Pre-specified Trajectory Research Articles

Robust sliding model control-based adaptive tracker for a class of nonlinear systems with input nonlinearities and uncertainties

A robust adaptive tracker is newly proposed for a class of nonlinear systems with input nonlinearities and uncertainties. Because the upper bounds of input nonlinearities and uncertainties are difficult to be acquired, the adaptive control integrated with sliding mode control (SMC) and radial basis function neural network (RBFNN) are utilized to cope with these undesired problems and effectively complete the robust tracker design. The main contributions are concluded as follows: (1) new sufficient conditions are obtained such that the proposed adaptive control laws can avoid overestimation; (2) A smooth [Formula: see text] function is introduced to eliminate the undesired chattering phenomenon in the traditional SMC systems; (3) A robust tracker is proposed such that the controlled system outputs can robustly track the pre-specified trajectories directly, even when subjected to unknown input nonlinearities and uncertainties. Finally, the numerical simulation results are illustrated to verify the proposed approach.

Adaptive region reaching control of fully actuated ocean surface vessels

ABSTRACT In this paper, region reaching controller is designed for fully actuated ocean surface vessels to reach a desired target region instead of a point. There are not the requirements for both the pre-specified trajectory outside the desired region and the desired pinpoint position inside the desired region. The controller design is based on the potential energy function, backstepping recursive design methodology, and the Lyapnov stability analysis theory. If the target region is specified arbitrarily small, the target region reduces to a point, and hence the region reaching control can be a generalisation of the setpoint control. Simulation results are presented to illustrate the performance of the proposed controller.

Lyapunov Based Robust Control for Tracking Control of Lower Limb Rehabilitation Robot with Uncertainty

This study designs a control of two-degree of freedom lower limb rehabilitation robot (LLRR) for the patient who needs the proper physical therapy after a spinal cord injury (SCI), stroke, or a surgical operation. The robot manipulator can perform specified passive exercises as well as copy exercise motions and perform them without the physiotherapist. Specifically, the uncertainties including the model uncertainty, initial condition deviation and the external disturbance are also considered. Firstly, a unilateral man-robot dynamical model is proposed based on Lagrange method. Then, we propose a Lyapunov based robust control to suppress the effect of uncertainties. The control algorithm consists of a PD feedback component and a piecewise function component. Theoretical analysis is provided to demonstrate that the controller can guarantee the uniform boundedness and uniform ultimate boundedness of the system. Moreover, the joint angle trajectory of a healthy person is explicitly obtained by the experimental platform and used as the pre-specified trajectory of the LLRR. Finally, numerical simulation is presented to illustrate the effectiveness and the trajectory-tracking control performance of the control.

Micro-UFO (Untethered Floating Object): A Highly Accurate Microrobot Manipulation Technique.

A new microrobot manipulation technique with high precision (nano level) positional accuracy to move in a liquid environment with diamagnetic levitation is presented. Untethered manipulation of microrobots by means of externally applied magnetic forces has been emerging as a promising field of research, particularly due to its potential for medical and biological applications. The purpose of the presented method is to eliminate friction force between the surface of the substrate and microrobot. In an effort to achieve high accuracy motion, required magnetic force for the levitation of the microrobot was determined by finite element method (FEM) simulations in COMSOL (version 5.3, COMSOL Inc., Stockholm, Sweden) and verified by experimental results. According to position of the lifter magnet, the levitation height of the microrobot in the liquid was found analytically, and compared with the experimental results head-to-head. The stable working range of the microrobot is between 30 µm to 330 µm, and it was confirmed in both simulations and experimental results. It can follow the given trajectory with high accuracy (<1 µm error avg.) at varied speeds and levitation heights. Due to the nano-level positioning accuracy, desired locomotion can be achieved in pre-specified trajectories (sinusoidal or circular). During its locomotion, phase difference between lifter magnet and carrier magnet has been observed, and relation with drag force effect has been discussed. Without using strong electromagnets or bulky permanent magnets, our manipulation approach can move the microrobot in three dimensions in a liquid environment.

Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system

ABSTRACTThis paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.

A generalised optimal linear quadratic tracker with universal applications – part 1: continuous-time systems

ABSTRACTThis paper presents a generalised optimal linear quadratic analog tracker (LQAT) with universal applications for the continuous-time (CT) systems. This includes: (1) a generalised optimal LQAT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQAT design for non-square non-minimum phase CT systems to achieve a minimum phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square CT system; and (4) a one-learning-epoch input-constrained iterative learning LQAT design for the repetitive CT system.

A generalised optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems

ABSTRACTContrastive to Part 1, Part 2 presents a generalised optimal linear quadratic digital tracker (LQDT) with universal applications for the discrete-time (DT) systems. This includes (1) a generalised optimal LQDT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQDT design for non-square non-minimum phase DT systems to achieve a minimum-phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square DT systems; and (4) a one-learning-epoch input-constrained iterative learning LQDT design for the repetitive DT systems.

Robotic Tower Crane Modeling and Control (RTCMC) with LQR-DRO and LQR-LEIC for Linear and Nonlinear Payload Swing Minimization

Fast and accurate positioning and swing minimization of payloads in large standing tall tower crane operation are challenging as well as conflicting tasks. Juggling the trolley back-and-forth manually by crane operator to suppress payload swing can make time consuming and cause fatigue and subsequently cause the crane collapse as well risk the whole working environment. Motivated by Robotic Tower Crane Modeling Control (RTCMC), this work investigates solutions where swing suppression is critical for highly nonlinear trolley-tower-payload crane operation and therefore this work proposes a range of issues in implementing RTCMC. Firstly, recent work of SimMechanics-visualized RTC model and its optimized mathematical linear model are briefly introduced for further controller designs. Secondly, to actively reject the disturbances caused by undesired source of inputs or unknown dynamics, LQR-Disturbance Rejection Observer (DRO) Control with Luenberger-based Extended State Observer is introduced. This research further examines the combination of error space approach with estimator, from which it is argued that the LQR-Estimator-Integral Control (LEIC) and LEIC-Antiwindup for linear model are necessary to achieve robust tracking. Finally, in order to achieve robust tracking control of highly nonlinear trolley translation-payload swing working environment fueled by wind disturbance, LQR-DRO control with torque compensator actuation is implemented on the interaction joints between trolley and payload cables. Proposed RTCMC demonstrated the ability to iteratively achieve desired trolley translation-loadswing geometry. Under this iterative method, all weighting Q-R matrices, Observer gains (L) matrix, and uncertainties gains have adapted to deferent input conditions until pre-specified trajectories of trolley-loadswing are achieved. Evidence of improvements in linear model controls using (LQR-DRO, LQR-LEIC, and LEIC-Antiwindup), and in nonlinear RTCMC using (LQR-DRO) are presented. Control solutions in this research focused on simplicity of implementation: general and straightforward reference-tracking control methods are preferred over Tower crane-tailored formulation. The benefit is that, the proposed RTCMC has potential applications to other types of crane operations and global crane research.

Admission Control for Multidimensional Workload input with Heavy Tails and Fractional Ornstein-Uhlenbeck Process

The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under suitable assumptions on the source arrival rate, the centered and scaled cumulative workload input process for the underlying processing system can be approximated by fractional Brownian motion. In many applications one is interested in the stabilization of the work inflow to the system by modifying the net input rate, using an appropriate admission control policy. In this paper we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a prespecified linear trajectory, uniformly over time. Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a d-dimensional stochastic differential equation driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the stochastic differential equation (averaged over the d-stations) is bounded uniformly for all times. In one special case of control policies, as time approaches ∞, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H &gt; ½.

Admission Control for Multidimensional Workload input with Heavy Tails and Fractional Ornstein-Uhlenbeck Process

The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under suitable assumptions on the source arrival rate, the centered and scaled cumulative workload input process for the underlying processing system can be approximated by fractional Brownian motion. In many applications one is interested in the stabilization of the work inflow to the system by modifying the net input rate, using an appropriate admission control policy. In this paper we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a prespecified linear trajectory, uniformly over time. Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a d-dimensional stochastic differential equation driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the stochastic differential equation (averaged over the d-stations) is bounded uniformly for all times. In one special case of control policies, as time approaches ∞, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H &amp;gt; ½.

Multigroup Equivalence Analysis for High-Dimensional Expression Data.

Hypothesis tests of equivalence are typically known for their application in bioequivalence studies and acceptance sampling. Their application to gene expression data, in particular high-dimensional gene expression data, has only recently been studied. In this paper, we examine how two multigroup equivalence tests, the F-test and the range test, perform when applied to microarray expression data. We adapted these tests to a well-known equivalence criterion, the difference ratio. Our simulation results showed that both tests can achieve moderate power while controlling the type I error at nominal level for typical expression microarray studies with the benefit of easy-to-interpret equivalence limits. For the range of parameters simulated in this paper, the F-test is more powerful than the range test. However, for comparing three groups, their powers are similar. Finally, the two multigroup tests were applied to a prostate cancer microarray dataset to identify genes whose expression follows a prespecified trajectory across five prostate cancer stages.

A Hierarchical Fuzzy Control Design for Indoor Mobile Robot

This paper presents a motion control for an autonomous robot navigation using fuzzy logic motion control and stereo vision based path-planning module. This requires the capability to maneuver in a complex unknown environment. The mobile robot uses intuitive fuzzy rules and is expected to reach a specific target or follow a prespecified trajectory while moving among unforeseen obstacles. The robot's mission depends on the choice of the task. In this paper, behavioral-based control architecture is adopted, and each local navigational task is analyzed in terms of primitive behaviors. Our approach is systematic and original in the sense that some of the fuzzy rules are not triggered in face of critical situations for which the stereo vision camera can intervene to unblock the mobile robot.

Vision-based adaptive prediction, planning, and execution of permissible and smooth trajectories for a 2DOF model helicopter

Vision-based control of Unmanned Aerial Vehicles (UAV) is gaining a global interest. Recent quantum leaps in the development of fast image acquisition–processing tools are making vision sensors omnipresent. Information obtained from the on-board imaging sensor of a UAV can be used for mapping the environment, localizing the UAV, visual odometry, and tracking pre-specified trajectories and (or) way points. The information obtained through vision sensors can be either fused with those obtained from a GPS or can be used in GPS-deprived scenarios such as indoor applications. A vision-based control strategy based on an adaptive prediction, planning, and execution framework is proposed with the objective to smoothly servo–track an object in near optimal time. A class of C2 continuous quintic polynomial based trajectories is planned at a higher level first taking the maximum permissible acceleration of the flyer into account. At a lower level, a Linear Quadratic regulator is used to track the planned trajectory. The replanning is carried out under two conditions: (i) when the flyer fails in tracking the planned trajectory closely, or (ii) the target object to track starts moving. This framework was tested on a 2 degrees of freedom model helicopter equipped with an on-board pinhole perspective camera via simulations.

Nonstationary LPV control for trajectory tracking: a double pendulum example

This article focusses on the implementation of recently developed nonstationary linear-parameter varying (NSLPV) control algorithms for the regulation of nonlinear systems about pre-specified trajectories. The trajectories of interest eventually settle into periodic orbits, and hence are duly called eventually periodic trajectories. Parameterising the nonlinear system equations about such trajectories results in eventually periodic NSLPV models, and then NSLPV controllers are designed for these models to ensure accurate trajectory tracking despite various disturbances and uncertainties. These control algorithms will be applied to control a double pendulum where a vessel containing fluid is rigidly attached to the end of the second link of the pendulum. The mass of the fluid varies in time and, together with its rate of variation, is available for measurement during plant operation.

Global trajectory tracking through output feedback for robot manipulators with bounded inputs

In this work, a globally stabilizing output feedback scheme for the trajectory tracking of robot manipulators with bounded inputs is proposed. It achieves the motion control objective avoiding input saturation and excluding velocity measurements. Moreover, it is not defined using a specific sigmoidal function, but any one on a set of saturation functions. Consequently, the proposed scheme actually constitutes a family of globally stabilizing output feedback bounded controllers. Furthermore, the control gains are not tied to satisfy any saturation-avoidance inequality and may consequently take any positive value, which may be considered beneficial for performance adjustment/improvement purposes. Further, a class of desired trajectories that may be globally tracked avoiding input saturation and excluding velocity measurements is completely characterized. Global asymptotic stabilization of the closed-loop system solutions towards the pre-specified desired trajectory is proved through a strict Lyapunov function. The efficiency of the proposed scheme is corroborated through experimental results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Global Trajectory Tracking Through Output Feedback for Robot Manipulators With Input Saturations

Abstract In this work, a globally stabilizing output feedback scheme for the motion control of robot manipulators with bounded inputs is proposed. It achieves the trajectory tracking goal avoiding input saturation and excluding velocity measurements. Moreover, it is not defined using a specific sigmoidal function, but any one on a set of saturation functions. Consequently, the proposed algorithm actually constitutes a family of globally stabilizing output feedback bounded controllers. Furthermore, the bound of such saturation functions is explicitly considered in their definition. Hence, the control gains are not tied to satisfy any saturation-avoidance inequality and may consequently take any positive value, which may be considered beneficial for performance adjustment/improvement purposes. Further, a class of desired trajectories that may be globally tracked avoiding input saturation and excluding velocity measurements is completely characterized. Global uniform asymptotic stabilization of the closed-loop system solutions towards the pre-specified desired trajectory is proved through a strict Lyapunov function. The efficiency of the proposed scheme is corroborated through experimental results.

A brain-actuated wheelchair: Asynchronous and non-invasive Brain–computer interfaces for continuous control of robots

Objective To assess the feasibility and robustness of an asynchronous and non-invasive EEG-based Brain–Computer Interface (BCI) for continuous mental control of a wheelchair. Methods In experiment 1 two subjects were asked to mentally drive both a real and a simulated wheelchair from a starting point to a goal along a pre-specified path. Here we only report experiments with the simulated wheelchair for which we have extensive data in a complex environment that allows a sound analysis. Each subject participated in five experimental sessions, each consisting of 10 trials. The time elapsed between two consecutive experimental sessions was variable (from 1 h to 2 months) to assess the system robustness over time. The pre-specified path was divided into seven stretches to assess the system robustness in different contexts. To further assess the performance of the brain-actuated wheelchair, subject 1 participated in a second experiment consisting of 10 trials where he was asked to drive the simulated wheelchair following 10 different complex and random paths never tried before. Results In experiment 1 the two subjects were able to reach 100% (subject 1) and 80% (subject 2) of the final goals along the pre-specified trajectory in their best sessions. Different performances were obtained over time and path stretches, what indicates that performance is time and context dependent. In experiment 2, subject 1 was able to reach the final goal in 80% of the trials. Conclusions The results show that subjects can rapidly master our asynchronous EEG-based BCI to control a wheelchair. Also, they can autonomously operate the BCI over long periods of time without the need for adaptive algorithms externally tuned by a human operator to minimize the impact of EEG non-stationarities. This is possible because of two key components: first, the inclusion of a shared control system between the BCI system and the intelligent simulated wheelchair; second, the selection of stable user-specific EEG features that maximize the separability between the mental tasks. Significance These results show the feasibility of continuously controlling complex robotics devices using an asynchronous and non-invasive BCI.

Control of nonstationary LPV systems

This paper considers control of nonstationary linear parameter-varying systems, and is motivated by interest in the control of nonlinear systems along prespecified trajectories. In the paper, synthesis conditions are derived for such systems using an operator theoretical framework with the ℓ 2 induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semi-definite programming problem. The paper concludes with an in-depth example on the control of a two-thruster hovercraft along an eventually periodic trajectory.

English

A trajectory correction flight control system is small and durable, and consists of a lateralpulsejet ring mounted on the rocket body. The pulsejet ring consists of a finite number of individualpulsejets. Each pulsejet on the ring imparts a single, short-duration, large force to the rocket inthe plane normal to the rocket axis of symmetry. Lateral pulsejets are used by flight controlsystem to assist the rocket to follow a pre-specified (command) trajectory. The trajectory-trackingflight control system computes the position error by comparing the measured position of therocket with the pre-specified trajectory. In actual application, the position of the rocket couldbe measured using in-house inertial measurement unit (IMU) or by ground-based-tracking radarsystem located at the firing site. A study has been undertaken to explore the feasibility of reducingthe impact point dispersion of a routinely-used artillery rocket using lateral pulsejets coupledto a trajectory correction flight control system. Simulation studies have been conducted to arriveat tuning parameters, namely the tracking error window size, the required elapsed time betweenthe pulsejet firings and the angle of tolerance between the tracking error and the individualpulsejet force. Further, the robustness of the methodology wrt measurement noise has also beenevaluated.Defence Science Journal, 2008, 58(1), pp.15-33, DOI:http://dx.doi.org/10.14429/dsj.58.1621

Robust linear time-varying control for trajectory tracking: computation and an experimental application

This paper provides computational and experimental verification of the use of recently developed linear time-varying (LTV) robust control synthesis methods for controlling systems along prespecified trajectories. The linearization of system dynamics along trajectories yield LTV systems, and we compute and design robust controllers with respect to such linearizations. The techniques employed require the computation of potentially large linear matrix inequalities and complexity reduction using new model reduction for LTV systems is also demonstrated.