Fuzzy-Logic Controllers for Autonomous Parking

School Rose-Hulman

Level Undergraduate

Method Mamdani fuzzy inference

Stack MATLAB Fuzzy Toolbox · Simulink

The idea

Fuzzy control is the opposite of learning a controller from data. Instead you write down the rules a human driver follows in words, and the controller interpolates smoothly between them. Rather than a hard threshold, the car is partly "too far left" and partly "centered" at the same time, and the rules blend accordingly.

The vehicle model has 3 degrees of freedom, the center of the rear axle (x_B, y_B) and the heading angle psi, and the controller output is the steering angle beta.

Backing into a space

For the back-parking case there are three input membership functions, for x_B, y_B and psi, and one output membership function for beta. The controller is formulated with 27 Mamdani rules.

Geometry of the back parking problem — The back-parking geometry: the car's rear axle, heading, and the target space.

Fuzzy inference system with three inputs and 27 rules — The inference system: 3 inputs, 1 output, 27 rules.

The controller is robust enough to park from a range of starting positions and headings, including the double-diamond case where the car has to swing out before it can come back in.

Back parking from a start position below the space — Starting below the space and backing straight in.

Back parking from an offset start on the left — Offset to the left, correcting into the space.

Back parking from an offset start on the right — The double-diamond case from the right, swinging out and back in.

Back parking from a start position far to the left and close to the obstacle — A hard start: far left and tight against the obstacle.

Parallel parking

For the parallel-parking case there are four input membership functions, for x_B, y_B, x_a and psi, and one output membership function for beta, where x_a is the front-axle displacement in the x-direction. The extra input matters because parallel parking is a tighter maneuver: the controller has to track the front of the car as well as the back to avoid clipping the vehicle ahead. This controller is formulated with 43 Mamdani rules.

Fuzzy inference system with four inputs and 43 rules — The inference system: 4 inputs, 1 output, 43 rules.

Parallel parking trajectory from a start below and to the left — Sweeping up into the space from below and to the left.

Parallel parking trajectory from a farther start — The same maneuver from farther out.

Parallel parking trajectory with a deep approach — A deeper approach, curling around into the slot.

Parallel parking trajectory from a start alongside the left obstacle — Starting alongside the left-hand car and pulling in.

Fuzzy Logic Mamdani Membership Functions Autonomous Parking MATLAB Simulink