Suspended Load Path Tracking Control Using a Tilt-rotor UAV Based on Zonotopic State Estimation

This work addresses the problem of path tracking control of a suspended load using a tilt-rotor UAV. The main challenge in controlling this kind of system arises from the dynamic behavior imposed by the load, which is usually coupled to the UAV by means of a rope, adding unactuated degrees of freedom to the whole system. Furthermore, to perform the load transportation it is often needed the knowledge of the load position to accomplish the task. Since available sensors are commonly embedded in the mobile platform, information on the load position may not be directly available. To solve this problem in this work, initially, the kinematics of the multi-body mechanical system are formulated from the load's perspective, from which a detailed dynamic model is derived using the Euler-Lagrange approach, yielding a highly coupled, nonlinear state-space representation of the system, affine in the inputs, with the load's position and orientation directly represented by state variables. A zonotopic state estimator is proposed to solve the problem of estimating the load position and orientation, which is formulated based on sensors located at the aircraft, with different sampling times, and unknown-but-bounded measurement noise. To solve the path tracking problem, a discrete-time mixed $\mathcal{H}_2/\mathcal{H}_\infty$ controller with pole-placement constraints is designed with guaranteed time-response properties and robust to unmodeled dynamics, parametric uncertainties, and external disturbances. Results from numerical experiments, performed in a platform based on the Gazebo simulator and on a Computer Aided Design (CAD) model of the system, are presented to corroborate the performance of the zonotopic state estimator along with the designed controller

Multi-rotor with suspended load: System Dynamics and Control Toolbox

There is an increasing demand for Unmanned Aerial Systems (UAS) to carry suspended loads as this can provide significant benefits to several applications in agriculture, law enforcement and construction. The load impact on the underlying system dynamics should not be neglected as significant feedback forces may be induced on the vehicle during certain flight manoeuvres. The constant variation in operating point induced by the slung load also causes conventional controllers to demand increased control effort. Much research has focused on standard multi-rotor position and attitude control with and without a slung load. However, predictive control schemes, such as Nonlinear Model Predictive Control (NMPC), have not yet been fully explored. To this end, we present a novel controller for safe and precise operation of multi-rotors with heavy slung load in three dimensions. The paper describes a System Dynamics and Control Simulation Toolbox for use with MATLAB/SIMULINK which includes a detailed simulation of the multi-rotor and slung load as well as a predictive controller to manage the nonlinear dynamics whilst accounting for system constraints. It is demonstrated that the controller simultaneously tracks specified waypoints and actively damps large slung load oscillations. A linear-quadratic regulator (LQR) is derived and control performance is compared. Results show the improved performance of the predictive controller for a larger flight envelope, including aggressive manoeuvres and large slung load displacements. The computational cost remains relatively small, amenable to practical implementations

A Hybrid Control Approach for the Swing Free Transportation of a Double Pendulum with a Quadrotor

In this article, a control strategy approach is proposed for a system consisting of a quadrotor transporting a double pendulum. In our case, we attempt to achieve a swing free transportation of the pendulum, while the quadrotor closely follows a specific trajectory. This dynamic system is highly nonlinear, therefore, the fulfillment of this complex task represents a demanding challenge. Moreover, achieving dampening of the double pendulum oscillations while following a precise trajectory are conflicting goals. We apply a proportional derivative (PD) and a model predictive control (MPC) controllers for this task. Transportation of a multiple pendulum with an aerial robot is a step forward in the state of art towards the study of the transportation of loads with complex dynamics. We provide the modeling of the quadrotor and the double pendulum. For MPC we define the cost function that has to be minimized to achieve optimal control. We report encouraging positive results on a simulated environmentcomparing the performance of our MPC-PD control circuit against a PD-PD configuration, achieving a three fold reduction of the double pendulum maximum swinging angle.This work has been partially supported by FEDER funds through MINECO project TIN2017-85827-P, and project KK-202000044 of the Elkartek 2020 funding program of the Basque Government. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777720

비선형 최적화를 이용한 멀티로터 현수 운송의 경로 계획 및 제어 기법

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2021.8. 김현진.경로 계획과 제어는 안전하고 안정적으로 멀티로터를 운용하기 위해서 필수적인 요소이다. 충돌을 회피하며 효율적인 경로를 생성하고 이를 실제로 추종하기 위해서는 동역학 모델이 고려되어야 한다. 일반 멀티로터의 동역학 모델은 높은 차원을 가진 비선형식으로 표현되는데, 현수 운송 물체를 추가할 경우 계산이 더욱 복잡해진다. 본 논문은 멀티로터를 이용한 현수 운송에 있어 경로 계획과 제어에 대한 효율적인 기법을 제안한다. 첫 번째로 단일 멀티로터를 이용한 현수 운송을 다룬다. 물체가 별도의 엑츄에이터 없이 운송될 경우 물체는 기체의 움직임에 의해서만 제어가 가능하다. 하지만, 동역학식의 높은 비선형성으로 운용에 어려움이 존재한다. 이를 경감시키기 위해서 회전 동역학식의 비선형성을 줄이고 자세 제어에 존재하는 시간 지연을 고려하여 동역학식을 간소화한다. 경로 계획에 있어서는 충돌 회피를 위해 기체, 케이블, 그리고 운송 물체를 다른 크기와 모양을 가진 타원체들로 감싸며, 효과적이면서도 덜 보수적인 방식으로 충돌 회피 구속조건을 부과한다. Augmented Lagrangian 방법을 이용하여 비선형 구속조건이 부과된 비선형 문제를 실시간 최적화하여 경로를 생성한다. 생성된 경로를 추종하기 위해서 Sequential linear quadratic 솔버를 이용한 모델 예측 제어기로 최적 제어 입력을 계산한다. 제안된 기법은 여러 시뮬레이션과 실험을 통해 검증한다. 다음으로, 다중 멀티로터를 이용한 협업 현수 운송 시스템을 다룬다. 해당 시스템의 상태 변수나 동역학식에서 연결된(coupled) 항의 개수는 기체의 수에 비례하여 증가하기 때문에, 효과적인 기법 없이는 최적화에 많은 시간이 소요된다. 높은 비선형성을 가진 동역학식의 복잡성을 낮추기 위하여 미분 평탄성을 사용한다. 경로 또한 piece-wise Bernstein 다항식을 이용하여 매개변수화하여 최적화 변수의 개수를 줄인다. 최적화 문제를 분해하고 충돌 회피 구속조건들에 대해 볼록화(convexification)를 수행하여 운송 물체의 경로와 장력의 경로에 대한 볼록한(convex) 하위문제들이 만들어진다. 첫 번째 하위문제인 물체 경로 생성에서는, 장애물 회피와 멀티로터의 공간을 확보하기 위하여 안전 비행 통로(safe flight corridor, SFC)와 여유 간격 구속조건을 고려하여 최적화한다. 다음으로, 장력 벡터들의 경로는 장애물 회피와 상호 충돌을 방지하기 위하여 안전 비행 섹터(safe flight sector, SFS)와 상대 안전 비행 섹터(relative safe flight sector, RSFS) 구속조건을 부과하여 최적화한다. 시뮬레이션과 실험으로 복잡한 환경에서 효율적인 경로 계획 기법을 시연하며 검증한다.Trajectory generation and control are fundamental requirements for safe and stable operation of multi-rotors. The dynamic model should be considered to generate efficient and collision-free trajectories with feasibility. While the dynamic model of a bare multi-rotor is expressed non-linearly with high dimensions which results in computational loads, the suspended load increases the complexity further. This dissertation presents efficient algorithms for trajectory generation and control of multi-rotors with a suspended load. A single multi-rotor with a suspended load is addressed first. Since the load is suspended through a cable without any actuator, movement of the load must be controlled via maneuvers of the multi-rotor. However, the highly non-linear dynamics of the system results in difficulties. To relive them, the rotational dynamics is simplified to reduce the non-linearity and consider the delay in attitude control. For trajectory generation, the vehicle, cable, and load are considered as ellipsoids with different sizes and shapes, and collision-free constraints are expressed in an efficient and less-conservative way. The augmented Lagrangian method is applied to solve a nonlinear optimization problem with nonlinear constraints in real-time. Model predictive control with the sequential linear quadratic solver is used to track the generated trajectories. The proposed algorithm is validated with several simulations and experiment. A system with multiple multi-rotors for cooperative transportation of a suspended load is addressed next. As the system has more state variables and coupling terms in the dynamic equation than the system with a single multi-rotor, optimization takes a long time without an efficient method. The differential flatness of the system is used to reduce the complexity of the highly non-linear dynamic equation. The trajectories are also parameterized using piece-wise Bernstein polynomials to decrease the number of optimization variables. By decomposing an optimization problem and performing convexification, convex sub-problems are formulated for the load and the tension trajectories optimization, respectively. In each sub-problem, a light-weight sampling method is used to find a feasible and low-cost trajectory as initialization. In the first sub-problem, the load trajectory is optimized with safe flight corridor (SFC) and clearance constraints for collision avoidance and security of space for the multi-rotors. Then, the tension histories are optimized with safe flight sector (SFS) and relative safe flight sector (RSFS) constraints for obstacle and inter-agent collision avoidance. Simulations and experiments are conducted to demonstrate efficient trajectory generation in a cluttered environment and validate the proposed algorithms.Chapter 1 Introduction 1 1.1 Literature Survey 5 1.2 Contributions 9 1.3 Outline 10 Chapter 2 Single Multi-rotor with a Suspended Load 11 2.1 Dynamics 11 2.2 Trajectory Generation 23 2.3 Optimal Control 31 Chapter 3 Multiple Multi-rotors with a Suspended Load 36 3.1 Problem Setting 36 3.2 Load Trajectory Generation 45 3.3 Tension History Generation 54 Chapter 4 Experimental Validation 68 4.1 Single Multi-rotor with a Suspended Load 68 4.2 Multiple Multi-rotors with a Suspended Load 79 Chapter 5 Conclusion 100 Appendix A Detailed Derivation of Dierential Flatness 102 B Preliminaries of Bernstein Polynomials 108 B.1 Denition of a Bernstein Polynomial 108 B.2 Convex hull property of a Bernstein Polynomial 110 B.3 Representation of a General Polynomial with Bernstein Basis Polynomials 111 B.4 Representation of the Derivative of a Bernstein Polynomial with Bernstein Basis Polynomials 112 References 113 Abstract (in Korean) 119박

A review of aerial manipulation of small-scale rotorcraft unmanned robotic systems

Small-scale rotorcraft unmanned robotic systems (SRURSs) are a kind of unmanned rotorcraft with manipulating devices. This review aims to provide an overview on aerial manipulation of SRURSs nowadays and promote relative research in the future. In the past decade, aerial manipulation of SRURSs has attracted the interest of researchers globally. This paper provides a literature review of the last 10 years (2008–2017) on SRURSs, and details achievements and challenges. Firstly, the definition, current state, development, classification, and challenges of SRURSs are introduced. Then, related papers are organized into two topical categories: mechanical structure design, and modeling and control. Following this, research groups involved in SRURS research and their major achievements are summarized and classified in the form of tables. The research groups are introduced in detail from seven parts. Finally, trends and challenges are compiled and presented to serve as a resource for researchers interested in aerial manipulation of SRURSs. The problem, trends, and challenges are described from three aspects. Conclusions of the paper are presented, and the future of SRURSs is discussed to enable further research interests

Model Predictive Control for Micro Aerial Vehicles: A Survey

This paper presents a review of the design and application of model predictive control strategies for Micro Aerial Vehicles and specifically multirotor configurations such as quadrotors. The diverse set of works in the domain is organized based on the control law being optimized over linear or nonlinear dynamics, the integration of state and input constraints, possible fault-tolerant design, if reinforcement learning methods have been utilized and if the controller refers to free-flight or other tasks such as physical interaction or load transportation. A selected set of comparison results are also presented and serve to provide insight for the selection between linear and nonlinear schemes, the tuning of the prediction horizon, the importance of disturbance observer-based offset-free tracking and the intrinsic robustness of such methods to parameter uncertainty. Furthermore, an overview of recent research trends on the combined application of modern deep reinforcement learning techniques and model predictive control for multirotor vehicles is presented. Finally, this review concludes with explicit discussion regarding selected open-source software packages that deliver off-the-shelf model predictive control functionality applicable to a wide variety of Micro Aerial Vehicle configurations

Aerial navigation in obstructed environments with embedded nonlinear model predictive control

We propose a methodology for autonomous aerial navigation and obstacle avoidance of micro aerial vehicles (MAV) using nonlinear model predictive control (NMPC) and we demonstrate its effectiveness with laboratory experiments. The proposed methodology can accommodate obstacles of arbitrary, potentially non-convex, geometry. The NMPC problem is solved using PANOC: a fast numerical optimization method which is completely matrix-free, is not sensitive to ill conditioning, involves only simple algebraic operations and is suitable for embedded NMPC. A C89 implementation of PANOC solves the NMPC problem at a rate of 20Hz on board a lab-scale MAV. The MAV performs smooth maneuvers moving around an obstacle. For increased autonomy, we propose a simple method to compensate for the reduction of thrust over time, which comes from the depletion of the MAV's battery, by estimating the thrust constant

A System of Autonomously Flying Helicopters for Load Transportation

Die Arbeit beschreibt Entwurf, Umsetzung und Validierung eines autonomen Lastentransportsystems, welches auf Basis mehrerer Modellhubschrauber realisiert wurde. Abhängig von den Anforderungen der zu transportierenden Last kann die Anzahl der verwendeten Hubschrauber individuell angepasst werden. Die präsentierten Modelle und Regler wurden durch Computersimulationen und reale Flugversuche verifiziert. Zwei nichtlineare Modelle werden präsentiert: Ein Model für Konfigurationen bestehend aus einem Helikopter und einer Last (single-lift) und eines für Konfigurationen bestehend aus zwei bzw. mehreren Helikoptern und einer Last (dual- und multi-lift). Neben diesen komplexen Modellen werden vereinfachte Modelle vorgestellt, die für den Reglerentwurf verwendet werden. Ein generischer Orientierungsregler wird entwickelt, der für die Regelung aller beschriebenen Transportkonfigurationen verwendet werden kann. Durch die Nutzung dieses Reglers vereinfacht sich der Entwurf der Translationsregler erheblich. Drei Translationsregler werden beschrieben: Ein Regler für single-lift Konfigurationen, der eine aktive Unterdrückung von Lastschwingungen erlaubt, und ein verteilter Regler für multi-lift Konfigurationen. Weiterhin wird ein dual-lift Regler präsentiert, der eine Kombination der anderen Regler darstellt. Die Regler für dual- und multi-lift Konfigurationen verwenden keine mechanischen Hilfskonstrukte wie Abstandshalter. Die Position der Last wird durch die Orientierung des Seils, gemessen nahe dem Helikopterrumpf, bestimmt. Externe Störungen wie Windstöße können eine Eigenschwingung des Seils anregen, welche die ermittelte Lastposition verfälscht. Die Eigenschwingung des Seils sowie der Einfluss der verwendeten Messeinrichtung werden analysiert. Auf Basis dieser Analyse wird ein Lastbeobachter entwickelt und in mehreren Experimenten verifiziert. Dieser Lastbeobachter ist von essentieller Wichtigkeit für den sicheren Betrieb des Lastentransportsystems, insbesondere bei schlechten Wetterbedingungen. Die entwickelten nichtlinearen Modelle des Systems wie auch die Regler der single- und multi-lift Konfigurationen wurden durch Flugversuche validiert. Dabei hat das System bewiesen, dass es auch bei sehr schlechten Wetterbedingungen einsetzbar iThis work covers the design, realization and validation of an autonomous load transportation system, utilizing several small size helicopters. The number of participating helicopters is configurable for the described system, depending on the requirements of the transported load. The presented models and controllers have been validated in computer simulation and flight experiments. Two non-linear models are presented: One model covers single-lift and one model covers dual- and multi-lift configurations. Simplified models are introduced beside the complex models, which are utilized for the translation controller design. A generic orientation controller is presented, which is applicable for the control of all presented slung load configurations. The utilization of this controller significantly simplifies the design of the translation controllers. The independence from the actual slung load configuration is achieved through measurement of the rope force vector in the rope attachment point, which is located on the helicopter fuselage. Three translation controllers are described: A controller for single-lift configurations, which allows the active compensation of load oscillations and a distributed controller for multi-lift configurations. A dual-lift translation controller is presented, which resembles a combination of single- and multi-lift translation controller. The presented controllers for dual- or multi-lift configurations do not utilize auxiliary constructs, like spreader-bars. The position of the load is estimated from the measured orientation of the rope, close to the helicopter fuselage. External disturbances, like wind gusts, are able to stimulate internal oscillations of the rope, which disturb the estimated load position. The internal motion of the rope as well as the influence of the used measurement device are analyzed and a flexible rope model is presented. Based on the results a load motion observer is developed and validated in several experiments. This load motion observer is essential for the safe operation of the slung load system, especially during bad weather conditions. The derived non-linear models of the system as well as the proposed controllers for single- and multi-lift configurations have been validated in flight experiments. The system has been proven to be operable even in presence of adverse weather conditions