Unacceptably Risky - Part 1 - Safety Report on Cruise's Crash
This is an excerpt from Retrospect’s exclusive report on Cruise’s June 3rd crash, titled “Unacceptably Risky – Part 1: Cruise’s Own Allegations Following the June 3rd Crash Establish a Reasonable Doubt.” You can download the full report here.
Physics 101: Violating Universal Laws
According to Cruise (Cruise LLC, 2022):
“…the Cruise AV predicted that the oncoming vehicle, which was traveling approximately 40 mph in the 25 mph right-turn lane, would turn right and directly into the path of the Cruise AV.”
The following analysis will show that the notion that the Cruise AV was predicting the Prius was going to turn right is completely false, as it demonstrates a gross violation of the understanding of basic physics and core competency in developing autonomous vehicles.
The intersection of Geary Blvd. and Spruce St. is a typical, 90-degree intersection of urban surface streets. It has a tight curb radius of about 5 meters or 15 feet. Most traffic would have to take that turn at about 10 mph. Maybe 15 mph or 16 mph if they were driving aggressively.
The turning radius assuming a max 0.5 g lateral acceleration changes with speed
Cruise repeatedly claims the Prius was traveling approximately 40 mph. The question to the reader is:
How well can a typical passenger car turn a 90-degree corner at 40 mph?
Warning: The reader should not attempt this in their vehicle. No driver can physically turn any passenger car 90 degrees on a tight city corner while traveling at 40 mph. The vehicle will collide into the opposite corner. There is no way such a turn could be made, even if a driver expressly intended to make such a turn.
Typically, normal passenger cars on normal roads would achieve an upper limit around 0.5 g lateral acceleration. Race cars with special tires on special tracks can get up to 1.0 to 2.0 g lateral acceleration with no downforce.
On real roads, one study in China analyzed the cumulative distribution of lateral accelerations. The 99’th percentile was found to be around 0.6 g (about 6 m/s2). The 91’st percentile was around 0.4 g, as shown in the following figure (Xu, 2015).
A study shows 91st and 99th percentiles of lateral acceleration around 0.4 and 0.6 g, respectively.
Considering the corner at Geary and Spruce, if we assume a turning radius for an optimal apex at the corner to be about a 10 m turning radius, then any car traveling at 40 mph would require 3.0 g’s of lateral acceleration to make the turn. Is 3.0 g’s of lateral acceleration feasible?
A lateral acceleration of 3.0 g’s would be impossible. 0.5 g would be more likely, with a 64 m radius.
To provide some perspective, 3.0 g’s is beyond Formula 1 race car capability at 40 mph, with no downforce. For AV developers, physics-based path planning is a core competency. In one paper, written by Uber ATG and UC Berkely, titled “Physically Feasible Vehicle Trajectory Prediction,” they describe setting up the physical limitations of their trajectories as follows (Giraseyx, 2020):
“In addition to evaluating our method and baselines on standard trajectory error metrics, we also evaluate them on other metrics that capture physical realism… we define a set of physical feasibility metrics below:
“Centripetal Acceleration Violation: …a trajectory contains a centripetal acceleration violation if at any given point t, the instantaneous centripetal acceleration is greater than 10 m/s2.” (10 m/s2 is about 1.0 g)
Centripetal Acceleration in their paper is slightly different, but closely associated with lateral acceleration, and again, they limit such acceleration to about 1.0 g based on “physical realism.” The trajectory described in Cruise’s statements would have violated that physical realism limit three times, or 300% error in estimating the physical limitations of an on-coming vehicle.
The previous figure illustrates the turning radius at 3.0 g lateral acceleration and a more realistic 0.5 g lateral acceleration, which is probably the upper 95’th percentile in most driving situations. As the figure shows, there is no way the vehicle could even partially complete a right turn onto Spruce given the realistic maximum lateral acceleration limits.
The likelihood of the Prius making a right turn at 40 mph with 3.0g’s of lateral acceleration is in the hypothetical “0.00001%” category. This is otherwise known as: “Impossible.”
Meanwhile, the likelihood of the Prius traveling more or less straight at 40 mph, illustrated below, within a reasonable limit of 0.5 g’s of lateral acceleration is in the “99.99999%” category. Otherwise known as: Guaranteed certainty.
The chance of the 40 mph Prius going straight is a guaranteed certainty; right turn is impossible
Could the Prius have slowed down to turn? If there was any expectation that the Prius was going to slow down to make a right turn, that presents a number of additional problems. First, on what basis was the Prius indicating it was about to slow down? Second, if we could measure the Prius slowing down, that would require knowing it was decelerating about 2.1 seconds in advance. It would also add about one second of additional time before reaching the point of collision than if it maintained 40 mph. Therefore, the Cruise AV could have either stopped in advance or continued ahead of the Prius if it thought the Prius was going to slow down to turn.
Since Cruise made no statement that the Prius was slowing down or that they predicted the Prius would slow down, no further consideration is given to this hypothetical case. Instead, Cruise has repeatedly stated that the Prius was traveling at about 40 mph and it would turn right immediately in front of the AV. That is the only explanation offered for why the AV did a hard stop.
Rather than present this publicly as a defense of the Cruise AV, this gross error in basic physics should have been the first clue that something was wrong with the Cruise AV’s prediction and path-planning and prompted further internal investigation. Apparently, nobody even understood the implications of stating this publicly.
Or, perhaps Cruise did understand the implications and decided it was better than disclosing an alternative reason for the AV’s hard stop.
Any human or machine driver evaluating a “risk” calculation that determines the following:
…is a driver that needs to be taken off the streets immediately.
Instead of defending themselves, Cruise’s own statement incriminates themselves. The Cruise AV was making safety-critical decisions based on a contradictory understanding of basic physics: the Prius must go straight and cannot turn right. That gives evidence of a gross error in a core competency of AV development. The result of the error was a hard stop in the middle of an intersection causing a high-risk side impact collision in front of a speeding vehicle that injured occupants of both vehicles.
The following figure summarizes all the relevant prediction scenarios that should have been considered, but were ignored. The result is the maximum risk was created by the Cruise AV’s decision to stop in front of the 40 mph Prius.
Apparently, the Cruise AV never evaluated the risk of the Prius traveling straight
Rather than analyze why the Cruise AV thought the Prius would turn right, when such a prediction is in error by over three times the physical threshold, Cruise reveals the presence of a gross error in their public statements. Furthermore, in preparing their statements, their analysis failed to recognize any abnormality in presenting a scenario in which a 40 mph Prius turns right immediately in front of their vehicle.
To read the rest of Retrospect’s exclusive report, download the full copy of “Unacceptably Risky – Part 1: Cruise’s Own Allegations Following the June 3rd Crash Establish a Reasonable Doubt”