This paper provides new results for control of complex flight maneuvers for a quadrotor unmanned aerial vehicle (UAV). The flight maneuvers are defined by a concatenation of flight modes or primitives, each of which is achieved by a nonlinear controller that solves an output tracking problem. A mathematical model of the quadrotor UAV rigid body dynamics, defined on the configuration space $\SE$, is introduced as a basis for the analysis. The quadrotor UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts; each flight mode is defined by solving an asymptotic optimal tracking problem. Although many flight modes can be studied, we focus on three output tracking problems, namely (1) outputs given by the vehicle attitude, (2) outputs given by the three position variables for the vehicle center of mass, and (3) output given by the three velocity variables for the vehicle center of mass. A nonlinear tracking controller is developed on the special Euclidean group $\SE$ for each flight mode, and the closed loop is shown to have desirable closed loop properties that are almost global in each case. Several numerical examples, including one example in which the quadrotor recovers from being initially upside down and another example that includes switching and transitions between different flight modes, illustrate the versatility and generality of the proposed approach.
Safety-Critical Control for Quadrotor UAVs via Decentralized Navigation Functions
Universidad Politécnica de Madrid（马德里理工大学）；School of Science and Technology, IE University（IE大学科学与技术学院）；Centre for Automation and Robotics (CSIC-UPM)（自动化与机器人中心（西班牙国家科学研究委员会-马德里理工大学））
Groups of unmanned aerial vehicles (UAVs) are increasingly utilized in transportation task as the combined strength allows to increase the maximum payload. However, the resulting mechanical coupling of the UAVs impose new challenges in terms of the tracking control. Thus, we design a geometric trajectory tracking controller for the cooperative task of four quadrotor UAVs carrying and transporting a rigid body, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that …
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 …
Experimental flight tests are reported about quadrotors UAVs via a recent model-free control (MFC) strategy, which is easily implementable. We show that it is possible to achieve acrobatic rate control of the UAV, which is beyond the previous standard. The same remote controller is tested on two physical vehicles without any re-tuning. It produces in both cases low tracking error. We show that MFC is robust even when the quadrotor is highly damaged. A video footage can be found at: https://youtu.be/wtSLalA4szc
This paper investigates tracking controls for an arbitrary number of cooperating quadrotor unmanned aerial vehicles with a suspended rigid body payload. Assuming that a rigid body is connected to multiple quadrotors by rigid massless links, control systems for quadrotors are constructed such that the rigid body asymptotically follows a given desired position and attitude trajectory. These are developed in a coordinate-free fashion to avoid singularities and complexities associated with local parameterizations.
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 an…
This paper deals with the dynamics and controls of a quadrotor unmanned aerial vehicle that is connected to a fixed point on the ground via a tether. Tethered quadrotors have been envisaged for long-term aerial surveillance with high-speed communications. This paper presents an intrinsic form of the dynamic model of a tethered quadrotor including the coupling between deformations of the tether and the motion of the quadrotor, and it constructs geometric control systems to asymptotically stabilize the coupled dynamics of the quadrotor and the tether. The proposed global formulation of dynamics …
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 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 dir…
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 pr…
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…
This dissertation presents nonlinear tracking control systems for quadrotor unmanned aerial vehicles (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. Next, we derived a coordinate-free form of equations of motion for a complete model of a q…
This paper presents an equivariant reinforcement learning framework for quadrotor unmanned aerial vehicles. Successful training of reinforcement learning often requires numerous interactions with the environments, which hinders its applicability especially when the available computational resources are limited, or when there is no reliable simulation model. We identified an equivariance property of the quadrotor dynamics such that the dimension of the state required in the training is reduced by one, thereby improving the sampling efficiency of reinforcement learning substantially. This is ill…
Universitá del Salento（萨兰托大学）；CNRS（法国国家科学研究中心）；LAAS；Univ de Toulouse（图卢兹大学）
In this paper we present a maneuver regulation scheme for Vertical Take-Off and Landing (VTOL) micro aerial vehicles (MAV). Differently from standard trajectory tracking, maneuver regulation has an intrinsic robustness due to the fact that the vehicle is not required to chase a virtual target, but just to stay on a (properly designed) desired path with a given velocity profile. In this paper we show how a robust maneuver regulation controller can be easily designed by converting an existing tracking scheme. The resulting maneuvering controller has three main appealing features, namely it: (i) …
Manipulation and grasping with unmanned aerial vehicles (UAVs) currently require accurate positioning and are often executed at reduced speed to ensure successful grasps. This is due to the fact that typical UAVs can only accommodate rigid manipulators with few degrees of freedom, which limits their capability to compensate for disturbances caused by the vehicle positioning errors. Moreover, UAVs have to minimize external contact forces in order to maintain stability. Biological systems, on the other hand, exploit softness to overcome similar limitations, and leverage compliance to enable aggr…
In this paper, we study the quadrotor UAV attitude control on SO(3) in the presence of unknown disturbances and model uncertainties. L1 adaptive control for UAVs using Euler angles/quaternions is shown to exhibit robustness and precise attitude tracking in the presence of disturbances and uncertainties. However, it is well known that dynamical models and controllers that use Euler angle representations are prone to singularities and typically have smaller regions of attraction while quaternion representations are subject to the unwinding phenomenon. To avoid such complexities, we present a Geo…
This paper presents the design of a geometric trajectory tracking controller for the cooperative task of two quadrotor UAVs (unmanned aerial vehicles) carrying and transporting a rigid bar, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the rod exponentially tracks a given desired trajectory for its position and attitude, under some assumptions on initial error…
Using quadrotors UAVs for cooperative payload transportation using cables has been actively gaining interest in recent years. Understanding the dynamics of these complex multi-agent systems would help towards designing safe and reliable systems. In this work, we study one such multi-agent system comprising of multiple quadrotors transporting a flexible hose. We model the hose as a series of smaller discrete links and derive a generalized coordinate-free dynamics for the same. We show that certain configurations of this under-actuated system are differentially-flat. We linearize the dynamics us…
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 t…
