Router.swift

import UIKit

protocol RouterProtocol: Presentable {

    func present(_ module: Presentable?)
    func present(_ module: Presentable?, animated: Bool)

    func push(_ module: Presentable?)
    func push(_ module: Presentable?, transition: UIViewControllerAnimatedTransitioning?)
    func push(_ module: Presentable?, transition: UIViewControllerAnimatedTransitioning?, animated: Bool)
    func push(_ module: Presentable?, transition: UIViewControllerAnimatedTransitioning?, animated: Bool,
              completion: (() -> Void)?)

    func popModule()
    func popModule(transition: UIViewControllerAnimatedTransitioning?)
    func popModule(transition: UIViewControllerAnimatedTransitioning?, animated: Bool)

    func dismissModule()
    func dismissModule(animated: Bool, completion: (() -> Void)?)

    func setRootModule(_ module: Presentable?)
    func setRootModule(_ module: Presentable?, hideBar: Bool)

    func popToRootModule(animated: Bool)
    func popToModule(module: Presentable?, animated: Bool)
}

final class Router: NSObject, RouterProtocol {

    // MARK: - Variables

    private weak var rootController: UINavigationController?
    private var completions: [UIViewController : () -> Void]
    private var transition: UIViewControllerAnimatedTransitioning?

    // MARK: - Presentable

    func toPresent() -> UIViewController? {
        return self.rootController
    }

    // MARK: - RouterProtocol

    func present(_ module: Presentable?) {
        present(module, animated: true)
    }

    func present(_ module: Presentable?, animated: Bool) {
        guard let controller = module?.toPresent() else { return }
        self.rootController?.present(controller, animated: animated, completion: nil)
    }

    func push(_ module: Presentable?) {
        self.push(module, transition: nil)
    }

    func push(_ module: Presentable?, transition: UIViewControllerAnimatedTransitioning?) {
        self.push(module, transition: transition, animated: true)
    }

    func push(_ module: Presentable?, transition: UIViewControllerAnimatedTransitioning?, animated: Bool) {
        self.push(module, transition: transition, animated: animated, completion: nil)
    }

    func push(_ module: Presentable?, transition: UIViewControllerAnimatedTransitioning?, animated: Bool,
              completion: (() -> Void)?) {
        self.transition = transition
        guard let controller = module?.toPresent(),
            (controller is UINavigationController == false)
            else { assertionFailure("Deprecated push UINavigationController."); return }

        if let completion = completion {
            self.completions[controller] = completion
        }
        self.rootController?.pushViewController(controller, animated: animated)
    }

    func popModule() {
        self.popModule(transition: nil)
    }

    func popModule(transition: UIViewControllerAnimatedTransitioning?) {
        self.popModule(transition: transition, animated: true)
    }

    func popModule(transition: UIViewControllerAnimatedTransitioning?, animated: Bool) {
        self.transition = transition
        if let controller = rootController?.popViewController(animated: animated) {
            self.runCompletion(for: controller)
        }
    }

    func popToModule(module: Presentable?, animated: Bool) {
        if let controllers = self.rootController?.viewControllers, let module = module {
            for controller in controllers
            where controller == module as! UIViewController {
                self.rootController?.popToViewController(controller, animated: animated)
            }
        }
    }

    func dismissModule() {
        self.dismissModule(animated: true, completion: nil)
    }

    func dismissModule(animated: Bool, completion: (() -> Void)?) {
        self.rootController?.dismiss(animated: animated, completion: completion)
    }

    func setRootModule(_ module: Presentable?) {
        self.setRootModule(module, hideBar: false)
    }

    func setRootModule(_ module: Presentable?, hideBar: Bool) {
        guard let controller = module?.toPresent() else { return }
        self.rootController?.setViewControllers([controller], animated: false)
        self.rootController?.isNavigationBarHidden = hideBar
    }

    func popToRootModule(animated: Bool) {
        if let controllers = self.rootController?.popToRootViewController(animated: animated) {
            controllers.forEach { controller in
                self.runCompletion(for: controller)
            }
        }
    }

    // MARK: - Private methods

    private func runCompletion(for controller: UIViewController) {
        guard let completion = self.completions[controller] else { return }
        completion()
        completions.removeValue(forKey: controller)
    }

    // MARK: - Init methods

    init(rootController: UINavigationController) {
        self.rootController = rootController
        self.completions = [:]
        super.init()
        self.rootController?.delegate = self
    }
}

// MARK: - Extensions
// MARK: - UINavigationControllerDelegate

extension Router: UINavigationControllerDelegate {

    func navigationController(_ navigationController: UINavigationController,
                              animationControllerFor operation: UINavigationController.Operation,
                              from fromVC: UIViewController,
                              to toVC: UIViewController) -> UIViewControllerAnimatedTransitioning? {
        return self.transition
    }

}

Hello, there's a way to animate setRootModule like a push animation?