Not a direct answer, but may help with: "Any references on this sort of questions?"

Computing the convex hull of the union of two polytopes $P_1 \cup P_2$
is NP-hard:

Tiwary, Hans Raj. "On the hardness of computing intersection, union and Minkowski sum of polytopes." *Discrete & Computational Geometry* 40, no. 3 (2008): 469-479. Author preliminary PDF download.

But the computation is polynomial for special polytopes:

Balas, Egon. "On the convex hull of the union of certain polyhedra." *Operations Research Letters* 7, no. 6 (1988): 279-283. Journal link.

Conforti, Michele, Marco Di Summa, and Yuri Faenza. "Balas formulation for the union of polytopes is optimal." arXiv:1711.00891 (2017).

**Added**.
Specializing to

$\mathbb{R}^3$, there is an algorithm
that constructs the boundary of the union,
which runs in

$O(k^3 + kn \log k \log n)$ expected time,
where

$k$ is the number of polyhedra and

$n$ is the
total number of faces:

Aronov, Boris, Micha Sharir, and Boaz Tagansky. "The union of convex polyhedra in three dimensions." *SIAM Journal on Computing* 26, no. 6 (1997): 1670-1688.
Journal link

^{
Aronov, Sharir, Tagansky.
}

Subsequently there was a specialized extension to $\mathbb{R}^4$:

Aronov, Boris, Alon Efrat, Vladlen Koltun, and Micha Sharir. "On the union of κ-round objects in three and four dimensions." *Discrete & Computational Geometry* 36, no. 4 (2006): 511-526. Journal link.