The House of Representatives had already passed its take on the bill in early September, so a Senate vote in favor would leave only the matter of reconciling the two bills and sending the result to the President's desk to sign.
Both bills exempt self-driving big rigs in the wake of pressure from labor unions, which are worried both about safety and job security for truckers. There's also no federal requirement for a fallback to human control. Instead, companies are free to make autonomous-only cars so long as they sell less than a certain number of units in a given year. In the finished version of the Senate bill, companies are capped at 15,000 vehicles in the first year, 80,000 in three years, and no cap in the fourth.
If it passes, the measure isn't going to please some people. There are concerns that AV START holds back progress in self-driving trucks, and that driverless car technology isn't sophisticated enough to relinquish control quite so quickly. Nonetheless, there's a lot of pressure to move forward: American legislators want the US to stay on the forefront of self-driving tech, and that means putting it on the road as quickly as possible.