LQR control for a quadrotor using unit quaternions: Modeling and simulation

H<inf>&#x221E;</inf> for quadrotor attitude stabilization

“…The controller was implemented to a linear quaternion simulator of quadrotors. Elias R. et al [8] presented a nonlinear quaternion mathematical model to describe the attitude dynamics of quadrotors. They implemented a LQR gain scheduling controller for trajectory tracking and attitude stability tasks.…”

Development of a Low-Cost Experimental Quadcopter Testbed using an Arduino controller for Video Surveillance

“…5 Popular control techniques include Proportional Integral Derivative (PID) controllers 5, 6 or a Linear Quadratic Regulator (LQR) controllers. 7,8 Once a stable plant is obtained, the quadcopter linear model is usually used to design desired control (gains) which are then applied to the actual plant dynamics. Generally speaking, the nominal position for a quadcopter is in hover mode, where the deviation from hover is calculated using Inertial Measurement Units (IMU) and fed back into the system for control.…”

Lateral-directional autopilot design of Unmanned Aerial Vehicles using quaternion feedback sliding mode approach

“…Many factors have an effect upon the performance of the controller, such as parametric uncertainty(changing mass, and aerodynamic characteristics), unmodelled dynamics, actuator magnitude and rate saturation, sensor noise, and atmospheric disturbances(turbulence, gust), and assumptions made during control design itself.Parametric uncertainty limits the operational envelope of the vehicle to where control designs are valid, whereas unmodelled dynamics and saturation can severely limit the achievable bandwidth of the system.The effect of uncertainty and unmodelled dynamics have been successfully handled using robust control techniques [1,2,3].Backstepping approach is proposed in [4] to control longitudinal and latero-directional motions, which uses mathematical model to describe the lateral directional motion of an aircraft.The combined adaptive control (CAC) law for an autopilot of the UAV attitude control is considered in [5].A new model reference robust control(MRRC) scheme is introduced in [6] and is applied to autopilot control law design.A decentralized SMC that enable a connected and leaderless swarm of UAVs to reach a consensus in altitude and heading angle are presented in [7].Euler based axis transformation and feedback methods are used in above mentioned research works.The basic disadvantage while employing Euler based approach is singularity(gimbal lock) and error due to sensors.Hence this can by removed by employing quaternion axis transformation and feedback design.Quaternion algebra can be used for generating rigid-body rotations in three-dimensional space.Rotation through quaternion are used in many applications such as virtual reality, aerospace engineering, and orbital mechanics [8].Quaternions are widely used as attitude representation parameter of rigid bodies such as space-crafts.This is due to the fact that quaternion inherently come along with some advantages such as no singularity and computationally less intense compared to other attitude parameters such as Euler angles or a direction cosine matrix [9].Quaternion-based backstepping controller is designed in [10] which is able to track a trajectory.The problem of attitude tracking control for rigid satellite is studied in [11].Based on the dynamic equation and kinematics equation using error quaternion and error angular velocity, a SMC is initially designed to solve this problem.Linear Quadratic Regulator(LQR) control for a quadrotor UAV using unit quaternions is simulated in [12].Full quaternion based attitude control for a quadrotor UAV is proposed in [13].Most of the existing approaches in this area are for the attitude control of satellite and quadrotor UAVs using quaternions.Sliding mode approach using quaternions for the attitude control of fixed wing UAV is not yet developed. The selection of a particular control technique generally depends upon the category of UAV and its mission requirements.An effort is made in this paper to design a lateral directional auto pilot using SMC technique and PI controller.The advantage of using SMC is that it can tolerate parameter uncertainties and external disturbances.Fuzzy logic is ...…”