We have removed the fear factor from self-driving cars …

… by creating a truly trustworthy driverless vehicle


MotionLab, LLC, CEO: Yutaka Kanayama, Ph.D.
YouTube: https://www.youtube.com/user/motionlabLLC/videos
Science Robot, Math Mind: Mac motion simulator at App Store,

August 2018

In January of this year, a self-driving car slammed into a fire truck on a freeway in Los Angeles. In March, a pedestrian was killed by a self-driving car in Arizona, and another self-driving car hit a lane divider in Northern California and burst into flames, killing the driver. These tragic accidents have put the self-driving car industry on notice: it must produce cars that are safer. But there are actually two goals that the industry must reach:

  • The first goal is to build safe, robust, and accident-free driverless cars.
  • The second goal is to earn trust from people.

These two goals are related, but the first one is purely technical and the second one has to do with people’s perceptions of self-driving cars. Recent polls tell the story:

  • Reuters reported that an AAA survey in 2018 found that 63% of American drivers said they would be afraid to ride in a self-driving car.
  • According to an Axios/Survey Monkey poll, 64% of Americans are fearful of riding in a driverless car.
  • The Bay Area Council has found that a 2018 survey of 1,000 registered voters in the nine-county San Francisco Bay Area showed 46 percent of respondents say they would ride in a self-driving car, down from 52 percent in 2017.

In short, more than half of drivers are not at ease riding in the current driverless cars. They’re not even at ease with having them on the road! The industry’s record of million-mile accident-free autonomous-driving experiences doesn’t make up for the publicity that stems from gruesome accidents. People just don’t trust driverless cars.

Human drivers do not usually frighten people because people, in general, trust drivers’ skills and their goodwill toward others. On the other hand, people know nothing about driverless cars’ algorithms. People regard a driverless car as a black box; they never trust a black box, especially in light of widely publicized accidents.

MotionLab has made substantial progress in eliminating the fear factor from driverless cars. A deductive approach and the groundbreaking theories did it in the driverless-car community for the first time.

Driverless cars must earn trust through their motions

A driverless car may appear to have no useful resources that might earn people’s trust; for instance, it does not speak. A driverless car’s only output is its motion, the sole interface between human and machine. Thus, a car’s motion is the only resource it possesses. If people are to trust a car, the car must create motions in a way that the motion itself earns trust. But is it possible for a driverless car to create motions that people will trust? Let’s look at how drivers learn to create trustworthy motions.

How do people learn to drive cars?

While driving a car, a driver executes the following two independent tasks, connected through a motion-specific interface:

  • The Decision-Making Task, which includes having the knowledge to evaluate the present situation, understanding traffic rules, recognizing traffic signals, recognizing and understanding the car’s surroundings with other cars, deciding how to turn at an intersection, and creating a motion specification, which is sent to the motion-creation task. 
  • The Motion-Creation Task, which receives the motion specification from the Decision-Making Task and executes it by maneuvering the steering wheel to control the path curvature κ and the gas pedal/brake to control the velocity v. (However, the driver may not be consciously aware of this division with the interface, motion specification.)

A 16-year-old boy who obtains a learner’s permit in California has few driving skills, especially when it comes to the second task. No one provides him with mathematical equations or a user manual about how to turn the wheel in a given situation. He can only watch what experienced drivers do in various situations. He cannot seamlessly translate what he recognizes into vehicle movement; his driving is, at first, less safe and less gentle. For him, there exists a steep learning curve before he masters the skill. Thus, we conclude that:

  • The motion-creation problem is neither easy nor trivial for people.
  • Likewise, the problem is neither easy nor trivial for driverless cars as well. We must treat the problem as an essential, independent, and self-contained one in building a driverless vehicle. So far, this has not been fully accomplished.

Now, there is good news! MotionLab has invented groundbreaking algorithms to mechanize the motion-creation skills, as shown in the following four steps, Step 1 to Step 4, which result in Benefit 1 to Benefit 4.

[Step 1] Dividing the Entire System into Decision-Making and Motion-Creation Subsystems
— divide-and-conquer approach —

MotionLab has built the autonomous vehicle Swan and the Science Robot simulator app using the following divided architecture:

  • The Decision-Making Subsystem that executes the Decision-Making Task
  • The Motion-Creation Subsystem that executes the Motion-Creation Task

The following diagram shows the correspondence between the human driver’s tasks and the divided subsystems in a driverless car:

The driverless-car industry has to solve two problems: the decision-making problem and the motion-creation problem. The first problem is related to sensors/AI/big-data/others and is much more complicated than the second one, but it still is far from trivial, as this entire website presents. MotionLab has spent the past several decades working on the motion-creation problem as a stand-alone, full-fledged, self-contained problem. This divide-and-conquer approach has produced numerous invaluable benefits and advantages.

[Step 2] Inventing Atomic Motions

MotionLab invented a set of motion-creation algorithms, which we call Atomic Motions, to embody the Motion-Creation Subsystem. We categorize all of the Atomic Motions (AMs) in the following five types. (Click here to read more about Atomic Motions)

  1. Direction-Tracking AMs: the car tracks a direction ‘α‘ with a negative feedback rule.
  2. Line-Tracking AMs: the car tracks an oriented line ‘L‘ with a negative feedback rule.
  3. Circle-Tracking AMs: the car tracks an oriented circle ‘C‘ with a negative feedback rule.
  4. Curvature-Defined AMs: The car creates a motion using a curvature function κ = κ(s), where s is arc length, 0 ≤ sS, and S a positive total arc length.
  5. Park AMs: the car moves forward or backward from the start frame ((0, 0), 0) to a target frame ((x, y), θ).

Thus, the interface from the Decision-Making Subsystem to the Motion-Creation Subsystem is the set of geometric objects. Each Atomic Motion creates vehicle motion (v, κ), given a geometrical object as input, and hence, each Atomic Motion is a converter from a geometrical object to vehicle motion; therefore, it is vehicle-hardware independent. Each Atomic-Motion algorithm executes mainly geometrical computations.

For instance, while a driverless car drives in a lane on a highway, the Decision-Making Subsystem senses the near-front part of the lane and makes a decision whether the part is linear or curved:

  • If the Decision-Making Subsystem makes a decision that the part is linear, the Subsystem sends the decision to the Motion-Creation Subsystem with the best estimate of an oriented line L = ((x, y), θ) and a smoothness σ.
  • If the Decision-Making Subsystem makes a decision that the part is curved, the Subsystem sends the decision to the Motion-Creation Subsystem with the best estimate of an oriented circle C = ((x, y), r) and a smoothness σ.

When the situation changes, only the directed line/circle data changes and the car quickly responds to the new input.

A sample motion “Hug wall” shown below mainly uses Line-Tracking Atomic Motions. At each instance, Swan robot’s sonars dynamically extract a linear feature of the present left-side wall, and the vehicle computes an oriented line to be tracked.

Here is a sonar-based, custom made autonomous vehicle Swan.

The Swan robot hugs a wall
with a left handed rule.

Notice the vehicle’s high fidelity motion.

Here is another example of exact motions, Parallel Parking.

Swan’s sonars report
the geometrical situations to the car,
which produces
backward and forward Park Atomic Motions
to create this “Parallel Parking” motion.

Notice that this high-fidelity motion is
responding to the geometrical situations.

This exact movement is reproducible.

Benefit 1: Outstanding Motion Precision and Reliability
Atomic-Motion algorithms create precise, safe, gentle, and reliable motions, which surpass the ones created by human drivers because humans’ driving skills cannot match geometrical equations. This Benefit 1 contributes driverless cars to earn people’s trust.

Benefit 2: Quick Computation Produces High-Fidelity Movement
Atomic Motions execute their algorithms quickly because they consist only of geometrical equations. Therefore, the fast computation makes a car responding against any surroundings with high-fidelity movementsThis Benefit 2 contributes driverless cars to earn people’s trust.
          Here is an example of such a high-fidelity movement:

The Swan robot hugs a “can formation.”
Line-Tracking Atomic Motions execute these successive obstacle-avoiding motions. Dynamic changes of obstacles are translated into dynamic changes of target lines.

Therefore, Swan responds to this complex object with a super high-fidelity motion.

The Decision-Making Subsystem may adopt AI algorithms, such as deep learning. However, the Motion-Creation Subsystem needs not and should not include such costly computations with an expensive computer system; we already have optimized and standardized exact low-cost Atomic-Motion geometrical computations. When such computationally costly AI algorithms are removed from the Motion-Creation Subsystem, a vehicle can respond to input quickly, enabling high-fidelity movement, as shown in the above demonstration.

[Step 3] Selecting the Best-Fit Atomic Motion
— Hypothesis K2 —

Driverless cars will eventually share common spaces with people; for instance, in garages, in the parking lot of a grocery store, at gas stations, and so forth. In these situations, people cautiously examine how a car responds to nearby static objects and humans in motion. A car has to find out a best-fit Atomic Motion to deal with a given situation appropriately. Each Atomic-Motion type possesses a unique character; no two types of Atomic Motions are interchangeable. This observation led us to the following hypothesis (Click here to read more about Characterizing Atomic Motions):

Hypothesis K2:
“One and only one Atomic Motion exists that accurately responds to a given purpose in a given situation.”

In other words, for any purpose and in any situation, we can find an Atomic Motion that accurately responds. Furthermore, there exists no situation where two Atomic Motions respond equally well. To date, we have seen no counterexample of this. When we select the sole appropriate Atomic Motion, the following happens:

Benefit 3: Natural Response as “Clear Box”
When a correct Atomic Motion is selected, the motion looks natural. The people precisely recognize the relationship between the input geometrical element and the created motion; they also immediately and intuitively understand the motion’s intention and anticipate what the car will do next. Thus, people no longer regard the car’s algorithm as a mysterious black box. This Benefit 3 contributes driverless cars earn people’s trust.

[Step 4] Optimizing Responsiveness in Tracking-Type Atomic Motions

There are three tracking-type Atomic Motions:

  1. Direction-Tracking Atomic Motions
  2. Line-Tracking Atomic Motions
  3. Circle-Tracking Atomic Motions

Each of these works under a feedback control rule in a critical-damping condition, demonstrating exponential convergence to a given target (direction, line, or circle). These Atomic Motions have one input parameter σ, which we call smoothness:

  • A smaller smoothness σ makes the convergence sharper and the transition part smaller.
  • A larger smoothness σ makes the convergence less sharp and the transition part larger.

If the smoothness σ is too small, the car’s too-quick response may frighten people; if the smoothness σ is too large, the car’s too-slow response may irritate people. Selecting an optimal smoothness σ in a given situation is essential to earn trust from people; the Swan robot handles that problem correctly, as many of its video demonstrations prove. For detailed discussions, Click here to read more about Responsiveness of Tracking-Type Atomic Motions.

Benefit 4: Optimal Responsiveness Earns People’s Trust
A car with optimal feedback-control responsiveness earns people’s trust from people. They regard the car as friendly.

Now, All of Benefits 1 – 4 Remove the Fear Factors
from Driverless Vehicles.

In conclusion, the combined Benefits 1, 2, 3, and 4 produce a friendly vehicle and earn people’s trust in a driverless car, as the following video demonstrates.

The Swan robot faithfully responds
to the object’s envelope
with an optimal smoothness σ here.
Andrew Harding intuitively understands
Swan’s intention and anticipates
what it will do next.

The Swan’s algorithm
is not a black box anymore;
Andrew comes to trust the Swan vehicle.
The Swan is now his friend!

Benefits for Carmakers

The divide-and-conquer approach and the invention of Atomic Motions have generated invaluable benefits and advantages. Specifically, Benefits 1, 2, 3, and 4 benefit car users. In addition to these benefits, the following Benefits 5, 6, 7, and 8 significantly change and improve car makers’ research and development plans:

Benefit 5: Optimizing and Standardizing Motion-Creation Subsystem
With Atomic Motions, MotionLab’s Motion-Creation Subsystem is optimized and standardized. Therefore, a firm can use and maintain only one copy of the Subsystem for all of its driverless cars built by the firm.

Benefit 6: Finalized Vehicle-Motion Creation Skills Ready to Use
A novice driver requires hundreds of behind-wheel learning to master motion-creation skills. However, our Standard Motion-Creation Subsystem is already a final product, which does not require any more learning or training. The subsystem is just a finite set of object-oriented classes.

Benefit 7: Reducing Hardware Costs
The removal of the use of AI in the Motion-Creation Subsystem significantly reduces the overall computational cost and hardware cost of a driverless car.

Each Atomic Motion requires only a geometric data input delivered from the Decision-Making Subsystem. Sensors in the Subsystem may obtain millions of bytes in a millisecond and the Subsystem may hold big data, but the critical geometrical data needed for the Motion-Creation Subsystem is only a couple of numbers per motion-control sampling cycle. This undemanding output requirement makes the Decision-Making Subsystem simpler and better organized:
Benefit 8: Motion-Creation Subsystem Improves and Better-Organizes Decision-Making Subsystem
Even though the Motion-Creation Subsystem (MCS) is a smaller software system compared with the Decision-Making Subsystem (DCS), the optimized and standard MCS functions as a stable, fixed-point anchor in the entire driverless-car algorithms; MCS gives significant influences in the functionality and system architecture of DCS.

Motion Abstractions

MotionLab is interested in discovering vehicle-motion abstractions rather than individual car motions in a particular car; the latter approaches may not produce any useful general rules in vehicle-motion science.

Notice that the set of Atomic Motions is already the first sample of motion abstraction; it applies to every vehicle that has input from any sensors. Besides Atomic Motions, MotionLab has discovered five more Motion Abstractions, as Motion Abstractions presents.

Symmetric Geometry
— from inductive to deductive approaches —

In classical sciences, such as physics, researchers have made advancements through both inductive and deductive approaches. Albert Einstein surprised colleagues by publishing several groundbreaking articles, including the theories of relativity with the famous hypotheses from 1900 to 1910. Physics has thus accomplished revolutionary advancements through both approaches.

On the other hand, in the driverless-car field, inductive approaches have dominated. Grand Challenges held by DARPA in 2004, 2005, and 2007 inspired us with the current standard testing method of cruising cars in deserts, highways, and streets. These inductive approaches have been successful in accumulating substantial experimental data and finding general rules.

However, driverless science is a vast, unexplored territory, and using only the inductive approaches may reveal only limited aspects of the area. We should and can build driverless cars with the solid support of deductive approaches as well. Every industry must possess a mathematical foundation, but the driverless-car sector has had none to date.

Some 50 years ago, robotics was said to be the science for “controlling time and space.” As to the “controlling time” part, the driverless community is well prepared with modern control theories. However, as to the “controlling space” part, we have no mathematical foundation, to the best of our knowledge. MotionLab contributes to driverless-car science in this respect.

As we worked on the Swan robot in the 1990’s, it became apparent that we needed a new mathematical vocabulary to describe and solve vehicle-motion-related geometrical problems. This realization led to the formulation of a groundbreaking mathematical theory, which we call Symmetric Geometry. This Geometry is the first attempt to contribute to the rock-solid mathematical foundation of the driverless-car industry. Without a doubt, Symmetric Geometry will hold its value over time. (Click here to read more about Symmetric Geometry)

An Essential Standard for Driverless Cars

MotionLab proposes that the novel concepts, theories, and algorithms described in this website should be an essential standard for every driverless car.