Control of a Quadrotor

The objective of this thesis is to investigate the use of commercial devices as user interfaces on a quadrotor and to investigate solutions to the problem of slung load control. A slung load is a uniform mass attached with a wire which is allowed to swing freely to the bottom of the quadrotor. The purpose of substituting the radio control (RC) controller with a commercial smartphone is that they are more easy to grasp and might therefore be easier to use for a novice than an RC controller. The existing radio control link does not exist on a smartphone so it was complemented by a wireless network connection via transmission control protocol (TCP) or user datagram protocol(UDP). The smartphone does not have the same interface as the RC controller either so the same functionalities were implemented by using the touch screen and the inertial measurement unit (IMU) of the smartphone. However, this requires altitude control since the lack of multitouch in Android does not allow several inputs at the same time, thus making it impossible to adjust the thrust as the pitch and roll is adjusted. Another commercial device that was investigated was a PlayStation 3R gamepad (PS3 gamepad), whose joysticks were very similar to the RC controller’s but its shape was smaller and more ergonomic. It also communicated via TCP or UDP over a wireless network connection. The purpose of slung load control is to reduce the oscillations of the slung load and its effect on the quadrotors flight performance, thus enabling it to handle heavier loads. The slung load control consisted of several subproblems; model of a slung load, altitude control, filtering of noisy sensors and the slung load control itself. These were all solved but the last one where the slung load control was not implemented on the quadrotor due to lack of time. The model of the slung load was done by letting the dynamics of two traversed simple pendulums approximate the slung load’s angular movement. The altitude control consists of a PID controller extended with anti-windup and bumpless transfer which is combined with a feedforward control of the tilt angle. The controller acts upon a low-pass filtered pressure sensor as a measurement signal and receives its setpoint from one of the commercial devices mentioned above. The low-pass filter of the pressure sensor is a second order Butterworth filter, whose purpose is to reduce noise and the impact of spikes induced by events in the surroundings

Exploiting Heterogeneity in Networks of Aerial and Ground Robotic Agents

By taking advantage of complementary communication technologies, distinct sensing functionalities and varied motion dynamics present in a heterogeneous multi-robotic network, it is possible to accomplish a main mission objective by assigning specialized sub-tasks to specific members of a robotic team. An adequate selection of the team members and an effective coordination are some of the challenges to fully exploit the unique capabilities that these types of systems can offer. Motivated by real world applications, we focus on a multi-robotic network consisting off aerial and ground agents which has the potential to provide critical support to humans in complex settings. For instance, aerial robotic relays are capable of transporting small ground mobile sensors to expand the communication range and the situational awareness of first responders in hazardous environments. In the first part of this dissertation, we extend work on manipulation of cable-suspended loads using aerial robots by solving the problem of lifting the cable-suspended load from the ground before proceeding to transport it. Since the suspended load-quadrotor system experiences switching conditions during this critical maneuver, we define a hybrid system and show that it is differentially-flat. This property facilitates the design of a nonlinear controller which tracks a waypoint-based trajectory associated with the discrete states of the hybrid system. In addition, we address the case of unknown payload mass by combining a least-squares estimation method with the designed controller. Second, we focus on the coordination of a heterogeneous team formed by a group of ground mobile sensors and a flying communication router which is deployed to sense areas of interest in a cluttered environment. Using potential field methods, we propose a controller for the coordinated mobility of the team to guarantee inter-robot and obstacle collision avoidance as well as connectivity maintenance among the ground agents while the main goal of sensing is carried out. For the case of the aerial communications relays, we combine antenna diversity with reinforcement learning to dynamically re-locate these relays so that the received signal strength is maintained above a desired threshold. Motivated by the recent interest of combining radio frequency and optical wireless communications, we envision the implementation of an optical link between micro-scale aerial and ground robots. This type of link requires maintaining a sufficient relative transmitter-receiver position for reliable communications. In the third part of this thesis, we tackle this problem. Based on the link model, we define a connectivity cone where a minimum transmission rate is guaranteed. For example, the aerial robot has to track the ground vehicle to stay inside this cone. The control must be robust to noisy measurements. Thus, we use particle filters to obtain a better estimation of the receiver position and we design a control algorithm for the flying robot to enhance the transmission rate. Also, we consider the problem of pairing a ground sensor with an aerial vehicle, both equipped with a hybrid radio-frequency/optical wireless communication system. A challenge is positioning the flying robot within optical range when the sensor location is unknown. Thus, we take advantage of the hybrid communication scheme by developing a control strategy that uses the radio signal to guide the aerial platform to the ground sensor. Once the optical-based signal strength has achieved a certain threshold, the robot hovers within optical range. Finally, we investigate the problem of building an alliance of agents with different skills in order to satisfy the requirements imposed by a given task. We find this alliance, known also as a coalition, by using a bipartite graph in which edges represent the relation between agent capabilities and required resources for task execution. Using this graph, we build a coalition whose total capability resources can satisfy the task resource requirements. Also, we study the heterogeneity of the formed coalition to analyze how it is affected for instance by the amount of capability resources present in the agents

Parameter-robust linear quadratic Gaussian technique for multi-agent slung load transportation

This paper copes with parameter-robust controller design for transportation system by multiple unmanned aerial vehicles. The transportation is designed in the form of string connection. Minimal state-space realization of slung-load dynamics is obtained by Newtonian approach with spherical coordinates. Linear quadratic Gaussian / loop transfer recovery (LQG/LTR) is implemented to control the position and attitude of all the vehicles and payloads. The controller's robustness against variation of payload mass is improved using parameter-robust linear quadratic Gaussian (PRLQG) method. Numerical simulations are conducted with several transportation cases. The result verifies that LQG/LTR shows fast performance while PRLQG has its strong point in robustness against system variation

Design and Demonstration of a Two-Dimentional Test Bed for UAV Controller Evaluation

A three degree-of-freedom (DOF) planar test bed for Unmanned Aerial Vehicle (UAV) controller evaluation was built. The test-bed consists of an instrumented tether and an experimental twin-rotor, planar UAV mounted with a one DOF manipulator mounted below the UAV body. The tether was constructed to constrain the UAV under test to motion on the surface of a sphere. Experiments can be conducted through the tether, approximating motion in a vertical plane by a UAV under test. The tether provides the means to measure the position and attitude of the UAV under test. The experimental twin-rotor UAV and one-link on-board manipulator, were designed and built to explore a unified control strategy for Manipulator on VTOL Aircraft (MOVA), in which the interaction of UAV body dynamics with the manipulator motion is of primary interest. The dynamics of the propulsion unit was characterized through experiments, based on which a phase lead compensator was designed to improve the UAV frequency response. A \u27separate\u27 controller based on independent nonlinear control of the VTOL aircraft and PD linear control of the on-board manipulator was designed as a reference for comparison to the unified MOVA controller. Tests with the separate controller show the negative effect that a coupled manipulator can have on the UAV body motion, while the tests on MOVA show the potential benefit of explicit compensation of the UAV and manipulator interaction

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

Adaptive Control For Autonomous Navigation Of Mobile Robots Considering Time Delay And Uncertainty

Autonomous control of mobile robots has attracted considerable attention of researchers in the areas of robotics and autonomous systems during the past decades. One of the goals in the field of mobile robotics is development of platforms that robustly operate in given, partially unknown, or unpredictable environments and offer desired services to humans. Autonomous mobile robots need to be equipped with effective, robust and/or adaptive, navigation control systems. In spite of enormous reported work on autonomous navigation control systems for mobile robots, achieving the goal above is still an open problem. Robustness and reliability of the controlled system can always be improved. The fundamental issues affecting the stability of the control systems include the undesired nonlinear effects introduced by actuator saturation, time delay in the controlled system, and uncertainty in the model. This research work develops robustly stabilizing control systems by investigating and addressing such nonlinear effects through analytical, simulations, and experiments. The control systems are designed to meet specified transient and steady-state specifications. The systems used for this research are ground (Dr Robot X80SV) and aerial (Parrot AR.Drone 2.0) mobile robots. Firstly, an effective autonomous navigation control system is developed for X80SV using logic control by combining ‘go-to-goal’, ‘avoid-obstacle’, and ‘follow-wall’ controllers. A MATLAB robot simulator is developed to implement this control algorithm and experiments are conducted in a typical office environment. The next stage of the research develops an autonomous position (x, y, and z) and attitude (roll, pitch, and yaw) controllers for a quadrotor, and PD-feedback control is used to achieve stabilization. The quadrotor’s nonlinear dynamics and kinematics are implemented using MATLAB S-function to generate the state output. Secondly, the white-box and black-box approaches are used to obtain a linearized second-order altitude models for the quadrotor, AR.Drone 2.0. Proportional (P), pole placement or proportional plus velocity (PV), linear quadratic regulator (LQR), and model reference adaptive control (MRAC) controllers are designed and validated through simulations using MATLAB/Simulink. Control input saturation and time delay in the controlled systems are also studied. MATLAB graphical user interface (GUI) and Simulink programs are developed to implement the controllers on the drone. Thirdly, the time delay in the drone’s control system is estimated using analytical and experimental methods. In the experimental approach, the transient properties of the experimental altitude responses are compared to those of simulated responses. The analytical approach makes use of the Lambert W function to obtain analytical solutions of scalar first-order delay differential equations (DDEs). A time-delayed P-feedback control system (retarded type) is used in estimating the time delay. Then an improved system performance is obtained by incorporating the estimated time delay in the design of the PV control system (neutral type) and PV-MRAC control system. Furthermore, the stability of a parametric perturbed linear time-invariant (LTI) retarded type system is studied. This is done by analytically calculating the stability radius of the system. Simulation of the control system is conducted to confirm the stability. This robust control design and uncertainty analysis are conducted for first-order and second-order quadrotor models. Lastly, the robustly designed PV and PV-MRAC control systems are used to autonomously track multiple waypoints. Also, the robustness of the PV-MRAC controller is tested against a baseline PV controller using the payload capability of the drone. It is shown that the PV-MRAC offers several benefits over the fixed-gain approach of the PV controller. The adaptive control is found to offer enhanced robustness to the payload fluctuations