Geometric nonlinear PID control of a quadrotor UAV on SE(3)

Abstract

Nonlinear PID control systems for a quadrotor UAV are proposed to follow an attitude tracking command and a position tracking command. The control systems are developed directly on the special Euclidean group to avoid singularities of minimal attitude representations or ambiguity of quaternions. A new form of integral control terms is proposed to guarantee almost global asymptotic stability when there exist uncertainties in the quadrotor dynamics. A rigorous mathematical proof is given. Numerical example illustrating a complex maneuver, and a preliminary experimental result are provided. Recently, the dynamics of a quadrotor UAV is globally expressed on the special Euclidean group, SE(3), and nonlinear control systems are developed to track outputs

Laser-based guidance of a quadrotor uav for precise landing on an inclined surface

“…The landing trajectory presented in this paper is based on geometric nonlinear control systems for quadrotor UAVs [8], [9], [10]. First, a position tracking controller guides the quadrotor to the determined landing site, and, as it nears the landing phase, an attitude-tracking controller is engaged to align the attitude of the quadrotor to the landing surface.…”

“…Consider a quadrotor UAV model illustrated in Fig. 1 [9]. This is a system of four identical rotors and propellers located at the vertices of a square, which generate a thrust and torque normal to the plane of this square.…”

“…Since it is only possible to achieve asymptotic output tracking for at most four quadrotor UAV outputs, we define two flight modes, namely (1) an attitude controlled flight mode, and (2) a position controlled flight mode [8], [9], [10] and design control systems for each mode.…”

“…Geometric control systems with a generalized integral term to eliminate the effects of disturbances are summarized as follows (see [9] for detailed development). a) Attitude Tracking Control: Suppose that a smooth attitude command R d (t) ∈ SO(3) satisfyingṘ d = R dΩd is given, where Ω d (t) is the desired angular velocity, which is assumed to be uniformly bounded.…”

Robust global trajectory tracking for a class of underactuated vehicles

“…A good overview of these different control techniques can be found in the work by Chaturvedi, Sanyal, and McClamroch (2011). Despite their relative success, the aforementioned papers provide a control solution for fully actuated vehicles, ruling out very common vehicles such as helicopters and underwater vehicles. In order to address this issue, other control solutions have been presented by Aguiar and Hespanha (2007), Goodarzi, Lee, and Lee (2013) and Lee, Leok, and Harris McClamroch (2011). However, such strategies rely on continuous controllers and it has been shown by Bhat and Bernstein (2000) that global asymptotic stabilization of a given set-point is not possible by means of continuous feedback.…”