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Currently, additive manufacturing is utilized to fabricate many different actuators suited for soft robots. However, an effective controller paradigm is essential to benefit from the advantages of soft robots in terms of power consumption, production costs, weight, and safety while operating near living systems. In this work, an artificial muscle is additively manufactured with soft silicone elastomer material capable of demonstrating several levels of stiffness. The 3D-printed muscle is equipped with carbon fibers to receive a stimulus signal and develop a programmable joint that can present different stiffnesses. A nonlinear controller is developed to autonomously control the variable stiffness joint based on a reinforcement learning algorithm. The controller exhibits a slight increase in settling time; however, it demonstrates a decrease in fluctuation amplitude by 33% and a substantial reduction in power consumption by 41% in comparison to the optimized proportional integral derivative controller. At the same time, it is adaptable to and reliable in new conditions. The variable stiffness muscle is also used as a controllable mechanism to suppress the low frequency vibration. The study shows that the muscle can successfully attenuate the vibration autonomously when it is increased.
A new OMA method to perform structural dynamic identification: numerical and experimental investigation
Product(s):
Shake Table IIAbstract
Operational modal analysis (OMA) methods are nowadays common in civil, mechanical and aerospace engineering to identify and monitor structural systems without any knowledge on the structural excitation provided that the latter is due to ambient vibrations. For this reason, OMA methods are embedded with stochastic concepts and then it is difficult for users that have no-knowledge in signal analysis and stochastic dynamics. In this paper an innovative method useful for structural health monitoring (SHM) is proposed. It is based on the signal filtering and on the Hilbert transform of the correlation function matrix. Specifically, the modal shapes are estimated from the correlation functions matrix of the filtered output process and then the frequencies and the damping ratios are estimated from the analytical signals of the mono-component correlation functions: a complex signals in which the real part represents the correlation function and the imaginary part is its Hilbert transform. This method is very simple to use since requires only few interactions with the users and thus it can be used also from users that are not experts in the aforementioned areas. In order to prove the reliability of the proposed method, numerical simulations and experimental tests are reported also considering comparisons with the most popular OMA methods.
A Portable Real-Time Test Bench for Dielectric Elastomer Actuators
Abstract
Recently, a significant amount of research has been devoted to soft robots. Artificial muscles belong to the most important components of soft robots. Dielectric elastomer actuators (DEAs) represent the technology that comes closest to the capabilities of a natural muscle, making them the best candidates for artificial muscles in robotics and prosthetics applications. To develop these applications, an analysis of DEAs in a test bench must be possible. It is important that the environmental conditions are known, and all components are specified, which is not the case in most publications. This paper focuses on the development of a real-time test bench for DEAs which provides environmental conditions and all components that are specified. Its goal is to open up the research field of dielectric elastomer actuators or soft robots. The stacked DEA used is powered by a high-voltage amplifier, which can be controlled via a real-time block diagram environment together with a data acquisition (DAQ) device. The response of the actuator is measured with a laser triangulation sensor. Furthermore, information about the applied voltage, the operating current, the temperature, and the humidity are collected. It was demonstrated that the selected laser sensor is a suitable device for this application. Moreover, it was shown that the selected high-voltage amplifier is adequate to power a DEA. However, the DAQ is not fast enough to measure the actuator current. It was demonstrated that housing keeps environmental conditions constant, is transportable, and offers the flexibility to investigate different DEAs.
A practical study of active disturbance rejection control for rotary flexible joint robot manipulator
Product(s):
Rotary Flexible JointAbstract
This research presents a practical study of active disturbance rejection control law (ADRC) for the control of robotic manipulators in the presence of uncertainties. The control objective of the proposed control law is to track the trajectory accurately and rejects the disturbance caused by robotic manipulators. First, Euler Lagrange’s equations are used to model the dynamic behavior of a rotary flexible joint manipulator system (RFJMS). Secondly, the ADRC is designed for the rejection of lump disturbances (modeling uncertainties, nonlinearities, and external disturbances) of the manipulator; to estimate the lump disturbances a fifth-order extended state observer is constructed. Furthermore, a state error feedback control law with disturbance compensation is designed, which needs only a few control parameters to be adjusted. Furthermore, we demonstrate the robustness and effectiveness of the proposed control law by comparing the experimental results with those of LQR and PID. Experimental results show that high precision position control as well as vibration suppression can be achieved with the proposed controller, which is superior to LQR and PID controllers. In spite of uncertainties and nonlinearity of the flexible joint, QUANSER's RFJMS exhibits excellent tracking behavior and disturbance rejection.
A Stretchable Filament Sensor with Tunable Sensitivity for Wearable Robotics and Healthcare Applications
Product(s):
QPIDe Data Acquisition DeviceAbstract
Taking a leaf out of evolutionary biology, soft robots have begun to utilize compliant materials and structures for improved interactions with humans and complex environments. However, these advances have not been followed closely by sensing mechanisms. Biology has had a head start on the development of advanced sensing systems. The human body and its skeletal muscles can tune their morphologies to interact with the surrounding environment. Inspired by such biological systems, this paper introduces a novel hydraulic soft filament sensor (SFS) with tunable sensitivity. The SFS is a type of hydraulic pressure-based tubular strain sensor, which has a sensing core made of a soft and stretchable micro-sized filament filled with incompressible fluid where its inner hydraulic pressure is changed with strain. The SFS can be customized to form a wide range of configurations such as a long fiber or a skin-like structure. To demonstrate the SFS capability, different configurations for the SFS are fabricated and experimentally validated. The scalable and tunable nature of the SFS makes it suitable for a wide range of wearable and medical applications.
A study of stabilization quanser linear inverted pendulum with MATLAB Simulink
Product(s):
Linear Servo Base Unit with Inverted PendulumAbstract
Inverted pendulum is a classical topic in control study. It is considered to be a good practice choice in studying stabilization control. The objective of this study is to balance the inverted vertical position of a pendulum. The pendulum can rotate about a point residing on a cart which can move linearly horizontally. Using Linear Quadratic Regulator methods, this research aims to determine the suitable state feedback controller. The experiment used the Quanser Linear Inverted Pendulum platform and MATLAB Simulink 2018A to gather the data. The feedback gain controller value was found to be K=[ -50.0 115.8391 -41.2611 21.5454] and compared between the simulation and the real-time data. With the feedback controller, the pendulum was balanced in the vertical inverted position by controlling the cart's movement.
Adaptive Asymptotic Tracking Control for Flexible-Joint Robots With Prescribed Performance: Design and Experiments
Product(s):
2 DOF Serial Flexible JointAbstract
This study reports the adaptive asymptotic tracking control problem for flexible-joint (FJ) robot systems, the output tracking error can be kept within the prescribed range in the initial stage of system operation, as time approaches infinity, the asymptotic tracking result can be obtained. The prescribed performance function and the positive integrable time-varying function are introduced simultaneously in the control design of FJ robot systems for the first time. The control scheme is designed under the frame of the adaptive backstepping method and command filtered technique, which successfully avoids the problem of complexity explosion. The radial basis function neural networks are used to deal with unknown uncertainties and the adaptive laws are designed to approximate the norms of weight vectors and approximation errors. Finally, the feasibility of the proposed scheme is proved by the simulation and the experiment of the 2-link FJ robot on the Quanser platform.
Adaptive quantized control of uncertain nonlinear rigid body systems
Product(s):
Quanser AEROAbstract
This paper investigates the attitude tracking control problem for uncertain nonlinear rigid body systems, where both inputs and states are quantized. It is common in networked control systems that sensor and control signals are quantized before they are transmitted via a communication network. An adaptive backstepping control algorithm is developed for a class of uncertain multiple-input multiple-output (MIMO) systems where a class of sector bounded quantizers is considered. It is shown that all the closed-loop signals are ensured uniformly bounded and tracking is achieved. Further, the tracking errors are shown to converge towards a compact set containing the origin and the set can be made small by the choice of the quantization parameters and the control parameters. For illustration of the proposed control scheme, experiments were conducted on a 2 degrees-of-freedom (DOF) helicopter system.
Adaptive quantized fault-tolerant control of a 2-DOF helicopter system with actuator fault and unknown dead zone
Product(s):
2 DOF HelicopterAbstract
This study proposes an adaptive quantized fault-tolerant control for a nonlinear two-degree of freedom (2-DOF) helicopter system with an unknown dead zone and actuator failures. First, a hysteresis quantizer is employed to reduce the jittering during signal quantization. Second, a radial basis function neural network is adopted to address the uncertainty in the nonlinear helicopter system. Bounded estimates, smoothing functions, and adaptive parameters are used to compensate for the effects of unknown dead zones, actuator faults, and quantization inputs. Subsequently, an adaptive neural network quantized fault-tolerant control strategy is developed for the nonlinear 2-DOF helicopter system using a backstepping technique. In addition, the closed-loop system is proved to be semi-globally uniformly bounded using rigorous Lyapunov stability analysis. Finally, the effectiveness of the derived control strategy is demonstrated through simulation and experimental results.
An adaptive neural network sliding mode controller for nonlinear active suspension with uncertain parameters and non-ideal actuators
Product(s):
Active SuspensionAbstract
Active suspension systems (ASSs) are contributed to improving ride comfort and maneuverability. However, practical ASSs commonly suffer from nonlinear characteristics, uncertain parameters and non-ideal actuators, which always significantly deteriorate the control performance in practice. To overcome these issues, this paper proposes an adaptive neural network sliding mode control (ANNSMC) strategy for an ASS to achieve suspension performance improvements. Firstly, the skyhook system as a reference model which doesn’t require real-time measurement of road input is adopted to provide reference trajectories for the sprung mass displacement and velocity. In addition, an adaptive radial basis function neural network is designed and presented to deal with the effects of uncertain nonlinear functions in the dynamic system. Furthermore, the stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed controller is verified by numerical simulation and experimental platform, and the advantages of the proposed ANNSMC controller in suppressing suspension vibration are illustrated by comparing the performance of passive suspension (PS), sliding mode control (SMC) and linear quadratic regulator (LQR) controlled active suspension under different road excitations. The simulation and experimental results further demonstrate that the proposed controller can effectively suppress sprung mass vibrations and offers superior control performance despite the existence of nonlinear dynamics, uncertain parameters and non-ideal actuators.
An adaptive sliding mode fault-tolerant control of a quadrotor unmanned aerial vehicle with actuator faults and model uncertainties
Product(s):
QBallAbstract
An adaptive sliding mode fault-tolerant control strategy is proposed for a quadrotor unmanned aerial vehicle in this article to accommodate actuator faults and model uncertainties. First, a new reaching law is proposed, with which a sliding mode control (SMC) law is constructed. The proposed reaching law is made up of a sliding variable and the distance between it and a designated boundary layer, and it can effectively suppress the unexpected control chattering while preserving the necessary system tracking performance. Then, an adaptive SMC scheme is proposed to further solve the fault and uncertainty compensation problem. The proposed adaptation law helps to prevent overestimation of the adaptive control parameters, as well as avoiding control chattering. Finally, a number of comparative simulation tests are carried out to validate the effectiveness and superiority of the proposed control strategy. The demonstrated quantitative comparison results confirm its advantages.
Application of Recurrent Neural-Network based Kalman Filter for Uncertain Target Models
Product(s):
3 DOF HoverAbstract
For various target tracking applications, it is well known that the Kalman filter is the optimal estimator(in the minimum mean-square sense) to predict and estimate the state(position and/or velocity) of linear dynamical systems driven by Gaussian stochastic noise. In the case of nonlinear systems, Extended Kalman filter(EKF) and/or Unscented Kalman filter(UKF) are widely used, which can be viewed as approximations of the(linear) Kalman filter in the sense of the conditional expectation. However, to implement EKF and UKF, the exact dynamical model information and the statistical information of noise are still required. In this paper, we propose the recurrent neural-network based Kalman filter, where its Kalman gain is obtained via the proposed GRU-LSTM based neural-network framework that does not need the precise model information as well as the noise covariance information. By the proposed neural-network based Kalman filter, the state estimation performance is enhanced in terms of the tracking error, which is verified through various linear and nonlinear tracking problems with incomplete model and statistical covariance information.
Attitude Control of the Quadrotor UAV with Mismatched Disturbances Based on the Fractional-Order Sliding Mode and Backstepping Control Subject to Actuator Faults
Product(s):
QDroneAbstract
Considering mismatched disturbances, aerodynamic interference, chattering, and actuator failure in the attitude control of the quadrotor unmanned aerial vehicle (UAV), this paper establishes a new quadrotor UAV model with mismatched disturbances, based on quaternion, and designs a fault tolerant controller. First, in order to reduce the chattering of the traditional reaching law, a new reaching law based on the sigmoid function is introduced into the design. Second, the sliding mode control and backstepping control methods are adopted, based on the new fractional-order sliding mode surface when the faults occur in quadrotor UAV actuators, and parameters in the sliding mode control are adaptively adjusted. The simulation results show that the fault tolerant control method can control the attitude of UAV quickly and achieve good robustness.
Automation of friction torque identification for vane-type semi-rotary pneumatic actuators
Product(s):
Q8-USB Data Acquisition DeviceAbstract
In precise control applications, estimating the friction under operating conditions would greatly improve the control performance. In literature, especially for pneumatic actuators, the existing friction estimation methodologies bear on manual experimental methodology which is prone to user errors, has the difficulty in measurement and data processing, and in addition it takes long experimental durations. In this study, all experimental steps of friction torque estimation for semi-rotary pneumatic actuators have been automated with MATLAB/Stateflow® tools to process correctly more experimental data and eliminate potential user or random errors by designing a comprehensive mechatronic setup. The automated system has been integrated with a graphical user interface to facilitate the utilization of the automated setup. With the help of efficient automation, friction torque characteristics with respect to Stribeck model have been investigated under various operating pressure and speed levels. Efficiency of the system has been tested on a vane-type cylinder by constructing friction torque surface graphs. The real-time open-loop control is applied to verify the identified friction parameters at loading-free conditions. Furthermore, closed-loop cascade PID technique has been successfully implemented for under-loading case to verify the results. The outstanding performance of the cylinder at both control approach has exhibited that the estimated friction parameters obtained with automated method were quite accurate and very helpful in the control applications.
Axis Control of a Nonlinear Helicopter Model Using Intelligent Controller
Product(s):
2 DOF HelicopterAbstract
Adaptive neuro-fuzzy inference system (ANFIS) based intelligent control is employed on a helicopter system in this paper. This helps to control the alterations of the pitch axis and yaw axis of helicopter, with the reference trajectory. Two different ANFIS logic modules are developed, one is to help adjust the angle variations in pitch axis and other is to help adjusting the yaw axis angle variations of a two degree of freedom (2 DOF) Quanser Helicopter system, so that the altitude and angular speed are controlled altogether. The whole execution framework utilizes standard configurations of MATLAB platform and simulation toolboxes. The results obtained in the process are then compared with the traditional LQR Controller and Fuzzy Controller on simulation platform.
Barrier Function Based Adaptive Global Sliding Mode Fault-tolerant Control of Quad-rotor UAV
Product(s):
QDroneAbstract
In this paper, Barrier function based adaptive global sliding mode fault-tolerant control and its application in quad-rotor UAV system are studied. Firstly, the global sliding mode surface is combined with Barrier function based adaptive sliding mode control, which omits the approach process of phase I of traditional Barrier adaptive sliding mode motion, thus improving the rapidity and accuracy of the algorithm. Secondly, the Barrier function adaptive law is used to adjust the gain of the switching term, so that the controller gain can change with the amplitude of the total disturbance in a timely and accurate manner, avoiding the overestimation problem and thus reducing the chattering of the control signal. Finally, the experimental results on the fault-tolerant control platform for multi-rotor UAVs prove the effectiveness and superiority of the proposed algorithm.
Complex Fractional-Order LQIR for Inverted-Pendulum-Type Robotic Mechanisms: Design and Experimental Validation
Product(s):
Rotary Inverted PendulumAbstract
This article presents a systematic approach to formulate and experimentally validate a novel Complex Fractional Order (CFO) Linear Quadratic Integral Regulator (LQIR) design to enhance the robustness of inverted-pendulum-type robotic mechanisms against bounded exogenous disturbances. The CFO controllers, an enhanced variant of the conventional fractional-order controllers, are realised by assigning pre-calibrated complex numbers to the order of the integral and differential operators in the control law. This arrangement significantly improves the structural flexibility of the control law, and hence, subsequently strengthens its robustness against the parametric uncertainties and nonlinear disturbances encountered by the aforementioned under-actuated system. The proposed control procedure uses the ubiquitous LQIR as the baseline controller that is augmented with CFO differential and integral operators. The fractional complex orders in LQIR are calibrated offline by minimising an objective function that aims at attenuating the position-regulation error while economising the control activity. The effectiveness of the CFO-LQIR is benchmarked against its integer and fractional-order counterparts. The ability of each controller to mitigate the disturbances in inverted-pendulum-type robotic systems is rigorously tested by conducting real-time experiments on Quanser single-link rotary pendulum system. The experimental outcomes validate the superior disturbance rejection capability of the CFO-LQIR by yielding rapid transits and strong damping against disturbances while preserving the control input economy and closed-loop stability of the system.
Contractivity-based variable gain dynamic motion control for a laser beam steering system: Synthesis and performance analysis
Abstract
This paper deals with the synthesis and experimental performance evaluation of a contractivity-based nonlinear dynamic motion control scheme for a Laser-Beam Steering (LBS) system, which includes a saturated integral action and a variable gain. The variable gain, in the control law, is used to discriminate between “signal” and “noise” in the velocity measurements, allowing to do a trade-off between the low-frequency tracking and disturbance rejection properties and high-frequency measurement noise amplification, an effect known as waterbed effect. Then, the contractivity-based framework handles the stabilization problem together with the closed-loop performance, allowing one to generalize key properties of linear control systems to analyze transient and steady-state solutions performances in the nonlinear case. The proposed control scheme is evaluated on an experimental platform for the set-point regulation and trajectory tracking problems under different scenarios. Moreover, the effectiveness of the proposed control scheme is compared with linear controllers for the LBS system available in the literature.
Control of Direct Current Motor by Using Artificial Neural Networks in Internal Model Control Scheme
Product(s):
Rotary Servo Base UnitAbstract
In this research, control of the Direct Current motor is accomplished using a neuro controller in the Internal Model Control scheme. Two Feed Forward Neural Networks are trained using historical input-output data. The first neural network is trained to identify the object's dynamic behavior, and that model is used as an internal model in the control scheme. The second neural network is trained to obtain an inverse model of the object, which is applied as a neuro controller. Experiment is conducted on the real direct current motor in laboratory conditions. Obtained results are compared to those achieved by implementing the Direct Inverse Control method with the same neuro controller. It was demonstrated that the proposed control method is simple to implement and the system robustness is achieved, which is a great benefit, aside from the fact that no mathematical model of the system is necessary to synthesize the controller of the real object.
Data-driven dissipative verification of LTI systems: multiple shots of data, QDF supply-rate and application to a planar manipulator
Product(s):
2 DOF Serial Flexible JointAbstract
We present a data-driven dissipative verification method for LTI systems based on using multiple input-output data. We assume that the supply-rate functions have a quadratic difference form corresponding to the general dissipativity notion known in the behavioural framework. We validate our approach in a practical example using a two-degree-of-freedom planar manipulator from Quanser, with which we demonstrate the applicability of multiple datasets over one-shot of data recently proposed in the literature.
Data-driven fixed-structure frequency-based H2 and H∞ controller design
Product(s):
QUBE – Servo 2Abstract
The frequency response data of a generalized system is used to design fixed-structure controllers for the H2 and H∞ synthesis problem. The minimization of the two and infinity norm of the transfer function between the exogenous inputs and performance outputs is approximated by a convex optimization problem involving Linear Matrix Inequalities (LMIs). A very general controller parametrization is used for continuous and discrete-time controllers with matrix transfer function or state-space representation. Numerical results indicate that the proposed data-driven method gives equivalent performance to model-based approaches when a parametric model is available.
Design of Disturbance Observer-Based Dynamic Sliding Mode Control
Product(s):
Rotary Servo Base UnitAbstract
This paper proposes the design and implementation of observer-based dynamic sliding mode control (DSMC). The designed disturbance observer (DO) estimates the uncertainties and disturbance in an integrated manner. It generate smooth and chattering-free control. The disturbance observer-based DSMC technique is validated through experimentation on DC motor setup. The results show the effectiveness of the combination of the controller–observer design for position control of DC motor against lumped uncertainty. The overall stability of the observer-based control system is proved by Lyapunov theory.
Developing advanced predictive tracking controllers for quadrotors
Product(s):
QDroneAbstract
In recent years, quadrotor unmanned aerial vehicles have attracted increasing attention from both industrial and academic communities. With characteristics such as vertical take-off and landing, single or team flight, and low-cost manufacturing, quadrotors have broad application value in military strategy [1], disaster rescue [2], tracking and shooting [3], and monitoring and recognition [4]. Quadrotor UAVs are underactuated and strongly coupled nonlinear systems, subject to structural uncertainties and unknown external disturbances. Therefore, designing an accurate and robust controller for the quadrotor to achieve autonomous flight and target tracking is a great challenge.
Recently, with the increasing development of fast computers, model predictive control approaches (MPC) have become real-time applicable for nonlinear mechatronic systems. MPC refers to a set of controllers that use a model to compute inputs from the current time to a future time to optimize the behavior of a model along the input trajectory. The predictive nature of the control design makes it ideal for high-performance trajectory tracking. A key advantage of MPC is that it offers the ability to design controllers with constraints while solving an optimal control problem along the given trajectory. Because of its efficiency and advantages, the predictive control strategy is regularly used to control robotic systems such as quadrotors [5]. In other words, predictive control has also been extended to the case of visual servoing (VS), giving rise to a new approach named visual predictive control (VPC) [6].
The development of Model Predictive Control (MPC) has provided the essential background to formulate Visual Servoing (VS) as a constrained optimization problem. The main objective of Visual Predictive Controllers (VPCs) is to provide a systematic framework to accomplish VS problems in a mathematically optimal fashion while considering the inputs, states, and task constraints into account. In most of the proposed VPC approaches, constraints due to the camera’s Field of View (FoV), the kinematics of the robot, and sensor/input saturation are considered. Despite this, no systematic strategy has been provided in the above-mentioned literature to deal with system/measurement uncertainties. Although VPC gives satisfactory performance in tracking a target, it suffers from some inconveniences due to various factors, including imperfect system models, measurement noises, and exogenous disturbances such as wind. Also, some uncertainties can arise from the VS system, such as having a parametric/deterministic nature (e.g., kinematics error in the quadrotor model or calibration error in the focal length of the camera).
The thesis work will be based on a particular application framework, namely, a fast-moving target for a quadrotor subject to many uncertainties, such as uncalibrated camera, wind disturbance, uncertain parameters, and measurement noise. Very few works can currently be identified for this type of application [7].
The work plan for this thesis will take place in the following chronological order:
Conduct a bibliographic study of visual predictive control and of robust control applied to robotic systems.
Develop an intelligent method to find a visual feature representation that is robust to big dynamic transformation movements and is suitable to be an optimization variable.
Study the visual predictive control strategy for quadrotor that allows the tracking of reference trajectory.
Develop and implement an approach that allows the quadrotor to follow a moving target despite the existence of uncalibrated camera, wind disturbance, and measurement noise.
Implement the developed advanced predictive controller in a drone (AR-drone, Quanser drone).
Compare the results and evaluate the performance.
DISTURBANCE OBSERVER-BASED EXTENDED STATE CONVERGENCE ARCHITECTURE FOR MULTILATERAL TELEOPERATION SYSTEMS
Product(s):
QUBE – Servo 2Abstract
In the existing extended state convergence architecture, k-master systems can control the motion of l-slave systems to perform a certain task in a remote environment. However, dependency of this control framework on systems’ parameters leads to a degraded control performance in the presence of significant parameter variations. In this study, we have integrated extended state observers in extended state convergence architecture to counter the effect of uncertainties, which has resulted in a more practical architecture for multilateral teleoperation systems. In order to validate the proposed enhanced architecture, simulations are performed in MATLAB/Simulink environment by considering a symmetric (2 × 2) as well as asymmetric (2 × 1) teleoperation system. A comparative assessment with the existing state convergence architecture proves the superiority of the proposed architecture. In addition, hardware experimentation is carried out on Quanser QUBE-servo systems by setting up an asymmetric (1 × 2) teleoperation system in the QUARC environment.
Dual-Extended State Observer-Based Feedback Linearizing Control for a Nonlinear System with Mismatched Disturbances and Uncertainties
Product(s):
Magnetic LevitationAbstract
This research article presents the nonlinear control framework to estimate and reject the mismatched lumped disturbances acting on the nonlinear uncertain system. It is an unfortunate fact that the conventional extended state observer (ESO) is not capable of simultaneously estimating the mismatched lumped disturbance and its derivative for the systems. Moreover, the basic ESO is only suitable for systems with integral chain form (ICF) structures. Similarly, the conventional feedback linearizing control (FLC) approach is not robust enough to stabilize systems in the presence of disturbances and uncertainties. Hence, the nonlinear control framework is proposed to overcome the above issues, which are composed of (a) a dual-extended state observer (DESO), and (b) a DESO-based FLC. The DESO provides information on the unmeasured state, mismatched disturbance, and its derivatives. The DESO-FLC utilizes the information from the DESO to counter the effects of such disturbances and to stabilize the nonlinear systems around the reference point. The detailed closed-loop analysis is presented for the proposed control framework in the presence of lumped disturbances. The performance robustness of the presented design was validated for the third-order, nonlinear, unstable, and disturbed magnetic levitation system (MLS). The results of the DESO-FLC approach are compared with the most popular linear quadratic regulator (LQR) and nonlinear FLC approaches based on the integral error criterion and the average electrical energy consumption.
Energy Consumption Analysis of the Selected Navigation Algorithms for Wheeled Mobile Robots
Abstract
The article presents the research on navigation algorithms of a wheeled mobile robot with the use of a vision mapping system and the analysis of energy consumption of selected navigation algorithms, such as RRT and A-star. Obstacle maps were made with the use of an RGBW camera, and binary occupation maps were also made, which were used to determine the traffic path. To recreate the routes in hardware, a programmed Pure Pursuit controller was used. The results of navigation were compared on the basis of the forward kinematics model and odometry measurements. Quantities such as current, except (x, y, phi), and linear and angular velocities were measured in real time. As a result of the conducted research, it was found that the RRT star algorithm consumes the least energy to reach the designated target in the designated environment.
Experimental Design of Fast Terminal Sliding Mode Control for Valve Regulation under Water Load Uncertainty for Precision Irrigation
Product(s):
Rotary Servo Base UnitAbstract
The application of control systems in precision irrigation is critical to ensure the accurate distribution of water in crops under various uncertainties. Shifts in the loading of the water supply on the control valve can be a significant uncertainty. Changes in weather and the uncertainty of the water level in the reservoir are also challenging issues. Sliding Mode Control (SMC) is a robust control technique that is simple to apply to deal with uncertainty, while Fast Terminal Sliding Mode Control (FTSMC) has the benefit of the rapid convergence. The DC electric motor, which is a common component of electric control valves, can be employed in designing control techniques for precision irrigation applications. This study aims to design a proposed experimental-based method, namely FTSMC for valve regulation under water load uncertainty for precision irrigation application. Modification of the signum function should be used to eliminate the chattering effect in real experiments.The results of experiments showed that the proposed method was superior to the conventional Proportional Integral Derivative (PID) and traditional SMC techniques in terms of overshoot, convergence rate and error. Because of those reasons, the FTSMC approach should be implemented on control valves against load uncertainty in precision irrigation applications.
Experimental Results on Composing Cooperative Behaviors in Networked Mobile Robots in the Presence of Unknown Control Effectiveness
Product(s):
QBot 2eAbstract
It is recently discovered that the distributed control architectures can be used to drive the agents to desired different positions by using a modified Laplacian matrix. In addition, adaptive control methods are powerful tools that can deal with the presence of unknown control effectiveness. The first contribution of this paper is to theoretically present a new adaptive control for the purpose of achieving desired behaviors in the networked robots in the presence of unknown control effectiveness. The second contribution is to present experimental results in order to demonstrate the efficacy of using distributed adaptive control architectures in the dynamics of multi agent system, where we used Quanser’s QBot-2e’s, differential-drive mobile robot research platforms.
Fault-tolerant attitude tracking control of tandem rotor helicopter considering internal actuator saturation and external wind gust
Product(s):
3 DOF HelicopterAbstract
Tandem rotor helicopter is configured with two main rotors distributed along the longitudinal direction and without anti-torque tail rotor. Therefore, the control strategy of tandem rotor helicopter can be quite different from that of traditional helicopter systems. In this article, a fault-tolerant attitude tracking controller is presented for tandem rotor helicopter, with considerations of external wind disturbance and internal actuator problem. First, attitude control oriented dynamic model of the tandem rotor helicopter is constructed, in which both actuator fault and saturation are involved. Base on statistical characteristics of practical wind condition as well as aerodynamic properties of the helicopter rotors, a detailed wind load model is further established. Then, a fault-tolerant attitude tracking controller is proposed for the tandem rotor helicopter system by incorporating nonsingular terminal sliding mode control with an adaptive super twisting algorithm, which allows a simultaneous regulation of the three angular motions via two propeller rotors. Finally, based on Quanser's 3-dof helicopter system, comparative simulation tests are performed to demonstrate the effectiveness as well as advantages of the proposed fault-tolerant controller design.
Feature-Based Occupancy Map-Merging for Collaborative SLAM
Product(s):
QCarAbstract
One of the most frequently used approaches to represent collaborative mapping are probabilistic occupancy grid maps. These maps can be exchanged and integrated among robots to reduce the overall exploration time, which is the main advantage of the collaborative systems. Such map fusion requires solving the unknown initial correspondence problem. This article presents an effective feature-based map fusion approach that includes processing the spatial occupancy probabilities and detecting features based on locally adaptive nonlinear diffusion filtering. We also present a procedure to verify and accept the correct transformation to avoid ambiguous map merging. Further, a global grid fusion strategy based on the Bayesian inference, which is independent of the order of merging, is also provided. It is shown that the presented method is suitable for identifying geometrically consistent features across various mapping conditions, such as low overlapping and different grid resolutions. We also present the results based on hierarchical map fusion to merge six individual maps at once in order to constrict a consistent global map for SLAM.
Friction force estimation in pneumatic cylinders by full automation of experimental procedures
Product(s):
Q8-USB Data Acquisition DeviceAbstract
The effective utilization of pneumatic cylinders in precise control applications requires the correct determination of unpredictable, variable, and non-linear friction resistance characteristics. Even though the friction characteristics depend on many structural and operating variables, the existing expensive experimental methodologies are prone to error, time-consuming, and have excessive computational burden. In this study, the full automation of friction force estimation processes has been designed and implemented with MATLAB/Stateflow including the execution of all experimental steps, processing of signals, extraction and classification of data, and estimation of parameters. An operational graphical user interface has been developed for entering the required input values of the experimental procedures, connecting to testing equipment, carrying out experiments, and presenting obtained model parameters. The friction force parameters of three pneumatic cylinders, two of which were identical, have been determined both with the automated method and the manual method. The automated method has produced better results compared to the manual method while reducing the total estimation duration drastically. The pressure tracking performance tests conducted to verify the friction model parameters have exhibited better tracking performances with the automated method results.
Fuzzy Cooperative Control for the Stabilization of the Rotating Inverted Pendulum System
Product(s):
QUBE – Servo 2Abstract
The rotating inverted pendulum is a nonlinear, multivariate, strongly coupled unstable system, and studying it can effectively reflect many typical control problems. In this paper, a parameter self-tuning fuzzy controller is proposed to perform the balance control of a single rotating inverted pendulum. Particle swarm optimization is used to adjust its control parameters, and simulation experiments are performed to show that the system can achieve stability with the designed parametric self-tuning fuzzy controller, with control performance better than that of the conventional fuzzy controller. Furthermore, the leader-follower control strategy is used to realize the cooperative control of multiple rotating inverted pendulums. Two QUBE-Servo 2 rotating inverted pendulums are used for a cooperative pendulum swing-up experiment and stabilization experiment, and the effectiveness of the proposed cooperative control strategy is verified.
Human Computer Interface For Data Collection in Individuals with Stroke
Product(s):
Q8-USB Data Acquisition DeviceAbstract
The Robotics and Sensorimotor Control Laboratory in the Department of Biomedical Engineering and Mechanics, hereafter identified as the RoSenCo Lab, is a research lab headed by Dr. Netta Gurari. The purpose of this project is to provide software to the RoSenCo Lab for conducting neurological research with people who have had strokes. Stroke is one of the most common causes of disability in the world. By studying the effects
of stroke on tactile perception, the RoSenCo Lab aims to contribute to the development of treatments to help those who have had strokes.
The RoSenCo Lab researchers have designed a variety of experiments to further these ends. The goal of this specific human-computer interface project is to develop software to enable these experiments, in an extensible way, such that other experiments are easy to create in the future. I have implemented software to: i) control actuators, ii) collect sensor data, iii) real-time
plot selected data streams, and iv) save the relevant data in the required format for offline analyses while the experiment is running at 1600 Hz. In addition, I included text-to-speechpowered audio-visual instructions for guiding participants throughout the experiment on the automated protocol. This software is called the RoSenCo Lab Experiment Manager, hereafter identified as RoSenCoExMan.
RoSenCoExMan is written in Python, and uses numerous libraries to implement features such as the real-time plotting, hardware access, and text-to-speech. The software uses multiprocessing techniques to achieve the required real-time (i.e., 1600 Hz) performance.
Opportunities for future work include extending the audio-visual participant feedback functionality to enable experiments utilizing more dynamic visuals, and the addition of a graphical user interface.
Human-Powered Master Controllers for Reconfigurable Fluidic Soft Robots
Product(s):
Q8-USB Data Acquisition DeviceAbstract
Fluidic soft robots have the advantages of inherent compliance and adaptability, but they are significantly restricted by complex control systems and bulky power devices, including fluidic valves, fluidic pumps, electrical motors, as well as batteries, which make it challenging to operate in narrow space, energy shortage, or electromagnetic sensitive situations. To overcome the shortcomings, we develop portable human-powered master controllers to provide an alternative solution for the master-slave control of the fluidic soft robots. Each controller can supply multiple fluidic pressures to the multiple chambers of the soft robots simultaneously. We use modular fluidic soft actuators to reconfigure soft robots with various functions as control objects. Experimental results show that flexible manipulation and bionic locomotion can be simply realized using the human-powered master controllers. The developed controllers which eliminate energy storage and electronic components can provide a promising candidate of soft robot control in surgical, industrial, and entertainment applications.
Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach
Abstract
This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo system, having one, two, and three parameters, were experimentally identified using both the classic least squares and the least squares of orthogonal distances. The models with two and three parameters were identified through numerical routines. The servo system model with a single parameter only considered the input gain. In this particular case, the analytical conditions for finding the critical points and for determining the existence of a minimum were presented, and the estimate of the input gain was obtained by solving a simple quadratic equation whose coefficients depended on measured data. The results showed that as opposed to the least squares method, the least squares of orthogonal distances method experimentally produced consistent estimates without regard for the classic persistency-of-excitation condition. Moreover, the parameter estimates of the least squares of orthogonal distances method produced the best tracking performance when they were used to compute a trajectory-tracking controller.
Jerk-bounded trajectory planning for rotary flexible joint manipulator: an experimental approach
Product(s):
Rotary Flexible JointAbstract
The fundamental criteria for industrial manipulator applications are vibration free and smooth motion with minimum time. This paper investigates the trajectory tracking and vibration control of rotary flexible joint manipulator with parametric uncertainties. Firstly, the dynamic modeling via Euler Lagrange equation for a single link flexible joint manipulator is discussed. Secondly, for the execution of smooth motion between two points, bounded and continuous jerk trajectory is developed and implemented. In addition, the prospective strategy uses the concatenation of fifth-order polynomials to provide a smooth trajectory between two-way points. In the planned algorithm, user can independently define the position, velocity, acceleration and jerk values at both initial and final positions. The feature of user-defined parameters gives the versatility to the suggested algorithm for generating trajectories for diverse applications of robotic manipulators. Moreover, the planned scheme is easy to implement and computationally efficient. In the last, the performance of the presented scheme is examined by comparison with cubic splines and a linear segment with parabolic blends (LSPB) techniques. Generated trajectories were evaluated successfully by carrying multiple experiments on QUANSER’s flexible joint manipulator.
Learning-Based Motion-Intention Prediction for End-Point Control of Upper-Limb-Assistive Robots
Product(s):
QPIDe Data Acquisition DeviceAbstract
The lack of intuitive and active human–robot interaction makes it difficult to use upper-limb-assistive devices. In this paper, we propose a novel learning-based controller that intuitively uses onset motion to predict the desired end-point position for an assistive robot. A multi-modal sensing system comprising inertial measurement units (IMUs), electromyographic (EMG) sensors, and mechanomyography (MMG) sensors was implemented. This system was used to acquire kinematic and physiological signals during reaching and placing tasks performed by five healthy subjects. The onset motion data of each motion trial were extracted to input into traditional regression models and deep learning models for training and testing. The models can predict the position of the hand in planar space, which is the reference position for low-level position controllers. The results show that using IMU sensor with the proposed prediction model is sufficient for motion intention detection, which can provide almost the same prediction performance compared with adding EMG or MMG. Additionally, recurrent neural network (RNN)-based models can predict target positions over a short onset time window for reaching motions and are suitable for predicting targets over a longer horizon for placing tasks. This study’s detailed analysis can improve the usability of the assistive/rehabilitation robots.
Neuro-Adaptive PID Helicopter Controller Based on Atomic Functions
Product(s):
2 DOF HelicopterAbstract
A feature of wavelets is that signals can be analyzed in time-frequency, unlike Fourier theory, which only does so in frequency. For many years, the most used wavelet functions for control applications have been Haar, Morlet, Rasp, Polywog, and Shannon, among others. This paper presents new functions called Atomic Function (AF) as activation functions in a radial basis neural network (RBF). Although, they maintain the same properties, one of the principal advantages of the AF is that they are easier to implement. The control of the Quanser helicopter with two degrees of freedom is presented to prove the effectiveness of the AF. In the proposed approach, the RBF neural network is used for: a) the input-output identification of the system and b) auto-tuning PID controllers. Numerical simulations show the performance of the closed-loop system together with the AF under different conditions.
Abstract
Unmanned vehicles are already in wide use. For instance, they can be applied for military purposes, space exploration, in routine life, delivery services, etc. Unmanned vehicles are in great demand since they can be exploited at places that are dangerous or unachievable for humans. This research aims to create a leader-follower system for unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) that could have many applications. The drone will fly ahead and scan the surface from above for information. While the robot will create its own route in order to get to the point determined by the drone. This can be used to explore hard-to-reach places where the drone is conducting reconnaissance, and the robot is collecting materials with a robotic arm. For the project, the Quanser system was used, which includes a tracking system, communications, QDrone as a UAV, and QBot 2e as a UGV. A fuzzy controller was created for QDrone, which ensures flight stability. This thesis details the dynamic models of vehicles and the subtleties of tuning the controller. In addition, methods for creating a leader-follower algorithm are described in detail. In addition to everything, an obstacle avoidance algorithm for QBot 2e was created, which was added to the leader-follower algorithm. The experiments conducted in this thesis with Fuzzy, PID and Fuzzy with prefilter controllers have shown that the Fuzzy controller performs more accurately and better in controlling the position of the quadcopter. An algorithm for the Leader-Follower system with obstacle avoidance was developed, and experiments were conducted to compare the Fuzzy and PID controllers under different conditions. Finally, the optimal Fuzzy controller was integrated into the Leader-Follower system with a Fuzzy controller. The results show that the proposed controller is effective in controlling the system and avoiding obstacles.
Perturbed Unicycle Mobile Robots: A Second-Order Sliding-Mode Trajectory Tracking Control
Product(s):
QBot 2Abstract
This paper contributes to the design of a secondorder sliding-mode controller for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy takes into account the design of two particular sliding variables, which ensure the convergence of the tracking error to the origin in a finite time despite the effect of some external perturbations. The straightforward structure of the controller is simple to tune and implement. The global, uniform and finite-time stability of the closed-loop tracking error dynamics is demonstrated by means of Lyapunov functions. Furthermore, the performance of the proposed approach is validated through some experiments using a QBot2 unicycle mobile robot.
Polarity assignment method (PAM), ANN, Neural networks strategy for the data of PAM for the single degree of freedom flexible joint robot
Product(s):
Rotary Flexible JointAbstract
This paper “describes” the investigation of the stability of a single Degree of Freedom (DOF) flexible robotic arm by the diagrams shown below. The derived model is based on Euler- Lagrange approach. Exploration of a flexible robotic arm with using state-of-the-art controllers is essential for intelligent applications. These robot arms have joints that work independently of each other in order to create a smooth connection between joints. They still ensures the natural properties like a real human arm. The use of polarity assignment method “helps” the system to achieve desired output signals which has not been thoroughtly studied before for this system. The author can also compare the effectiveness of control methods for this system to find the most effective method for control strategies. In particular, ANN ( artificial neural network) is the most modern technique currently applied to this system to investigate the security and stability of the system through this program. This is new and it has never been used before for a system of this type. Neural networks strategy has been implemented in this paper as an application of artificial intelligence. It has successfully performed a mission in re-simulating functions of another control method: Polarity assignment method. Simulation results are done by Matlab.
Prescribed-Time Adaptive Backstepping Control of an Uncertain Nonlinear 2-DOF Helicopter
Product(s):
2 DOF HelicopterAbstract
This paper addresses the prescribed-time attitude tracking issue for an uncertain nonlinear 2-Degree of Freedom (DOF) helicopter. Based on the Euler-Lagrange equations, a nonlinear model is developed for the 2-DOF helicopter, where the system parameters and control input constant coefficients are unknown. The proposed prescribed-time control is based on adaptive backstepping and utilized to track the desired pitch and yaw positions separately. Using the theory of Lyapunov stability, we show that the proposed prescribed-time control and adaptive law ensure the boundedness of all the closed-loop signals of the system for all future time. A noticeable advantage of the proposed method is that the upper bound of the settling time can be specified in advance. Finally, to verify the efficacy and control capabilities of the proposed scheme, simulations are conducted on the Quanser 2-DOF helicopter system.
Prospects of Autonomous Vehicle Learning Kits in Education Systems
Product(s):
QCarAbstract
The Autonomous Vehicles (AV) is a self-driving vehicle capable of sensing its environment and operating with minimal or no human intervention converting into a fully or partially automated vehicle. These automated vehicles have great potential to revolutionize the automotive industry and our daily lives. Thus, it is receiving a lot of attention from automotive industries, governments, suppliers, educational sectors, researchers, and many other stakeholders. According to global financial service firm UBS, the AV market could reach more than $2 trillion by 2030. These projections will become reality if enough skilled workforces are produced with a high level of broad technical competencies specifically for the automotive environment. This will also require consumer education on AVs that could bring all the comfort and excitement across all segments of the population. This brings a substantial opportunity for the educational sectors in generating the workforce required in AV sectors by enhancing the existing curricula in the areas related to AVs or developing a cross-disciplinary course or capstone project that could expose students with a technical background in computer science, computer engineering, electrical engineering, and Mechatronics. Since AV has many technologies involved, it is challenging to design an appropriate curriculum and provide hands-on activities. Small-scale learning kits may be an affordable and effective solution for introductory courses on AVs or for beginners. This paper will discuss the use of those widely available small-scale learning kits, their benefits, and their challenges.
qLPV modeling and mixed-sensitivity L2 control for a magnetic levitation system
Product(s):
Magnetic LevitationAbstract
This paper proposes a comprehensive mixed-sensitivity L2 control design for an experimental magnetic levitation (Maglev) system. The control strategy can be seen as an extension of the H∞ loop-shaping procedure for discrete-time linear parameter-varying (LPV) systems using linear-fractional representation (LFR). By making use of an efficient quadratic approach given in the form of linear matrix inequalities (LMIs), a functional and computationally attractive gain-scheduling technique is achieved. Despite the rigorous mathematical considerations to obtain the L2 controller, the guidelines to its practical implementation are presented as a straightforward method using LMIs. A detailed modeling of the Maglev plant manufactured by Quanser® is carried out to illustrate the procedure, including a description of the nonlinear equations embedding process to obtain a discretized quasi-LPV (qLPV) model. Experimental results demonstrate the effectiveness of the proposed control design.
Robust Stabilization of Furuta’s pendulum based on Continuous High Order Sliding Mode Controllers
Product(s):
Rotary Inverted PendulumAbstract
In this manuscript a robust stabilization controller for the Furuta’s pendulum in presence of parametric uncertainties is proposed. We used a normal form transformation and partial feedback linearisation to tackle the problem with a cascade system approach, then a continuous sliding mode algorithm stabilize the cascade system. A closed-loop stability analysis is presented to proof asymptotic stability of the Furuta’s pendulum equilibrium point. Also, experiments over a real Furuta’s pendulum are presented to corroborate the theoretical results shown.
Robust Tracking Control for Nonlinear Systems: Performance optimization via extremum seeking
Product(s):
QUBE – Servo 2Abstract
This paper presents a controller design and optimization framework for nonlinear dynamic systems to track a given reference signal in the presence of disturbances when the task is repeated over a finite-time interval. This novel framework mainly consists of two steps. The first step is to design a robust linear quadratic tracking controller based on the existing control structure with a Youla-type filter Q~. Secondly, an extra degree of freedom: a parameterization in terms of Q~, is added to this design framework. This extra design parameter is tuned iteratively from measured tracking cost function with the given disturbances and modeling uncertainties to achieve the best transient performance. The proposed method is validated with simulation placed on a Furuta inverted pendulum, showing significant tracking performance improvement.
Shaking Table Design for Testing Earthquake Early Warning Systems
Product(s):
Shake Table IIAbstract
The unpredictability in time of seismic activities and the dependence of tectonic movements on a multitude of factors challenges specialists to identify the most accurate related methods to avoid catastrophes associated with hazards. Early warning systems are critical in reducing negative effects in the case of an earthquake with a magnitude above 5 MW. Their precision is all the better as they corroborate and transmit more information collected from the regional or on-site sensory nodes to a central unit that discloses events and estimates the epicentral location, earthquake magnitude, or ground shaking amplitude. The shaking table is the proper instrument for evaluating an early warning systems’ dynamic response and performance under specific vibration conditions. To this issue, the paper presents a laboratory single-axis shaking table with a small-scale, low-cost design and an accurate displacement control. Experiments based on a suite of 12 real earthquakes provided results with very small errors related to similar models, bearing out the designed shaking table is suitable for early earthquake warning system response testing for high magnitude earthquakes.
T-S fuzzy controller design for Rotary Inverted Pendulum with input delay using Wirtinger-based integral inequality
Product(s):
Rotary Servo Base UnitAbstract
This paper investigates a Takagi-Sugeno fuzzy descriptor approach for designing a input delay controller for a rotary inverted pendulum. The rotary inverted pendulum, under-actuated system, is considered a benchmark for verifying the performance of linear or nonlinear control laws in control system theory because this system has nonlinearities, such as gravity and centripetal force. The Takagi-Sugeno fuzzy modeling technique transformed the rotary inverted pendulum system into several local linear models, and a parallel distributed compensation (PDC) based fuzzy controller was designed. By constructing suitable Lyapunov-Krasovskii functionals and utilizing some mathematical techniques, a stabilization criterion for a T-S fuzzy system with input delay was derived in linear matrix inequalities. Finally, the designed controller was experimented on the ‘Quanser SRV-02’ platform compared to the linear controller designed using LMI Toolbox of MATLAB under the same conditions.
The Boundary and Excitation Effect of Non-Spherical Granular Material
Product(s):
Shake Table IIAbstract
Non-spherical grains have been gradually receiving attention from both researchers and the industry because of their behavior. Even though these grains possess complex macroscopic orientations that are associated with different applications, such as the pharmaceutical industry, they sometimes can also cause challenges, like jamming while passing collectively through certain narrowed passages. Most published articles have presented studies about granular materials, based on spherical grains and have mainly examined the grain size but ignored the grain’s shape and orientation, especially concerning the interaction of these grains with their boundaries. Further, literature reported that the mechanical properties of the granular materials are critically affected by the alignment of non-spherical grains as conducted in various simulations and associated experiments. To explore more about the shape and orientational effect of non-spherical grains with respect to boundaries, a detailed initial-level observational study is done with the help of different boundary shapes and grains ranging from elongated rice to long cylindrical grains. The collision of grains with boundaries generates an orientational field that results from their interaction with boundaries and neighboring grains. This research shows that the excitation of grains occurs due to their collision with boundaries, and these boundaries can play an important role in the orientation of non-spherical grains. The study provides ‘thought-provoking’ directions for exploring more about the orientation of non-spherical grains.
Trajectory tracking double two-loop adaptive neural network control for a Quadrotor
Product(s):
QBall 2Abstract
In this paper, the development and experimental validation of a novel double two-loop nonlinear controller based on adaptive neural networks for a quadrotor are presented. The proposed controller has a two-loop structure: an outer loop for position control and an inner loop for attitude control. Similarly, both position and orientation controllers also have a two-loop design with an adaptive neural network in each inner loop. The output weight matrices of the neural networks are updated online through adaptation laws obtained from a rigorous error convergence analysis. Thus, a training stage is unnecessary prior to the neural network implementation. Additionally, an integral action is included in the controller to cope with constant disturbances. The error convergence analysis guarantees the achievement of the trajectory tracking task and the boundedness of the output weight matrix estimation errors. The proposed scheme is designed such that an accurate knowledge of the quadrotor parameters is not needed. A comparison against the proposed controller and two other well-known schemes is presented. The obtained results showed the functionality of the proposed controller and demonstrated robustness to parametric uncertainty.