Farhad A. Goodarzi

Geometric stabilization of a quadrotor UAV with a payload connected by flexible cable

This paper deals with dynamics and control of a quadrotor UAV with a payload that is connected via a flexible cable, which is modeled as a system of serially-connected links. It is shown that a coordinate-free form of equations of motion can be derived for an arbitrary number of links according to Lagrangian mechanics on a manifold. A geometric nonlinear control system is also presented to asymptotically stabilize the position of the quadrotor while aligning the links to the vertical direction. These results will be particularly useful for aggressive load transportation that involves deformation of the cable. The desirable properties are illustrated by a numerical example and a preliminary experimental result.

Geometric Adaptive Tracking Control of a Quadrotor Unmanned Aerial Vehicle on SE(3) for Agile Maneuvers

This paper presents nonlinear tracking control systems for a quadrotor unmanned aerial vehicle (UAV) 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.

Geometric control of a quadrotor UAV transporting a payload connected via flexible cable

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 asymptotically 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.

Dynamics and control of quadrotor UAVs transporting a rigid body connected via flexible cables

This paper is focused on the dynamics and control of arbitrary number of quadrotor UAVs transporting a rigid body payload. The rigid body payload is connected to quadrotors via flexible cables where each flexible cable is modeled as a system of serially-connected links. It is shown that a coordinate-free form of equations of motion can be derived for arbitrary numbers of quadrotors and links according to Lagrangian mechanics on a manifold. A geometric nonlinear controller is presented to transport the rigid body to a fixed desired position while aligning all of the links along the vertical direction. Numerical results are provided to illustrate the desirable features of the proposed control system.

Stabilization of a Rigid Body Payload With Multiple Cooperative Quadrotors

This paper presents the full dynamics and control of arbitrary number of quadrotor unmanned aerial vehicles (UAV) transporting a rigid body. The rigid body is connected to the quadrotors via flexible cables where each flexible cable is modeled as a system of arbitrary number of serially connected links. It is shown that a coordinate-free form of equations of motion can be derived for the complete model without any simplicity assumptions that commonly appear in other literature, according to Lagrangian mechanics on a manifold. A geometric nonlinear controller is presented to transport the rigid body to a fixed desired position while aligning all of the links along the vertical direction. A rigorous mathematical stability proof is given and the desirable features of the proposed controller are illustrated by numerical examples and experimental results.

Global Formulation of an Extended Kalman Filter on SE(3) for Geometric Control of a Quadrotor UAV

An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an intrinsic form of linearization on SE(3) to estimate the state of the quadrotor from noisy measurements. The proposed estimator considers all of the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion. The desirable features of the proposed EKF are illustrated by numerical examples and experimental results for several scenarios. The proposed estimation scheme on SE(3) has been unprecedented and these results can be particularly useful for aggressive maneuvers in GPS denied environments or in situations where parts of onboard sensors fail.

Extended Kalman filter on SE(3) for geometric control of a quadrotor UAV

An extended Kalman filter (EKF) is developed on the special Euclidean group, SE(3) for geometric control of a quadrotor UAV. It is obtained by performing an extensive linearization on SE(3) to estimate the state of the quadrotor from noisy measurements. Proposed estimator considers all the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion. The desirable features of the proposed EKF are illustrated by numerical examples and experimental results for several scenarios. The proposed estimation scheme on SE(3) has been unprecedented and these results can be particularly useful for aggressive maneuvers in GPS denied environments or in situations where parts of onboard sensors fail.

Stability analysis of the hydraulic wind energy transfers model

Gearless hydraulic wind power transfers are considered noble candidates for wind energy harvesting. In this method, high-pressure hydraulics is utilized to collect the energy of multiple wind turbines and transfer it to a central generation unit. The mathematical model of the gearless wind energy transfer system is described in the previous literature. This paper determines the stability of the mathematical model by careful assessment of the state-space representations of the model of the hydraulic system. The existence of limit cycle is investigated for the nonlinear model and the equilibrium point of the system is calculated. The results show that both linear and nonlinear models are stable.