The realistic guide to safer Autopilot, with model and back-of-envelope calculation.

TL;DR1: for people new with Autopilot: how to use it safer.
TL;DR2: for Autopilot safety: One argument is that Autopilot gives people false sense of safety, leading people to be less attentive, which may make it less safe than without. Let's see if that stands by check how much less attentive people can be with Autopilot to get the same accident rate.

Intro

One reason Tesla owners are spoiled and never want to go back to non-Tesla car is Autopilot. It is such a great experience to drive with Autopilot. It can make daily commute way more enjoyable, and make long road trip relaxing instead of tiring.

About my usage


I got my Long Range RWD Model 3 May 2018 and have driven it for more than 13k miles. My commute is around 25 miles each day, 90% of them on crowded US-101. Autopilot make it extremely relaxing. All I have to do it drive on the highway, get onto the carpool lane, turn on Autopilot and then relax till the car move it self to the highway exit and slows down, then take over. I use it off highway also, usually following another car(Autopilot doesn't take care of red light or stop sign, so following another car make things easier) until I have to turn.

I drove to Tahoe for skiing several times in the winter. While it does take a tiny bit of effort to plan for supercharging, I prefer Tesla with no hesitation over my ICE SUV for a ski trip, just because of Autopilot. It made road trip much easier. For people not living in the Bay Area, Tahoe is around 4 hour away from the Bay Area, most of the drive is on I-80. After 4 hours of driving, you usually don't want to ski anymore, not to mention you have drive 4 hours back; but with Autopilot, it is just a piece of cake.

Driving to LA is even better:




However, using it wrong, Autopilot can be dangerous. We all remember the tragedy from that Model X owner who crashed and eventually get killed using Autopilot without paying attention. I think Tesla is not doing enough work to educate new Tesla drive on the capability of Autopilot, and only put a "keep your hands on the wheel all the time", which is unrealistic and not even followed by Elon Musk himself.

This is a guide on how to use Autopilot safer AND more relaxing and comfortable.
This is NOT a guide to tell you "pay 100% full attention on the road and keep your hands on the wheel all the time".
This is NOT a guide to tell you how to achieve 100% accident-free drive.

The goal here is to be safer than drive without Autopilot, and enjoy the convenience of it.

This is a theoretical analysis. Use at your own discretion. I am not responsible for any accident you have using Autopilot with or without following this guide.

How

My favorite way to describe how you should think about driving with Autopilot is: you're sitting beside your 13 year old son/daughter(who happened to be a bit slow on learning) who is behind the wheel, and you trust him/her, but you want to be sure as a loving parent.

Using Autopilot safely is all about attention management. Without Autopilot, you need to be 100% attention all the time; with Autopilot, if you manage your attention correctly, you will be safer even with lower average attention level.

For off-highway drive. Don't use it when there are expected to have pedestrians. Otherwise, use Autopilot all you want but pay full attention and be ready to take over anytime, just like you're driving without Autopilot. For off-highway usage, Autopilot can still make it safer and comfortable for you, as it can still keep the car from most unexpected lane departures, but it cannot stop for traffic light or stop sign and may not stop for people or animals.

For highway, the rules:
  1. Keep your eyes on the road as much as you can, but relax: you can look around, reach for a phone charger, drink some water; but please don't leave your eye off the road for more than X seconds. (X can be 10 and defined below). 
  2. Pay extra attention in the following conditions, (cut your X by half):
    1. Unfamiliar road
    2. Autopilot just updated
    3. mild weather conditions
  3. Pay full attention when you're close to these places, (X should be close to 0). If you are following the rule 1, you should be able to detect these upcoming places in time.
    1. Upcoming junction.
    2. Upcoming lane merge around your lane. 
    3. Upcoming exits if your car is around the exit lane.
    4. Upcoming known place where you know Autopilot doesn't work well. 
    5. Bad weather conditions.
    6. Construction site.
    7. Your exit.
  4. Never fall asleep. Stop for a quick nap if you're tired. Tesla is an EV, so you don't need to worry about exhausted air when using the AC. I have a "sleep" setting in my profiles to put the seats down and back, and keep a pair of eye mask in the car. Take a nap whenever you want(but remember to park it safely first). 

Why

TL;DR: when you know the route, average 40X attention off-time is okay to be as safe compare to not using Autopilot; when you don't know the route, 18X attention off-time is acceptable.  Be sure to understand what attention off-time means here before you apply this to your daily driving. 

Disclaimer: I did use backs of 3 envelopes for the calculation; no more envelope is hurt during the process.

Autopilot by itself, if we human always pays full attention, is for sure safer than without, no one doubt that, however, one argument is that Autopilot gives people false sense of safety, leading people to be less attentive, which may make it less safe than without.

Let's see if that stands. We want to know how much attention we can lost when using Autopilot can we still be safer than no attention lost. 

To measure attention, we use a probability of N-seconds attention absence( $P_a$), assuming anything happened within N second can be corrected but not if longer than N second. We will show that the selection of N doesn't really matter.

For human we use the plain symbol and for Autopilot we use the '. 

We want $P'(P_a)< P(P_a')$, we call $k = P_a'/P_a$.

 The ratio k can be considered the upper boundary of the ratio of attention off-time compare to driving without Autopilot. 

The simplest model

A simplest model will be, a random incident(happens with $P_i$) can happen and without intervention(failed intervention: $P_h$), it will become an accident. $P = P_iP_h$. 

For human, $P_h = P_a $ so $P = P_i  P_a$
For when we use Autopilot, assuming the probability of Autopilot failed to handle it $P_p$ , $P_h = P_p P_a'$, so $P' = P_iP_a' P_p$
To make sure $P' < P$, we just need $k = P_a'/P_a < 1/P_p$

OK, so if we assume $P_p = 0.05$, that Autopilot can handle 95% of the time, that means k < 20, aka, as long as we are not more likely to have N-second attention than 20 times of driving without Autopilot, we are safer.

This is a too simple model and $P_p = 0.95$ is picked arbitrarily and not convincing at all.

We need a more detailed model.

A static world and a dynamic world

Talking about driving, we can divide the world into 2 elements:

  1. static incident( $P_s$): for any point in the trip, assuming average traffic condition for that time and location, and everyone else on the road just follow the rules. This can be incident here when the road is curvy and N-sec-loss-attention will result in run into other lane or out of road. $P_s$ can be pretty high since it is extremely likely an accident anywhere when you're driving a thousand-pound metal machine and loss N seconds of attention.
  2. dynamic incident( $P_d$): unpredictable incident, like sudden stopped vehicle, cut-in, a deer on the way. This is very likely way smaller than static one. $P_d << P_s$
now $P = P_s(1 - P_{hs}) + P_d(1 - P_{hd})$
For human, $P_{h?}$ is always $P_a$ so $P = (P_s+P_d)P_a$
For Autopilot, $P_{pd}$ is probably rather high, but $P_{ps}$ can be pretty low, so $P' = P_sP_{hs} + P_dP_{hd}=(P_sP_{ps} + P_dP_{pd})P_a'$

For a safer Autopilot usage: $k = P_a'/P_a < \frac{r+1}{P_{ps}r + P_{pd}}, r = P_s/P_d$

If we assume $r= P_s/P_d = 100, P_{pd} = 0.5, P_{ps}=0.02$, we will have $k < 101/2.5 = 40.4$.

Let's reason about the assumption:
  1. r: If not paying attention, it is 100X more likely to drive off road/into wrong lane than something unexpected like sudden stopped car. This is reasonable in the sense that, it is probably 100X more likely to finish a trip without seeing any dynamic incident than finish a trip blindfolded. One can argue that can be even more, let's assume 1000 and the number k will be 48.9, the different is not that much.
  2. $P_{pd} = 0.5$, for a dynamic incident, 50% chance Autopilot can handle it in time, this is a pretty conservative assumption, and as Autopilot improve and long-tail issues resolved, this is only getting better; $P_{ps}=0.02$, 98% chance Autopilot can handle it. However, this is again an arbitrarily chosen number and we may need better model to reason about it. If that number is 0.05 like before, k will be around 20, which is still pretty high. 
Now we reason about the $P_{ps}$ with better model.

Commute vs Roadtrip

Now let's look at 2 typical driving scenarios:
  • Commute: you go this path everyday and you know where Autopilot works and where not.
  • Roadtrip: not necessarily road trip, but anytime you're not familiar with the route and you don't know if Autopilot will work or not.
So for Commute, for the part where you know Autopilot doesn't work, you should always pay high attention, like when you're driving without Autopilot, for other part, you can use Autopilot very confidently. Let's write the ratio of time you spend on "Autopilot works" part vs "Autopilot doesn't work" part $m$.
Then we have the average attention loss, $P_a' = \overline{P_a'(t)} = \frac{mP_a'' + P_a}{m + 1}; k =\frac{mk'+1}{m+1}$, assuming pay attention of $P_a''$ when Autopilot is working.

Then $P_{hs} = \frac{mP_{pss}P_a''+ P_aP_{psf})}{m + 1}$, where $P_{pss}$ is the probability of Autopilot failed to handle static incident where we know it works, we can safely assume a very low number; and $P_{psf}$ is the probability of Autopilot failed to handle static incident where we know it didn't work, and it should be close to 1. 

For highway, m can be pretty high, assuming 20. 

Assuming $P_{psf} = 1, P_{pss} = 0.02$, going back to equation, we have $k' = P_a''/P_a < 40$. This means, assuming 98% confident that $P_{pss}$ can handle a known working place, exclude the part where we know it doesn't work and pay full attention, we can be 40X less attentive. And the average attention, including the part we pay full attention, is still 38X less (k < 38). 

For Roadtrip, we don't know about whether it works or not, so we should pay more attention, let's assume a way more conservative $P_{ps} = 0.05, P_{pd} =0.5$, meaning 95% confident it can handle a static incident(the average we get from Commute) and 50% confident it can handle a dynamic one, we have k < 18! Pay 2 times more attention than Commute, but still 18X less attention needed than without Autopilot. 

Note, after a software update to Autopilot, you should consider anything Roadtrip(2X attention than a verified software!).

So what does these actual mean?

Extremely rough estimation: for human, we use a number of 1 accident per 100K miles, and translate that to 1 accident per 2000 hours. And assume N-sec is 10-sec(driving 10 second blindly on highway, close to 100% accident). We have a $P_a = 1/2000$, that is average total 18s of absence of attention for absence over 10s, per hour. For the same accident rate, 6 mins of absence attention with autopilot per hour to have the same accident rate.

Use my refer link to get a Tesla and enjoy a safer and way more comfortable drive!  And give you and me both some free Supercharger credit!

Comments

Popular posts from this blog

Tesla Autonomous day, from a AI engineers' perspective

Tesla new Browser capabilities!