In this paper, we propose a novel framework using formal methods to
synthesize a navigation control strategy for a multi-robot swarm system with
automated formation. The main objective of the problem is to navigate the robot
swarm toward a goal position while passing a series of waypoints. The formation
of the robot swarm should be changed according to the terrain restrictions
around the corresponding waypoint. Also, the motion of the robots should always
satisfy certain runtime safety requirements, such as avoiding collision with
other robots and obstacles. We prescribe the desired waypoints and formation
for the robot swarm using a temporal logic (TL) specification. Then, we
formulate the transition of the waypoints and the formation as a deterministic
finite transition system (DFTS) and synthesize a control strategy subject to
the TL specification. Meanwhile, the runtime safety requirements are encoded
using control barrier functions, and fixed-time control Lyapunov functions
ensure fixed-time convergence. A quadratic program (QP) problem is solved to
refine the DFTS control strategy to generate the control inputs for the robots,
such that both TL specifications and runtime safety requirements are satisfied
simultaneously. This work enlights a novel solution for multi-robot systems
with complicated task specifications. The efficacy of the proposed framework is
validated with a simulation study