  In fields such as mining, search and rescue, and archaeological exploration,
ensuring real-time, collision-free navigation of robots in confined, cluttered
environments is imperative. Despite the value of established path planning
algorithms, they often face challenges in convergence rates and handling
dynamic infeasibilities. Alternative techniques like collision cones struggle
to accurately represent complex obstacle geometries. This paper introduces a
novel category of control barrier functions, known as Polygonal Cone Control
Barrier Function (PolyC2BF), which addresses overestimation and computational
complexity issues. The proposed PolyC2BF, formulated as a Quadratic Programming
(QP) problem, proves effective in facilitating collision-free movement of
multiple robots in complex environments. The efficacy of this approach is
further demonstrated through PyBullet simulations on quadruped (unicycle
model), and crazyflie 2.1 (quadrotor model) in cluttered environments.
