Race Car MPC with Spline-Based Trajectory Tracking

This project implements a Model Predictive Control (MPC) system for autonomous race car trajectory tracking using cubic splines and a bicycle model. It is based on the race-car example from the acados project, with enhancements for spline-based trajectory generation and improved visualization.

Overview

The system combines:

• Bicycle Model: Simplified vehicle dynamics for racing applications
• Cubic Spline Interpolation: Smooth trajectory generation from track waypoints
• MPC Controller: Real-time optimization for trajectory following using acados
• Clothoid Splines: Advanced spline fitting for racing track representation

Visual Results

Race Car Trajectory

Vehicle trajectory following the racing track with MPC control

Progression Analysis

Control Signals and The Progression of States through the lap

Project Structure

├── MPC_race_cars_simplified/    # Main MPC implementation
│   ├── bicycle_model.py         # Vehicle dynamics model
│   ├── acados_settings_dev.py   # MPC solver configuration
│   ├── plotFcn.py              # Visualization functions
│   ├── time2spatial.py         # Coordinate transformations
│   └── tracks/                 # Track data files
├── Utils/                      # Utility modules
│   ├── symbolic_cubic_spline.py    # Symbolic spline implementation
│   ├── clothoid_spline.py          # Clothoid spline fitting
│   └── 2d_symbolic_cubic_spline.py # 2D spline utilities
├── examples/                   # Usage examples
│   ├── race_cars_simplified.py     # Main racing simulation
│   └── test_clothoid_spline.py     # Spline testing
└── c_generated_code/           # Auto-generated acados C code

Features

Vehicle Model

• Bicycle Model: Simplified 4-state model (progress, lateral deviation, heading, velocity)
• Constraints: Lateral acceleration limits, steering and acceleration bounds
• Spatial Parameterization: Track-following using curvilinear coordinates

Trajectory Generation

• Cubic Splines: Symbolic Cubic-Splines for piece-wise references
• Clothoid Splines: Advanced spline fitting for racing applications, in reality this is an implementation of a curve with cubic-spline curvature, so it isn't technically a 'clothoid'
• Real-time Adaptation: Dynamic spline updates based on current position

MPC Controller

• acados Integration: High-performance optimization solver
• Receding Horizon: Configurable prediction horizon and discretization
• Constraint Handling: Hard constraints on vehicle dynamics and track boundaries

Installation

Prerequisites

• Python 3.7+
• acados (follow official installation guide)

Dependencies

pip install -r requirements.txt

Required packages:

• numpy >= 1.21.0
• scipy >= 1.7.0
• matplotlib >= 3.5.0
• acados_template >= 0.2.0
• casadi >= 3.5.0

Usage

Basic Racing Simulation

from MPC_race_cars_simplified.acados_settings_dev import acados_settings
from Utils.symbolic_cubic_spline import SymbolicCubicSpline

# Setup MPC
Tf = 5.0  # prediction horizon
N = 50    # discretization steps
track = "LMS_Track.txt"
constraint, model, acados_solver = acados_settings(Tf, N, track, num_points=50)

# Create spline for trajectory
clothoid_spline = SymbolicCubicSpline("tracks/LMS_Track.txt")

# Run simulation
# (see examples/race_cars_simplified.py for complete example)

Running the Example

python3 examples/race_cars_simplified.py

This will:

1. Load the racing track data
2. Initialize the MPC controller with bicycle model
3. Run a complete lap simulation
4. Display results including:
   • Vehicle trajectory
   • Control inputs (acceleration, steering)
   • Lateral acceleration constraints
   • Track projection

Configuration

MPC Parameters

• Prediction Horizon: Adjustable via Tf parameter
• Discretization: Control via N parameter
• Cost Weights: Modify Q, R matrices in acados_settings_dev.py
• Constraints: Lateral acceleration limits in bicycle_model.py

Track Data

• Track files are stored in MPC_race_cars_simplified/tracks/
• Format: Text files with waypoint coordinates
• Custom tracks can be added following the existing format

Troubleshooting

Common Issues

1. acados Compilation Errors: Ensure acados is properly installed and compiled
2. QP Solver Issues: Try switching between QPOASES and HPIPM solvers
3. Version Compatibility: Check acados and acados_template versions match

Performance Tuning

• Adjust prediction horizon Tf for computation vs. performance trade-off
• Modify cost weights for different racing styles
• Tune constraint limits based on vehicle capabilities

License

This project uses the 2-Clause BSD License, as indicated in the source files.