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Introduction
This is the final result, the MPC-controlled car is speeding through the icy turn while continuously planning ahead 1.2 seconds, as seen from the predicted points of the orange dots in front of the car. The lateral error is only 1 cm, 8 times smaller than Stanley's. Let's get started. Hello, welcome to episode five of the MPC Path Tracking Autonomous Vehicle series. The MPC formulation is ready. Today we'll implement it with the Residing Horizon principle. At each step, solve the optimization for the entire horizon, apply only the first input, then repeat in the next step with the new state. We also create the car's animation.
Step 1: Receding horizon & solver 0SOP
We continue working on the mpc.py file with the call method, so that the MPC object can be called like other control functions. First, create the planned speed profile and reference horizon from the vehicle's position. Then, for each step in the horizon, compute the linear model RK4 at the reference point and fill in the values of A, B, and C. The problem is solved using the OSQP solver with Warm Start, using the previous solution as an initial guess. If the solver fails, we retain the previous input to ensure the car remains safe. Only the first input is returned, and the state prediction is saved for drawing.
Step 2: MPC vs Pure Pursuit vs Stanley
Create the run_underscore mpc.py file. We wrap up the MPC with a function that records the prediction horizon at each step, Run it through the S curve at a speed of 10 meters per second, along with Pure Pursuit and Stanley. Run. MPC solves 144 quadratic programs on average around 10 milliseconds per step, fast enough for real-time. The lateral RMS error of the MPC is only 0.011 meters with a maximum of 3.1 cm, compared to 0.101 meters for Pure Pursuit and 0.084 meters for Stanley.
Step 3: Prediction horizon & animation
Continue with visualization. The car body function draws a 4.5-meter long car body from the rear axle position and direction. We draw the MPC path along with the car body and prediction points every 2.5 seconds, as well as the third steering angle controller graph. Then the animation creates the car animation and its horizon prediction. saved as mpc underscore animation dot gif. Let's take a look at the graph. The orange point in front of each car is the MPC plan, which has curved to follow the turn before the car arrives there. On the steering wheel graph, MPC starts turning the steering wheel earlier than Pure Pursuit and Stanley. This is the advantage of MPC, He sees the upcoming bend, not only the current error.
Done!
Done. We have already implemented MPC with CVXPY and OSQP using the Residing Horizon approach. Comparing it with Pure Pursuit and Stanley, as well as creating images and vehicle animations. In the final episode, we test all three on a winding circuit with various speeds. Working on thesis, thesis, Or are you involved in research in the field of autonomous vehicles and control systems? Cerdas Inovasi Digital helps implement vehicle control systems, from the bicycle model, reference path, Pure Pursuit and Stanley, until model predictive control with CVXPY, as well as opening a Python programming course for electrical engineering and mechatronics. Want to master the entire series, From the vehicle model to circuit testing with various speeds? All 6 episodes, complete with PDF step-by-step 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 a single class? Buy individual classes with lifetime access. Subscribe now on the premium page cerdasinovasidigital.com. Contact us via WhatsApp, or visit cerdasinovasidigital.com. Thank you for watching, see you in the next episode. Thank you for watching,
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Cerdas Inovasi Digital Team
Software developers, BIM & 3D engineers, and AI practitioners
52 video classes1,276 episodes
We build software, BIM models, games and AI automations for clients every day, and turn that hands-on work into step-by-step classes: every step is shown on screen and comes with a PDF guide you can keep.
