[fideloper]

The orbital physics used is always impressive.

I assume some velocity adjustment is done by the drone to intersect with the asteroids? Or are the orbits that precise?

[loa_in_]

They are very precise. Take note of this video, recreating one of the real missions that took place four decades (!) ago. It recreates the orbit in Kerbal Space Program with a mod called Principia that enables N-body simulation using original mission specs and calculations.

https://www.youtube.com/watch?v=l3PCCJZzVvg

[onetwentythree]

The spacecraft will make corrections with its onboard thrusters over the course of the mission.