Controllability analysis of a pair of 3D Dubins vehicles in formation

• The controllability analysis of two 3D Dubins vehicles constrained to maintain constant distance is proposed.
• Necessary and sufficient conditions for the existence of a limited control to steer the system between any two configurations are provided.
• The control laws that verify distance constraints are also furnished.
• The results are relevant for aerial or underwater vehicles that are e.g. physically constrained to a payload to be deployed.

In this paper we consider the controllability problem for a system consisting of a pair of Dubins vehicles moving in a 3D space (i.e. pair of 3D-Dubins vehicles) while maintaining constant distance. Necessary and sufficient conditions for the existence of a limited control effort to steer the system between any two configurations are provided. The proposed controllability analysis and the developed motion planning algorithm are a step toward the solution of planning problems for example in case the robots are physically constrained to a payload to be deployed. Moreover, results obtained in this paper are relevant in order to solve formation control problems for multiple robots as aerial or underwater vehicles, which move in 3D spaces. Simulation results highlight the sufficiency of the obtained conditions showing that even from critical configurations an admissible control can be determined.