Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

Control of a class of multibody underactuated mechanical systems with discontinuous friction using sliding-mode

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper studies sliding-mode control of a class of multibody underactuated systems with discontinuous friction presenting on the unactuated configuration variable with consideration of parametric uncertainties. Global motion for this class system including sticking, stick-slip, and slip regimes are analyzed, and their corresponding equilibria are identified. Our control objective is to avoid the sticking and stick-slip regimes while track a desired velocity in the slip regime. The proposed sliding-mode controllers are robust to parametric uncertainties, and their stabilities are proved by using the Lyapunov direct method. Two examples, a mass-spring-damping system and a drill-string system, are used to demonstrate the validity of the proposed controllers.The author(s) received no financial support for the research, authorship, and/or publication of this articl

Robust trajectory tracking control for unmanned surface vessels under motion constraints and environmental disturbances

To achieve a fully autonomous navigation for unmanned surface vessels (USVs), a robust control capability is essential. The control of USVs in complex maritime environments is rather challenging as numerous system uncertainties and environmental influences affect the control performance. This paper therefore investigates the trajectory tracking control problem for USVs with motion constraints and environmental disturbances. Two different controllers are proposed to achieve the task. The first approach is mainly based on the backstepping technique augmented by a virtual system to compensate for the disturbance and an auxiliary system to bound the input in the saturation limit. The second control scheme is mainly based on the normalisation technique, with which the bound of the input can be limited in the constraints by tuning the control parameters. The stability of the two control schemes is demonstrated by the Lyapunov theory. Finally, simulations are conducted to verify the effectiveness of the proposed controllers. The introduced solutions enable USVs to follow complex trajectories in an adverse environment with varying ocean currents

Comprehensive review on controller for leader-follower robotic system

985-1007This paper presents a comprehensive review of the leader-follower robotics system. The aim of this paper is to find and elaborate on the current trends in the swarm robotic system, leader-follower, and multi-agent system. Another part of this review will focus on finding the trend of controller utilized by previous researchers in the leader-follower system. The controller that is commonly applied by the researchers is mostly adaptive and non-linear controllers. The paper also explores the subject of study or system used during the research which normally employs multi-robot, multi-agent, space flying, reconfigurable system, multi-legs system or unmanned system. Another aspect of this paper concentrates on the topology employed by the researchers when they conducted simulation or experimental studies

Upravljanje pozicijom električki pokretanog brzog površinskog vozila korištenjem unaprijedne projekcije izlazne povratne veze

Robust tracking is an issue of vital practical importance to the ship This paper addresses the design of a trajectory tracking controller for fast underactuated ships in the presence of model uncertainties without velocity measurements in the yaw and surge directions. An observer-based trajectory tracking controller is proposed for the fast underactuated ship model. Then, the dynamic surface control approach is effectively exploited to propose a tracking controller considering the actuator dynamics. Adaptive robust techniques are also adopted to cope with the parametric and non-parametric uncertainties in the fast underactuated ship model. A Lyapunov-based stability analysis is utilised to guarantee that tracking and state estimation errors are uniformly ultimately bounded. Simulation results are presented to illustrate the feasibility and efficiency of the proposed controller.Robusno praćenje je pitanje od vitalnog praktičnog značaja za brod. Ovaj se rad bavi projektiranjem regulatora za praćenje trajektorije za brze podaktuirane brodove s modelima nesigurnosti bez mjerenja brzine u smjerovima zaošijanja i uzdužnog napredovanja. Regulator za praćenje putanje zasnovan na observeru predložen je za brz podaktuiran model broda. Upravljanje površinskom dinamikom je učinkovito iskorišteno kako bi se predložio regulatora za praćenje trajektorije s obzirom na dinamiku aktuatora. Također su primjenjene adaptivne robusne tehnike kako bi se nosile sa parametarskim i neparametarskim nesigurnostima u modelu brzog podaktuiranoga broda. Analiza stabilnosti temeljena na Lyapunovu se koristi kako bi se zajamčilo da se pogreške praćenja i estimacije stanja adaptivne robusne tehnike također usvajaju kako bi se nosile s parametarskim i neparametarskim nesigurnostima u brzom neaktivnom brodskom modelu. Analiza stabilnosti temeljena na Lyapunovu se koristi kako bi se zajamčilo da su pogreške praćenja i procjene stanja jednoliko konačno ograničene. Prikazani su simulacijski rezultati koji ilustriraju izvedivost i učinkovitost predloženog regulatora

ETC-based control of underactuated AUVs and AUV formations in a 2D plane

This master thesis is aimed at single auv (autonomous underwater vehicle) and auv formation control in two-dimensional horizontal plane. For sake of increasing services life and saving communication resources, event-triggered mechanism is taken into consideration. two coordinate systems are introduced: earth-fixed frame and body-fixed frame. Some motion parameters and force analysis are used in the process of establishing mathematical model. then the related theorems, lemmas and control method commonly used in analyzing control systems are introduced. then, the auv control system is divided into two subsystems with cascade relationship. considering each subsystem separately, a controller is designed that can simultaneously carry out trajectory tracking and point stabilization. considering the service life of actuator equipment, an event-triggered controller was designed, which can reduce the frequency of actuator adjustment, prolong the service life of equipment. finally, combining the idea of light-of-sight method and virtual structure method, the auv formation tracking control problem is solved similarly to single auv. in deep sea conditions, an event- triggered communicating mechanism is designed to reduce the frequency of communication and adapt to limited communication resources, which balances the reliability and economy. matlab simulink is used to simulate the controller designed in the thesis, and confirms the feasibility of the controller

Experimental Validation Of An Integrated Guidance And Control System For Marine Surface Vessels

Autonomous operation of marine surface vessels is vital for minimizing human errors and providing efficient operations of ships under varying sea states and environmental conditions which is complicated by the highly nonlinear dynamics of marine surface vessels. To deal with modelling imprecision and unpredictable disturbances, the sliding mode methodology has been employed to devise a heading and a surge displacement controller. The implementation of such a controller necessitates the availability of all state variables of the vessel. However, the measured signals in the current study are limited to the global X and Y positioning coordinates of the boat that are generated by a GPS system. Thus, a nonlinear observer, based on the sliding mode methodology, has been implemented to yield accurate estimates of the state variables in the presence of both structured and unstructured uncertainties. Successful autonomous operation of a marine surface vessel requires a holistic approach encompassing a navigation system, robust nonlinear controllers and observers. Since the overwhelming majority of the experimental work on autonomous marine surface vessels was not conducted in truly uncontrolled real-world environments. The first goal of this work was to experimentally validate a fully-integrated LOS guidance system with a sliding mode controller and observer using a 16’ Tracker Pro Guide V-16 aluminium boat with a 60 hp. Mercury outboard motor operating in the uncontrolled open-water environment of Lake St. Clair, Michigan. The fully integrated guidance and controller-observer system was tested in a model-less configuration, whereby all information provided from the vessel’s nominal model have been ignored. The experimental data serves to demonstrate the robustness and good tracking characteristics of the fully-integrated guidance and controller/observer system by overcoming the large errors induced at the beginning of each segment and converging the boat to the desired trajectory in spite of the presence of environmental disturbances. The second focus of this work was to combine a collision avoidance method with the guidance system that accounted for “International Regulations for Prevention of Collisions at Sea” abbreviated as COLREGS. This new system then needed to be added into the existing architecture. The velocity obstacles method was selected as the base to build upon and additional restrictions were incorporated to account for these additional rules. This completed system was then validated with a software in the loop simulation

Formation control of underactuated ships with elliptical shape approximation and limited communication ranges

Based on the recent theoretical development for formation control of multiple fully actuated agents with an elliptical shape in Do (2012), this paper develops distributed controllers that force a group of NN underactuated ships with limited communication ranges to perform a desired formation, and guarantee no collisions between any ships in the group. The ships are first fitted to elliptical disks for solving collision avoidance. A coordinate transformation is then proposed to introduce an additional control input, which overcomes difficulties caused by underactuation and off-diagonal terms in the system matrices. The control design relies on potential functions with the separation condition between elliptical disks and the smooth or pp-times differentiable step functions embedded in

Experimental Validation Of A Robust Surge Speed Controller For Marine Surface Vessels

The focus of the current work is on providing experimental validation for the robust performance and good tracking characteristic of a surge speed controller for autonomous piloting of an under-actuated 16 ft boat in the completely uncontrolled setting of open-water Lake Saint Clair, Michigan. The controller is designed based on the sliding mode methodology and completely ignores the dynamics of the marine surface vessel (MSV) in its formulation. The testing was conducted under considerable unstructured uncertainties and unpredictable environmental disturbances induced by waves, sea-currents, and wind. The experimental results serve to validate the robust tracking characteristic of the controller and prove the successful implementation of the controller without prior knowledge of the system dynamics; thus, yielding a robust model-less controller