Control Design of Quadcopter for UAV catch and return.

The proposed project is an implementation of the Linear Quadrotor Regulator (LQR) theory for the control of a quadrotor that spans the given restricted airspace. Moroever, the idea focuses on the capture and retrieval of unknown aerial intruders such as a UAV.

This project implements a Linear Quadratic Regulator (LQR) controller for autonomous quadrotor flight, with a focus on capturing and retrieving unknown aerial intruders (UAVs) within a restricted airspace.

Problem Statement

Unauthorized UAVs operating in restricted airspace pose a growing security and safety threat. This project proposes an autonomous quadrotor system capable of:

  • Navigating the restricted airspace with stability
  • Intercepting an unknown aerial intruder
  • Executing a capture and retrieval maneuver

System Modeling

Nonlinear Dynamics

The quadrotor’s full nonlinear equations of motion are derived, capturing:

  • 6-DOF rigid body dynamics (3 translational + 3 rotational)
  • Rotor thrust and torque interactions
  • Gyroscopic effects from spinning rotors

Linearization

The nonlinear model is linearized around a hover equilibrium point using a first-order Taylor series expansion, producing a linear state-space model suitable for LQR design.

LQR Controller Design

The LQR minimizes a quadratic cost function:

\[J = \int_0^\infty \left( x^T Q x + u^T R u \right) dt\]
  • Q matrix — penalizes state deviations (position, velocity, orientation errors)
  • R matrix — penalizes control effort (rotor forces)
  • Optimal gain matrix K computed by solving the Algebraic Riccati Equation (ARE)

Mission Profile: Catch & Return

The controller was designed to handle:

  1. Launch — stable takeoff and entry into restricted airspace
  2. Trajectory Control — smooth pursuit of the intruder UAV
  3. Capture — precise interception with minimal overshoot
  4. Return — stable return flight with the captured UAV

Key performance factors evaluated: response time, trajectory smoothness, and capture accuracy.

Simulation

The full simulation is implemented in MATLAB (Quadrotor_LQR_Sim.m) and validated the controller’s ability to stabilize the quadrotor and execute the capture mission across multiple flight scenarios.