Optimal Control of Multiple Quadrotors for Transporting a Cable Suspended Payload

In this thesis, the main aim is to improve the flight control performance for a cable suspended payload with single and two quadrotors based on optimised control techniques. The study utilised optimal controllers, such as the Linear Quadratic Regulator LQR, the Iterative based LQR (ILQR), the Model Predictive Control MPC and the dynamic game controller to solve tracking control problems in terms of stabilisation, accuracy, constraints and collision avoidance. The LQR control was applied to the system as the first control method and compared with the classical Proportional-Derivative controller PD. It was used to achieve the load path tracking performance for single and two quadrotors with a cable slung load. The second controller was ILQR, which was developed based on the LQR control method to deal with the model nonlinearity. The MPC technique was also applied to the linearised nonlinear model LMPC of two quadrotors with a payload suspended by cables and compared with a nonlinear MPC (NMPC). Both MPC controllers LMPC and NMPC considered the constraints imposed on the system states and control inputs. The dynamic game control method was developed based on an incentive strategy for a leader-follower framework with the consideration of different optimal cost functions. It was applied to the linearised nonlinear model. Selecting these control techniques led to a number of achievements. Firstly, they improved the system performance in terms of achieving the system stability and reducing the steady-state errors. Secondly, the system parameter uncertainties were taken into consideration by utilising the ILQR controller. Thirdly, the MPC controllers guaranteed the handling of constraints and external disturbances in linear and nonlinear systems. Finally, avoiding collision between the leader and follower robots was achieved by applying the dynamic game controller. The controllers were tested in MATLAB simulation and verified for various desired predefined trajectories. In real experiments, these controllers were used as high-level controllers, which produce the optimised trajectory points. Then a low-level controller (PD controller) was used to follow the optimised trajectory points

Data-driven system identification and model predictive control of a multirotor with an unknown suspended payload

Thesis (MEng)--Stellenbosch University, 2022.ENGLISH ABSTRACT: This thesis considers the problem of stabilised control for a multirotor with an unknown suspended payload. The swinging payload negatively affects the multirotor flight dynamics by inducing oscillations in the system. An adaptive control architecture is proposed to damp these oscillations and produce stable flight with different unknown payloads. The architecture includes a data-driven system identification method that assumes no prior knowledge of the payload dynamics. This method is demonstrated in simulation and with practical flight data. Model Predictive Control (MPC) is applied for swing damping control and is verified with Hardware-in-the-Loop (HITL) simulations. A parameter estimator and Linear Quadratic Regulator (LQR) is used as a baseline control architecture. The LQR uses a predetermined model of the system, which is completed with estimates of the payload mass and cable length. The newly proposed architecture uses Dynamic Mode Decomposition with Control (DMDc) to estimate a linear state-space model and approximate the dynamics without using a predetermined model. The architecture was also tested with a Hankel Alternative View Of Koopman (HAVOK) algorithm which was extended in this work to account for control. An MPC uses the data-driven model to control the multirotor and damp the payload oscillations. A Simulink™ simulator was designed and verified with practical data. Within simulations both the baseline and proposed architectures produced near swing-free control with different payload masses and cable lengths. Even with a dynamic payload producing irregular oscillations, both methods achieved stabilised control. Both architectures also showed effective disturbance rejection. Despite the baseline method using an accurate predetermined model, the proposed method produced equal performances without prior knowledge of the dynamics. The baseline performance degraded significantly with a changed multirotor mass because this parameter was not considered as an unknown. In contrast, the proposed method consistently produced good performances. The accuracy of the DMDc models was verified with practical flight data. The proposed control architecture was also demonstrated in HITL simulations. The hardware executed the MPC at the desired frequency, producing near swing-free control within a Gazebo simulator. Overall, it was shown that the proposed control architecture is practically feasible. Without knowledge of the payload dynamics, a data-driven model can be used with MPC for effective swing damping control with a multirotor.AFRIKAANSE OPSOMMING: Hierdie tesis hanteer die probleem van gestabiliseerde beheer vir ’n multirotor hommeltuig met ’n onbekende hangende loonvrag. Die swaaiende loonvrag be¨ınvloed die vlugdin amika deur ossillasies in die stelsel te veroorsaak. ’n Aanpasbare beheerargitektuur word voorgestel om hierdie ossillasies te demp vir stabiele vlugte met verskillende onbekende loonvragte. Die argitektuur maak gebruik van ’n datagedrewe stelsel-identifikasiemetode wat geen voorafkennis van die loonvragdinamika gebruik nie. Hierdie metode word in simulasies en met praktiese vlugdata gedemonstreer. Model Voorspellende Beheer (MVB) word toegepas vir swaaidempingsbeheer en word geverifieer met Hardeware-in-die-Lus (HIDL) simulasies. ’n Parameter-afskatter en Lineˆere Kwadratiese Gaussiese (LKG) word in die basislyn beheerargitektuur gebruik. Die LKG gebruik ’n voorafbepaalde model van die sisteem wat voltooi word met afskattings van die loonvragmassa en kabellengte. Die nuwe voorgestelde argitektuur gebruik Dinamiese Modus Ontbinding met beheer (DMOb) om ’n lineˆere toestand-ruimte model te bereken en die dinamika af te skat sonder ’n voorafbepaalde model. Die argitektuur is ook getoets met ’n Hankel Alternatiewe Siening van Koopman (HASK)-algoritme wat in hierdie werk uitgebrei is om beheer in te sluit. ’n MVB gebruik die data-gedrewe model om die multirotor te beheer en die loonvrag se ossillasies te demp. ’n Simulink™-simululeerder is ontwerp en geverifieer met praktiese data. In simulasies het beide die basislyn en voorgestelde argitekture byna-swaaivrye beheer met verskillende loon vragmassas en kabellengtes geproduseer. Selfs met ’n dinamiese loonvrag wat onre¨elmatige ossillasies voortbring, het beide metodes gestabiliseerde beheer tot gevolg gehad. Beide ar gitekture het ook effektiewe versteuringsverwerping getoon. Al gebruik die basislynmetode ’n akkurate voorafbepaalde model, het die voorgestelde metode gelyke prestasies gelewer sonder voorafkennis van die dinamika. Die basislyn prestasie het aansienlik afgeneem vir ’n aangepaste multirotormassa omdat hierdie parameter nie as ’n onbekende beskou is nie. Daarteenoor het die voorgestelde metode deurgaans goeie prestasies gelewer. Die akkuraatheid van die DMOb modelle is geverifieer met praktiese vlugdata. Die voorgestelde beheerargitektuur is ook in HIDL-simulasies gedemonstreer. MVB is teen die verlangde frekwensie uitgevoer en het byna-swaaivrye beheer in ’n Gazebo-simululeerder gelewer. In die geheel is dit gewys dat die voorgestelde beheerargitektuur prakties uitvoerbaar is. Sonder kennis van die loonvragdinamika kan ’n data-gedrewe model met MVB gebruik word vir effektiewe swaaidempingsbeheer met ’n multirotor.Master