[Paper Review] Trajectory Tracking Control of UAV Bicopter using Linear Quadratic Gaussian

Fahmizal Fahmizal, Hanung Adi Nugroho+2 more|arXiv (Cornell University)|Sep 15, 2023

Adaptive Control of Nonlinear Systems4 citations

TL;DR

This paper proposes a Linear Quadratic Gaussian (LQG) controller to improve trajectory tracking performance of a UAV bicopter under inertial disturbances from payload, outperforming a standard LQR controller. The LQG controller integrates state estimation via Kalman filtering with optimal control, reducing root mean square error (RMSE) in circular and '8'-shaped trajectory tracking under disturbance.

ABSTRACT

This paper describes the design of a linear quadratic gaussian (LQG) for trajectory tracking control of UAV Bicopter. In this work, disturbance in the form of payload significantly affects the trajectory tracking control process on the UAV Bicopter when using a linear quadratic regulator (LQR) controller. The use of a LQR control will be optimal in the case of a state regulator towards an equilibrium point in a system, but for the tracking case, the LQR controller is not capable of optimally, especially in systems that have high levels of nonlinearity and system dynamic changes such as inertial disturbances. Therefore, this paper proposes the design of a LQG control that is expected to overcome system dynamic changes, in this case in the form of inertial disturbances to the UAV Bicopter when carrying a payload. The success of LQG control was tested in two scenarios, the first trajectory tracking at a circular position and the second with the position of the trajectory number "8". The simulation results show that the proposed LQG controller successfully overcame inertial disturbances when the UAV Bicopter performs trajectory tracking. When given an inertial disturbance, the trajectory tracking test results show that the LQG control has a lower root mean square error (RMSE) value than the LQR control.

Motivation & Objective

• Address the limitation of Linear Quadratic Regulator (LQR) controllers in handling trajectory tracking under high nonlinearity and dynamic changes.
• Overcome the poor performance of LQR in tracking scenarios involving inertial disturbances, such as payload changes.
• Design and validate an LQG controller that combines optimal control with state estimation to improve robustness against dynamic disturbances.
• Demonstrate the effectiveness of LQG control in two complex trajectory scenarios: circular and '8'-shaped paths under inertial disturbance.
• Quantify performance improvement using RMSE as a metric for tracking accuracy under disturbance conditions.

Proposed method

• Develop a nonlinear dynamic model of the bicopter UAV in 3D Cartesian space, including translational and rotational motion.
• Linearize the bicopter dynamics around equilibrium points to enable application of LQR and LQG control design.
• Implement an LQR controller for optimal state regulation toward a desired trajectory without disturbances.
• Integrate a Kalman filter for state estimation in the LQG framework to handle process and measurement noise.
• Design the LQG controller by combining the LQR feedback gain with the Kalman filter's state estimates to improve disturbance rejection.
• Tune the weighting matrices (Q, R, w, v) to balance control effort, tracking accuracy, and disturbance rejection in simulation.

Experimental results

Research questions

• RQ1 Can the LQG controller effectively reduce trajectory tracking error compared to LQR when inertial disturbances from payload are introduced?
• RQ2 How does the LQG controller perform in complex trajectory tracking tasks such as circular and '8'-shaped paths under disturbance?
• RQ3 What is the impact of different Q-matrix weightings on the transient response and RMSE in LQR-controlled bicopter systems?
• RQ4 Does the inclusion of state estimation via Kalman filtering in the LQG framework significantly improve disturbance rejection compared to LQR alone?
• RQ5 To what extent does the LQG controller maintain stability and accuracy when the system's inertia changes due to payload?

Key findings

• The LQG controller achieved a 15.4% reduction in RMSE at position x during circular trajectory tracking under inertial disturbance (LQR: 1.0204, LQG: 0.8630).
• For the '8'-shaped trajectory, the LQG controller reduced RMSE at position x by 37.8% compared to LQR (LQR: 1.1891, LQG: 0.7395).
• The LQG controller showed a consistent improvement in tracking accuracy, with minimal overshoot and faster settling times under disturbance.
• The LQG controller reduced RMSE at position y by 1.46% during circular tracking and 1.20% during '8'-shaped tracking, indicating robustness across all axes.
• The LQG controller outperformed LQR in both scenarios, demonstrating superior disturbance rejection and tracking precision.
• The use of Kalman filtering in LQG effectively estimated system states under uncertainty, enabling better control performance than LQR alone.