Optimal Controllers for an Autonomous Buggy

24.695 Modern Control Theory (Fall 2022)

Objective: As a student in 24.695, CMU’s Control Theory class, I was assigned the challenge of creating an efficient controller and estimator for a small self-driving vehicle. Given the projected expansion of the driverless car industry to reach 93 billion by 2028, this project is geared towards addressing that growth. For this project, we drew inspiration from CMU’s yearly buggy competition for our track design and developed an optimal controller for the car.

Solution:
To approximate the motion of the car, a simple bicycle model was used to define system dynamics. The car is modeled as a two wheeled vehicle with two degrees of freedom described by its longitudinal and lateral dynamics. As such, I designed a two-part controller that generates control commands including desired steering angle δ and longitudinal force f. Given a desired trajectory of waypoints, I implemented a:

  1. PID Controller
  2. State Feedback Controller
  3. LQR Controller
  4. MPC Controller

To optimize the performance of the PID controller, I tuned the associated proportional, derivative, and integral gains. For the static LQR controller, I discretized the continuous error dynamics of the nonlinear system using a zero order hold, and then designed an infinite horizon LQR controller for the system. Similarly, to implement the MPC, I implemented an iterative finite horizon LQR for a tunable horizon size N in the future. Ultimately, the controller was able to get the buggy to accelerate on the straight portions of the track, while slowing accordingly for turns. In the event that localization information is missing from GPS, autonomous cars often use CV/LIDAR based methods for obstacle avoidance. In an effort to incorporate this into our model, I implemented EKF SLAM, a sensor fusion method used to augment our position estimate with local measurements.

Taking advantage range and bearing measurements to the next waypoint, the buggy was able to maintain a stable estimate of position and heading over the entire track.

Results: To assess the performance of our simulation, we tested the model on a track modeled after CMU’s buggy course. Driving simulations were then performed using Webots software. The model was able to complete the track in under 120 seconds and had an average deviation of less than 3 meters from the optimal tracked path. This performance was substantially better than the real-world buggy raced every year at CMU. By the end of the course, each controller design was able to clear desired performance evaluations.

Applied Skills: Python, Webots, Extended Kalman Filter SLAM, MPC, LQR, State Feedback, PID