Distributed and Differentiable Vector Field Control within a Curved Virtual Tube for a Robotic Swarm under Field-of-View Constraints

To guide a robotic swarm in a cluttered environment, a curved virtual tube is proposed in our previous work. In this paper, the swarm controller design is generalized to the condition that all robots have field-of-view (FOV) constraints. Two distributed vector field controllers are proposed for different objectives. One controller focuses on the robots' safety in theory, while the other focuses on the feasibility in real practice at the cost of sacrificing safety slightly. Different from existing results, no centralized planning or switching mechanism is needed as robots are controlled to move forward within the curved virtual tube. To guarantee that these two controllers are always twice differentiable, we model the curved virtual tube in the Frenet-Serret frame using appropriate mathematical descriptions. Finally, the effectiveness of the proposed method is validated by numerical simulations and real experiments. We release our implementation as an open-source package for the community.