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.
Creation of Polygonal Cone
For polygonal obstacles, the cone can be directly constructed using their vertices. These vertices are selected to ensure comprehensive coverage of the entire polygon. The relative position vector ($\prel$) is oriented towards the midpoint of the line connecting these two vertices. Let’s denote the vector that forms the most substantial angle with $\prel$ as $k’$, and the other one as $m’$. To account for the width of the ego vehicle ($w$) \footnote{The width of the ego vehicle can be predetermined (e.g., the diagonal of the vehicle) or dynamically adjusted}, the line joining these two vertices is extended by $\frac{w}{2}$ on both sides, forming vectors $k$ and $m$ (corresponding to vectors $k’$ and $m’$, respectively) as depicted in Fig