Quadcopter Drone Flight Dynamics: Physics Explained

IMU (Inertial Measurement Unit) is a sensor mainly used to detect and measure acceleration and rotational motion, realized through the law of inertia. These sensors range from small MEMS sensors to laser gyroscopes with very high measurement accuracy. The most basic inertial sensors consist of three accelerometers and three gyroscopes. Gyroscopes detect angular velocities in three directions, while accelerometers detect accelerations in three directions. Position information relative to the starting point is obtained by integrating the signals of the accelerometer and gyroscope. Since IMU is not affected by wind and other environmental conditions, its independence makes it one of the key technologies in automatic driving.

The Inertial Measurement Unit (IMU), also called the Inertial Reference Unit, measures the linear and angular accelerations from the accelerometers and gyroscopes and provides this information to other systems. This unit serves as the central processing component that integrates sensor data for navigation calculations.

IMUs combine gyroscopes and accelerometers for tracking. Gyroscopes measure rotational velocity via the Coriolis force (MEMS technology), while accelerometers measure linear acceleration. Integrating these measurements twice yields position, but accumulated drift occurs over time. Gravity subtraction is challenging because the direction is unknown. Combining both sensors in an IMU exploits their complementary strengths, though drift still requires combination with other sensor types for long-term accuracy.

The IMU (Inertial Measurement Unit) consists of gyroscopes and accelerometers. Gyroscopes measure angular velocities and orientations, while accelerometers measure linear accelerations. When combined, these sensors can compute the vehicle's motions and orientations, which are then integrated to derive positions. Magnetometers can be added as additional sensors to compute heading.

An Inertial Measurement Unit (IMU) is a collection of gyroscopes and accelerometers that measure angular rates and accelerations on three axes (3D). These measurements can be integrated to calculate velocities and then integrated again to determine trajectory. IMUs provide continuous data at high frequencies (100-250 Hz) but have inherent measurement instability that accumulates over time, requiring external constraints like GPS for absolute positioning.

State estimation is the process of mixing information from multiple sensors (proximity sensors, inertial sensors, GPS, cameras, pressure sensors) to estimate a robot's true state (position, velocity, angular position). Since we can never know the exact true values (similar to how humans can only approximate measurements), state estimation provides approximations. This leads to sensor fusion, which involves combining data from multiple sensors using algorithms called filters to extract useful information while filtering out noise.

The Kalman Filter is an optimal estimation algorithm that combines noisy sensor measurements with mathematical models to estimate the true state of a system, consisting of two fundamental stages: prediction (using the mathematical model to forecast the next state) and update (correcting the prediction using actual sensor measurements). This algorithm is widely used in autonomous vehicle positioning systems, where it fuses data from multiple sensors like GPS, IMU (gyroscope, accelerometer, magnetometer), and odometry to achieve more accurate and reliable position, velocity, and orientation estimates than any single sensor could provide alone.

Kalman filtering is a mathematical technique that combines data from multiple sensors to produce more accurate state estimates by recursively predicting the system state using a dynamic model and then updating this prediction with sensor measurements, where each measurement is weighted according to its uncertainty (represented by covariance matrices), allowing devices like smartphones and drones to accurately determine their position and orientation by integrating information from complementary sensors such as GPS, accelerometers, and gyroscopes.

Sensor fusion relies on probabilistic state estimation, asking what is the most likely true state given noisy measurements rather than choosing one sensor over another. The predict-correct loop forms the foundation: predict using physics and motion models to estimate next state, measure using sensors for new data, and correct by comparing predictions with measurements while weighing them based on uncertainty. The Kalman filter implements this for linear systems with Gaussian noise, providing optimal estimates through prediction and update steps with Kalman gain determining trust between prediction and measurement. It is widely used in GPS/IMU fusion, tracking, and navigation systems.

The Kalman filter serves as a sensor fusion algorithm that combines data from multiple sensors to produce an optimal state estimate. When additional sensors (such as IMUs) are incorporated, the dimensions of the measurement vector y, observation matrix C, and Kalman gain matrix K change accordingly. However, the fundamental algorithmic logic remains consistent: multiple probability density functions from different sensors are multiplied together to find the optimal estimate, improving overall estimation accuracy through complementary sensor information.

Sense and avoid systems enable unmanned aerial vehicles to detect obstacles and navigate around them autonomously. These systems use sensors to identify obstacles and require computer algorithms to calculate appropriate avoidance maneuvers, including determining direction (left or right) and distance to navigate safely around detected obstacles.

UAV autonomy includes several key features: 1) Obstacle avoidance using ultrasonic sensors to detect and avoid obstacles, 2) Autopilot systems with onboard computers, 3) Localization (identifying exact position using GPS for outdoor environments or alternative technologies for indoor/underground areas), 4) Path planning (calculating routes between current position and destination while avoiding obstacles and restricted zones), 5) Navigation (following planned paths). Path planning must also consider remaining battery power to ensure the mission can be completed.

This project demonstrates an autonomous drone navigation system using ArduPilot in a Gazebo-based Software-in-the-Loop (SITL) simulation. The drone, modeled as an Iris platform, operates in an outdoor forest/garden environment and is equipped with a 3D LiDAR sensor that continuously scans surroundings to construct an OctoMap. A custom global path planner node subscribes to this map and receives a goal position via a ROS service, computing an obstacle-free route to the destination. A separate execution node then commands the drone to follow this path using ArduPilot’s control interface. During the demonstration, an unexpected obstacle—a tree—is introduced by copy-pasting a model directly into the drone’s planned route. Although the global planner operates on a static map, the system includes an emergency detection cone at the drone’s front that senses dynamic or unseen obstacles outside the map. When triggered, this local sensor triggers an immediate stop, prevents collision, and initiates a replanning sequence to safely reroute toward the original goal. The system thus integrates global path planning with real-time local obstacle avoidance to enhance safety and adaptability in dynamic environments. The simulation leverages ROS2, ArduPilot, Gazebo, and LiDAR-based mapping to achieve autonomous navigation without human intervention.

This comprehensive section presents the complete autonomous UAV navigation system developed in the thesis, spanning from foundational challenges to experimental validation. The system achieves 100% onboard perception and computation with no prior environmental knowledge, addressing the fundamental challenge of creating small UAVs capable of navigating through cluttered environments at high speeds. Key trade-offs are explored: large aircraft offer more sensing power but are unwieldy; smaller aircraft under 5 kg are safer but face integration challenges. Two navigation approaches are contrasted: mapping-based systems requiring pre-known environments versus fully onboard 3D sensing. The pushbroom stereo innovation exploits UAV motion faster than environmental features, achieving 120 fps on small computers by asking 'is this pixel block at 10 meters?' rather than searching all depths. For state estimation, the solution combines barometric altimeters and pitot tubes with an open-source estimator, providing reliable attitude and velocity estimates. The model-based control architecture uses identified dynamic models with 12 states and 3 control inputs, employing flat plate aerodynamics approximations. Trajectory generation uses both manual flight replay and model-based optimization, with LQR controllers providing stabilization. Experimental validation across 16 flights covering 1.5 kilometers demonstrated successful obstacle avoidance at 27 mph, executing over 150 trajectories with dynamic maneuvers including 100-degree rolls. Failure analysis revealed equal splits between vision failures (low-contrast environments, poor calibration) and control failures (insufficient maneuver libraries, incorrect trajectory selection). Future directions include multi-disparity search, GPU acceleration, wind sensing, and integrated vision-control simulation environments.

A single-actuated UAV called PULSAR extends its sensor field of view through natural self-rotation induced by motor counter-torque, achieving 6.65g/W flight efficiency and enabling autonomous navigation in unknown environments with obstacle detection and avoidance capabilities.