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

Abstract

This paper proposes a state feedback controller for the attitude stabilization problem of quadrotors. The quadrotor attitude is represented by unit quaternion and disturbance of the attitude model is taken into consideration. A robust controller is synthesized via H∞ optimal design approach. Solving the nonlinear H∞ optimal control problem using state feedback is meltdown to finding a solution to a Hamilton-Jacobi inequality. Based on the quadrotor attitude dynamics, an appropriate parameterized Lyapunov function is selected and the corresponding state feedback controller is derived. Then the parameters are found from a Hamilton-Jacobi inequality. The resultant state feedback controller can lead to closed-loop nonlinear system having L2-gain less than or equal to a constant γ, and establish the asymptotically stability of the closed-loop nonlinear system without external disturbance. The simulation provides the results to show the stability and the robust performance against to disturbance. I. INTRODUCTIONIn recent years, research in control of Quadrotor has been growing due to its simplicity in design and low cost. Quadrotors have several advantages over fixed-wing aircrafts, such as take-off and landing vertically in a limit space, easy hover over fixed or dynamic targets, which give them efficiency in applications that fixed-wing aircrafts cannot do, and they are safer [1][2] [3]. Quadrotors can be used to perform several tasks in the applications of dangerous area for a manned aircraft in a high level of accuracy. It can be used in different applications, such as inspection of power lines, oil platforms, search and rescue operations, and surveillance [4] [5]. Control of a quadrotor helicopter is a challenging task. The difficulty comes from the complexity of modeling its dynamic system, their underactuated mechanism, and various external disturbances [5] [6].The attitude control is to stabilize the orientation of quadrotors, which is a first step towards more complex control systems [5]. Researchers have been focusing on design and implementation of many types of controller to control the attitude of individual quadrotors. A nonlinear proportional squared control algorithm was proposed in [7] for attitude control. 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. A bounded control law was presented to obtain

A Review on Comparative Remarks, Performance Evaluation and Improvement Strategies of Quadrotor Controllers

“…Literature shows the implementations of the controller on the quadrotor platform in different ways. Some researchers use simple linear [43][44][45] while others introduce non-linearly [46][47][48]. Another group of researchers is interested in combining with other controllers in order to improve the performance of the controller when the system is surrounded by noise and disturbance [47,49,50].…”

Novel Lyapunov-Based Autonomous Controllers for Quadrotors

“…Numerous research studies have examined the attitude and position control design and implementation to retain satisfactory performance operation. Some of the several control algorithms proposed in the literature includes proportional integral derivative (PID) [10], [11], linear quadratic regulator (LQR) [8], [10], [12], sliding mode control [13], [14], H ∞ [15], backstepping control [9], fuzzy logic [16], and visual-based techniques [17]. Another interesting methodology by Chen and Sun in 2019 [18], which generally deals with the control of underactuated systems that can treat various system constraints, could be used to control quadrotors.…”

Nonlinear H∞ control scheme for a flying robot

“…A nonlinear robust scheme using nonlinear H∞ was proposed for attitude stability of a flying robot and a backstepping control scheme was developed for path tracking (Guilheme et al, 2008). In (Jasim and Gu, 2014), a candidate storage function V(x) was considered for the rotational dynamics and developing a nonlinear H∞ scheme for the stability of the orientation of quadrotor. In Raffo et al (2008), a composite control approach using backstepping technique and nonlinear H∞ were used to perform the robust tracking problem of a quadrotor.…”