Creating New Driving Experiences Through Dynamics Emulation
This is the third and final post in a series on key developments in TRI’s Human Interactive Driving technologies.
In a previous blog post, we introduced the Global Research Innovation Platform, or GRIP — a research vehicle with front steering, rear steering, independent electric motors, and independent brakes on each tire. In this post, we will explore how TRI is using GRIP to research a wide array of new driving experiences made possible by something we call dynamics emulation. With dynamics emulation, we are able to change how the driver experiences the car fundamentally — switching between scenarios as varied as driving on ice to driving a bus. As with all our research, dynamics emulation is an important research tool to help us make driving safer and more enjoyable.
Dynamics Emulation: Introduction
Essentially, dynamics emulation is using a vehicle with extra control inputs, like GRIP, to replicate the motion of a different vehicle. You might think this is like a simulator, but GRIP’s dynamics emulation capabilities go far beyond traditional driving simulators’ capabilities. With GRIP, a driver feels exactly the same forces as the emulated vehicle. The emulated vehicle can be a sports car with a quick steering response, a bus that accelerates slowly and turns awkwardly, or either one of those vehicles driving on ice. A driver has the normal inputs: a steering wheel, accelerator pedal, and brake pedal, but GRIP will move as though it is a totally different car in each scenario.
GRIP achieves this through its extra control inputs that include rear steering and independent motors. The velocity of a vehicle can be represented using three states: longitudinal speed, lateral speed, and rotation rate. In most cars, the driver can control only two of the vehicle velocity states — the longitudinal velocity through throttle and brakes and the rotation rate of the car through steering. The driver cannot independently control the lateral velocity of the car without also affecting the rotation rate.
Think about the difficulty of parallel parking because a normal car can’t move sideways. Because GRIP has a large rear steering capability, the lateral velocity can be directly controlled alongside the longitudinal acceleration and rotation rate. The extra actuator allows all velocity states of the vehicle to be tracked, and parallel parking is now much easier.
Some new production cars on the market also have rear steering — however, the maximum rear steering angle is usually between two to five degrees. GRIP’s maximum rear steering angle is over 40 degrees. This extra controllability allows GRIP to replicate the motion of many different vehicles and road conditions.
Dynamics Emulation: How It Works
Dynamics emulation starts with choosing the vehicle the driver wishes to experience; this is called the emulated vehicle model. The emulated model is like a conventional driving simulator or video game; the steering, throttle, and brake commands from the driver are passed into the simulation, and the emulated model calculates the motion and forces that the driver would feel if they were driving that car. Then, GRIP calculates what combination of front steering, rear steering, motor, and brake inputs will replicate the forces of the emulated driver’s position.
The implementation for dynamics emulation is based on Russell and Gerdes (2015). In the simplest case, the emulated model is represented as a single-track bike model.
Defining terms, Fᵧ𝒻 and Fᵧᵣ are the lateral forces of the front and rear tire respectively, Fₓ𝒻 and Fₓᵣ are the longitudinal forces of the front and rear tire, Uᵧ and Uₓ are the lateral and longitudinal velocities, “r” is the rotational velocity, δ is the front steering angle, and finally “a” and “b” are the distances from the center of gravity to the front and rear axles.
To change the behavior of the emulated model, various vehicle parameters can be updated including the friction coefficient of the tires, the understeer or oversteer tendencies of the car (e.g., “a” and “b”), the steering ratio, and many additional parameters. The forces at the center of gravity of the emulated vehicle can be calculated using the equations below. For simplicity, the transform between the vehicle center of gravity location and the position of the driver is temporarily ignored.
The tire forces are calculated using any tire model. We choose the nonlinear Fiala tire model for its accuracy and simplicity. The equations of motion for the emulated vehicle can then be written as:
Now that the forces and motion of the emulated model are known, GRIP must calculate the combination of inputs that will best replicate the emulated forces. Again, in the simplest case, GRIP is modeled as a single-track bike model with rear steering.
Despite GRIP’s fast actuators, it will never perfectly track the emulated forces, hence, a feedback controller is used to keep tracking error to a minimum. The velocity errors are defined as:
Minimizing these errors ensures that the visual experience in GRIP is consistent with what the driver would experience in the emulated vehicle.
The last step in the pipeline is to calculate the tire forces that GRIP must create to replicate the motion of the simulated model, or in other words, to keep the velocity errors as close to zero as possible. To minimize the velocity errors, proportional feedback gains are added to the desired tire forces on GRIP. In order to make the closed loop controller response a linear function with respect to the error states, the desired tire forces are defined to be:
Finally, steering commands are calculated by converting the desired lateral tire forces into steering angles by inverting the Fiala tire model, and motor or brake commands are calculated by converting longitudinal forces into motor and brake torques.
Creating New Driving Experiences
The first application of dynamics emulation we’re exploring is low friction emulation. Here, GRIP makes the driver feel as though they are driving on ice, even if it’s a dry hot summer day in California. The friction coefficient of the tires in the emulated model is reduced, and the dynamics emulation pipeline handles the rest. Again, because of the large steering angles on GRIP, the driver can experience the joy of highly dynamic driving. For example, GRIP can emulate drifting donuts in an icy parking lot, as displayed in the video below:
Drifting is a difficult task that requires practice and teaching, which raises the next advantage of dynamics emulation: task difficulty modulation. If a driver wishes to learn how to drift, they can start practicing in a car that is easy to drift and on road conditions that are conducive to learning. With the simple update of a couple parameters, the dynamics emulation can simulate a more difficult drifting scenario as the student learns. In addition, the dynamics of the vehicle can change based on the vehicle’s position, simulating a sudden loss of traction or driving over an ice patch. Dynamics emulation with task difficulty modulation is one aspect of the Driving Sensei research thrust occurring in TRI.
What’s Next
TRI is constantly searching for new ways to enhance the driving experience. While the current iteration of GRIP has provided an excellent platform for dynamics emulation, it is still limited by the power output and steering angles. For example, GRIP does not have enough power to actually drift, and it does not have enough steering angle to accurately reproduce a spin in the emulated model. Future test beds in development at TRI will address both points.
The Driving Sensei project will also continue to rely on the dynamics emulation pipeline. The future research direction of this project is focused on leveraging the unique capabilities of GRIP’s dynamics emulation system through advanced shared control techniques. Leveraging the expert-level autonomous controllers TRI has created for drifting (Goh et al., 2022) and racing (Dallas et al., 2023), dynamics emulation will eventually grow into an automated driver trainer, allowing customers to become better drivers and have fun in the process.
References
H. E. B. Russell and J. C. Gerdes, “Design of Variable Vehicle Handling Characteristics Using Four-Wheel Steer-by-Wire,” in IEEE Transactions on Control Systems Technology, vol. 24, no. 5, pp. 1529–1540, Sept. 2016, doi: 10.1109/TCST.2015.2498134.
Jonathan YM Goh, Michael Thompson, James Dallas, and Avinash Balachandran. Nonlinear model predictive control for highly transient autonomous drifting. In 15th International Symposium on Advanced Vehicle Control, 2022.18
James Dallas, Michael Thompson, Jonathan Goh, and Avinash Balachandran. A hierarchical adaptive nonlinear model predictive control approach for maximizing tire force usage in autonomous vehicles. Field Robotics, 3(1):222–242, Jan 2023. doi: 10.55417/fr.2023006.
