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Introduction
This is the final result, two classic path tracking controllers, Pure Pursuit and Stanley, which make the car follow the path through lanes and turns with an error of just tens of centimeters. Both become the benchmarks for MPC later. Let's get started. Hello, welcome to episode three of the MPC Path Tracking series on autonomous vehicles. Before building MPC, good research always has a benchmark. We use two of the most popular geometric controllers. Pure Pursuit, which chases a point ahead, and Stanley, which was used by the winning car in the 2005 DARPA Grand Challenge.
Step 1: Pure Pursuit
Create a benchmark.py file. Speed is controlled by a simple proportional controller. Pure Pursuit selects a point on the path at a distance ahead of the car. Then it calculates the circular arc that connects the rear axle to that point. The steering angle is calculated as the inverse tangent of two L-sinus alphas divided by look ahead, with alpha being the angle between the car's direction and the target point. Look ahead is made adaptive, 3 meters plus half the speed, because at high speeds, the car must look further ahead.
Step 2: Stanley
Stanley works on the front axle. The steering angle consists of two parts, minus the heading error, so the car aligns with the path, and minus the inverse tangent of the lateral error divided by speed, so the car returns to the path. Dividing by speed makes the correction gentle at high speeds and firm at low speeds.
Step 3: Test path switching & turn $
Create a test_underscore_benchmark_dot_py file and run it at 10 meters per second. On lane changes, Pure Pursuit has a lateral RMS error of 0.084 meters, and Stanley are much smaller, 0.024 meters. On the S curve, Pure Pursuit is 0.101 meters and Stanley is 0.084 meters. But Stanley pays for its accuracy with more frequent steering changes, 0.26 degrees per step compared to 0.18 for Pure Pursuit. Let's look at the graphs.
Step 4: Path & lateral error
During lane change, Pure Pursuit cuts the corner because it chases the point ahead, while Stanley is more compact. The lateral error graph on the S curve shows both deviating the furthest exactly at the part of the path where the curvature changes, because both only react to the current error, without looking ahead at the upcoming curve. This weakness will be addressed by MPC.
Done!
Done. We have already built Pure Pursuit with adaptive look ahead and Stanley. Then compared them on two paths. In the next episode, we will formulate MPC, model linearization, prediction horizon, cost function, and steering constraints. Currently working on a thesis, dissertation, or research in the field of autonomous vehicles and control systems? Cerdas Inovasi Digital helps implement vehicle control systems, from bicycle model, reference path, Pure Pursuit and Stanley, up to model predictive control with CVX-Py, as well as opening Python programming courses for electrical and mechatronic engineering. Want to master the entire series, from vehicle models to complex circuit tests with various speeds? All six episodes, complete with step-by-step PDF guides and source code, are available to premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or pay once Rp999.000 for lifetime access. Want just one class? Buy individual classes with lifetime access. Subscribe now at the premium page cerdasinovasidigital.com. Contact us via WhatsApp, or visit cerdasinovasidigital.com. Thank you for watching, see you in the next episode.
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Cerdas Inovasi Digital Team
Software developers, BIM & 3D engineers, and AI practitioners
53 video classes1,283 episodes
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