algorithms, all robots can cooperatively obtain a uniform variation parameter, which is exactly the weighted average of the constrained local variation policies. This ensures that the bearing is maintained in dynamic formation maneuvers. Therefore, the proposed method can be deployed to multi-robot systems in a distributed manner. Finally, numerical simulations and experiments are conducted to demonstrate the feasibility of the proposed method and its potential in industrial applications.