Endpoint interpolation: The curve connects $\vp_0$ and $\vp_n$, i.e., $\vp(0) = \vp_0$ and $\vp(1) = \vp_n$
$C^n$ smoothness
Convex hull property: The curve lies inside the convex hull of their control points, i.e., $\vp(t) \in ConvexHull\{\vp_0,\ldots,\vp_n\}\ \forall t\in[0, 1]$
Let $q_1,\ldots,q_K$ be a set of configurations on the state space $\mathcal Q$. The Voronoi region is defined as
$$
R_k = \{ q \in \mathcal Q\mid d(q, R_k) \leq d(q, R_j), \text{ for all } j \neq k\}
$$
Collision Avoidance Via Buffered Voronoi Cells (BVC)
Sense neighbor robots' position
Compute Voronoi regions (safe polyhedra per robot)
Shrink ("buffer") regions to account for robot size (still polyhedra)
Trajectory optimization / control with constraint to stay within safe region for some time