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Register a new userGeometric Control of a Quadrotor UAV Transporting a Payload Connected via Flexible Cable
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We derived a coordinate-free form of equations of motion for a complete model of a quadrotor UAV with a payload which is connected via a flexible cable according to Lagrangian mechanics on a manifold. The flexible cable is modeled as a system of serially-connected links and has been considered in the full dynamic model. A geometric nonlinear control system is presented to exponentially stabilize the position of the quadrotor while aligning the links to the vertical direction below the quadrotor. Numerical simulation and experimental results are presented and a rigorous stability analysis is provided to confirm the accuracy of our derivations. These results will be particularly useful for aggressive load transportation that involves large deformation of the cable.
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Equations of motion and dynamics of a quadrotor transporting a load with a flexible cable modeled as a chain pendulum is obtained using Euler-Lagrange equations by taking variations on manifolds. An arbitrary number of links considered in a series models the flexible cable connecting the load to the quadrotor while the whole system can undergo complex motion in 3D. Geometric nonlinear control asymptotically stabilizes the load and cable bellow the quadrotor. A linearization about the equilibrium and the corresponding lyapunov stability analysis is provided. We produced numerical simulations and validated our work experimentally using a quadrotor UAV.
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.
This paper presents nonlinear tracking control systems for a quadrotor unmanned aerial vehicle under the influence of uncertainties. Assuming that there exist unstructured disturbances in the translational dynamics and the attitude dynamics, a geometric nonlinear adaptive controller is developed directly on the special Euclidean group. In particular, a new form of an adaptive control term is proposed to guarantee stability while compensating the effects of uncertainties in quadrotor dynamics. A rigorous mathematical stability proof is given. The desirable features are illustrated by numerical example and experimental results of aggressive maneuvers.
This paper addresses the problem of designing a trajectory tracking control law for a quadrotor UAV, subsequent to complete failure of a single rotor. The control design problem considers the reduced state space which excludes the angular velocity and orientation about the vertical body axis. The proposed controller enables the quadrotor to track the orientation of this axis, and consequently any prescribed position trajectory using only three rotors. The control design is carried out in two stages. First, in order to track the reduced attitude dynamics, a geometric controller with two input torques is designed on the Lie-Group $SO(3)$. This is then extended to $SE(3)$ by designing a saturation based feedback law, in order to track the center of mass position with bounded thrust. The control law for the complete dynamics achieves exponential tracking for all initial conditions lying in an open-dense subset. The novelty of the geometric control design is in its ability to effectively execute aggressive, global maneuvers despite complete loss of a rotor. Numerical simulations on models of a variable pitch and a conventional quadrotor have been presented to demonstrate the practical applicability of the control design.
We present a new quadrotor geometric control scheme that is capable of tracking highly aggressive trajectories. Unlike previous works, our geometric controller uses the logarithmic map of SO(3) to express rotational error in the Lie algebra, allowing us to treat the manifold in a more effective and natural manner, and can be shown to be globally attractive. We show the performance of our control scheme against highly aggressive trajectories in simulation experiments. Additionally, we present an adaptation of this controller that allows us to interface effectively with the angular rate controllers on an onboard flight control unit and show the ability of this adapted control scheme to track aggressive trajectories on a quadrotor hardware platform.
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