Autonomous Adaptive Controller for 🚗Tesla Model 3 and 🚁 Quadrotor

Modern Control Theory and Design

Carnegie Mellon University

Pittsburgh, PA

Sept 2023 - Dec 2023

🎯 Objective

Develop a unified control pipeline for autonomous vehicles and drones using modern control theory — progressing from PID and state-feedback control to LQR, A*, EKF-SLAM, and MRAC adaptive control.

The goal was to design controllers capable of trajectory tracking, optimal planning, and fault-tolerant stabilization in both ground and aerial platforms simulated in Webots.

Quadrotor coordinate frames showing thrust forces (F₁–F₄) and attitude angles (ϕ, θ, ψ) relative to the inertial frame.

💡 Motivation

Autonomous navigation demands robust, real-time control under model uncertainty — from ground vehicles navigating constrained tracks to UAVs compensating for actuator failures.

This project was driven by the need to bridge theoretical control design with realistic robotic applications, building intuition on system linearization, observability, optimal control, and adaptive stability.

Each stage of the project contributed to mastering a core element of autonomy: planning, control, estimation, and robustness.

⚙️ Approach

Part 1 – PID Control and Linearization

Linearized the nonlinear bicycle model for a Tesla Model 3 and designed lateral and longitudinal PID controllers.
Tuned proportional and derivative gains for minimal deviation from the racing track.

Part 2 – Full-State Feedback (Pole Placement)

Analyzed controllability and observability at varying vehicle speeds.
Designed a state-feedback controller via pole placement for stable lateral control.

PID control tracking

Part 3 – Optimal Control (LQR) and Path Planning (A*)

Implemented discrete-time infinite-horizon LQR for optimal steering control, minimizing deviation and control effort.
Developed A*-based trajectory planner for overtaking obstacles dynamically.

Part 4 – EKF-SLAM for Localization

Designed an Extended Kalman Filter to estimate the vehicle’s position and heading using noisy sensor data.
Simultaneously estimated map features and trajectory without relying on GPS.

🚁 Part 5 – UAV LQR + Adaptive Control (MRAC)

Modeled and linearized a quadrotor system near hover conditions.
Implemented LQR baseline control and extended with Model Reference Adaptive Control (MRAC) for fault tolerance.
Validated stable flight under 50–70 % motor thrust loss, where LQR failed but MRAC maintained altitude and attitude stability.

Simulation Flow

📈 Results

PID and pole-placement controllers achieved < 10 cm deviation and ~350 s loop completion on the CMU Buggy track.
LQR reduced tracking deviation to 3.5 m average, completing the circuit in under 250 s.
A* planner successfully executed overtaking maneuvers on dynamic tracks.
EKF-SLAM maintained accurate localization even under missing GPS input.
MRAC restored stable hover within 2 s post 50 % thrust loss, outperforming static LQR.

LQR controller performance on the CMU Buggy track showing position, velocity, and control inputs over time.

A*-path planning results on three costmaps showing obstacle avoidance and optimal route generation.

EKF-SLAM estimated trajectory (red) vs. ground truth (blue), showing accurate pose and landmark estimation over time.

Quadrotor LQR altitude control showing smooth tracking of step commands with <0.21 m steady-state error.

Under nominal conditions, both LQR and MRAC track the step command accurately with minimal overshoot and steady-state error.

Under 50–70 % thrust loss, LQR fails to recover altitude, while MRAC successfully adapts to actuator degradation and maintains stable flight under 2s.

🌍 Impact

This multi-stage framework demonstrates progressive mastery of control theory applied to real robotic systems:

From model-based linearization → optimal control → adaptive robustness.
Provides a foundation for deploying autonomous ground and aerial robots that can plan, adapt, and recover from dynamic disturbances.
Bridges the gap between theoretical control design and simulation-based robotics research, supporting future work in fault-tolerant autonomy and coordinated UAV–UGV systems.

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