Trajectory Tracking Experiments Research Articles

A Physics-Informed Neural Network Approach to Augmented Dynamics Visual Servoing of Multirotors.

This article presents a visual servoing strategy that integrates the capabilities of a physics-informed neural network (PINN) to estimate system uncertainties and inaccuracies with a dynamics-centered visual servoing technique for multirotors. The proposed method effectively combines these approaches, eliminating the need for inverse Jacobian calculations to determine multirotor motion by directly relating pixel variations to the multirotor's torque and thrust inputs, while also strengthening the method's robustness through the utilization of the PINN to model and address uncertainties in camera and multirotor parameters, as well as the modeling inaccuracies inherent in the dynamics-centered visual servoing technique. In contrast to existing state-of-the-art data-driven approaches, the proposed PINN approach requires, on average, 65% less labeled data to characterize uncertainties and inaccuracies. To ensure real-time implementation of the visual servoing model, the PINN-learned model is combined with an adaptive horizon monotonically weighted nonlinear model predictive controller (NMPC), capable of processing control efforts at rates 10 times faster than existing Tube MPC and Adaptive MPC strategies. These findings are validated through real-time trajectory tracking experiments, which not only highlight the effectiveness of the proposed approach in approximating modeling inaccuracies but also its capability in handling uncertainties upto 70% in camera parameters.

Adaptive control of an amplified piezoelectric-driven micropositioning stage based on notch filter structure inspiration and neural network online tuning

Abstract Piezoelectric-driven flexure micro/nanopositioning stages often exhibit a low-damping resonance mode, which can easily excite mechanical resonance during high-speed movement, and significantly impact the control system’s stability, control bandwidth, and trajectory tracking accuracy. To mitigate the reliance on the precise modeling of stage dynamics inherent in current resonant controllers, an adaptive control method based on a back propagation (BP) neural network was designed to suppress resonance in real-time. First, a piezoelectric-driven flexure micro/nanopositioning stage system was constructed. Next, a feedback controller similar to a notch filter was designed, with bilinear transformation applied based on the system’s inherent parameters to determine the initial values. Finally, the designed adaptive control method was tested through trajectory tracking experiments using a triangular wave signal. The experimental results showed that, when tracking the triangular wave signal, the maximum tracking error was reduced by 74.62% compared to proportional-integral (PI) control alone and by 69.91% compared to proportional integral control combined with a traditional notch filter. The tracking results demonstrate a significant improvement in the stage’s stability and tracking accuracy.

A Novel Robust Hybrid Control Strategy for a Quadrotor Trajectory Tracking Aided with Bioinspired Neural Dynamics

This paper introduces a novel hybrid control strategy for quadrotor UAVs inspired by neural dynamics. Our approach effectively addresses two common issues: the velocity jump problem in traditional backstepping control and the control signal chattering in conventional sliding mode control. The proposed system combines an outer-loop bioinspired backstepping controller with an inner-loop bioinspired sliding mode controller, ensuring smooth trajectory tracking even under external disturbances. We rigorously analyzed the system’s stability using Lyapunov stability theory. To validate our algorithm’s effectiveness, we conducted trajectory tracking experiments in both disturbance-free and step-disturbance conditions, comparing it with the traditional backstepping control, conventional sliding mode control, and saturated sliding mode control. The results demonstrate that our algorithm not only tracks trajectories more effectively but also significantly outperforms these methods in suppressing velocity jumps and signal chattering.

Research on ground mobile robot trajectory tracking control based on MPC and ANFIS

This study focuses on the control strategy for a ground mobile robot (GMR) with independent three-axis six-wheel drive and four-wheel independent steering, performing double lane change trajectory tracking in complex scenarios. Initially, a dynamic model of the six-wheel independent drive and steering GMR was constructed. Utilizing Model Predictive Control (MPC) technology, the challenge of trajectory tracking at low speeds was effectively addressed. For high-speed conditions, by thoroughly analyzing the impact of the predictive time-domain, this study innovatively introduced an Adaptive Neuro-Fuzzy Inference System (ANFIS) to dynamically adjust the prediction horizon of the MPC. A novel trajectory tracking algorithm integrating MPC and ANFIS was developed, with the network structure being trained using backpropagation (BP) method and the least squares method. Compared to traditional MPC, this hybrid strategy significantly improves trajectory tracking accuracy and stability at high speeds, with computational efficiency increased by 48.65%. Additionally, the algorithm demonstrated excellent adaptability and control effectiveness in various rigorous tests, including different speed levels, complex steering paths, load changes, sudden obstacles, and variable terrain. A 70 km/h trajectory tracking experiment on a physical vehicle yielded a root mean square (RMS) error of 0.1904 m, verifying its superior tracking performance and practical reliability. This provides a pioneering solution for high-performance trajectory control of ground mobile robots.

State Space Representation of Jiles-Atherton Hysteresis Model and Application for Closed-Loop Control.

Hysteresis is a fundamental characteristic of magnetic materials. The Jiles-Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications.

Dynamics Modeling and Parameter Identification for a Coupled-Drive Dual-Arm Nursing Robot

A dual-arm nursing robot can gently lift patients and transfer them between a bed and a wheelchair. With its lightweight design, high load-bearing capacity, and smooth surface, the coupled-drive joint is particularly well suited for these robots. However, the coupled nature of the joint disrupts the direct linear relationship between the input and output torques, posing challenges for dynamic modeling and practical applications. This study investigated the transmission mechanism of this joint and employed the Lagrangian method to construct a dynamic model of its internal dynamics. Building on this foundation, the Newton-Euler method was used to develop a dynamic model for the entire robotic arm. A continuously differentiable friction model was incorporated to reduce the vibrations caused by speed transitions to zero. An experimental method was designed to compensate for gravity, inertia, and modeling errors to identify the parameters of the friction model. This method establishes a mapping relationship between the friction force and motor current. In addition, a Fourier series-based excitation trajectory was developed to facilitate the identification of the dynamic model parameters of the robotic arm. Trajectory tracking experiments were conducted during the experimental validation phase, demonstrating the high accuracy of the dynamic model and the parameter identification method for the robotic arm. This study presents a dynamic modeling and parameter identification method for coupled-drive joint robotic arms, thereby establishing a foundation for motion control in humanoid nursing robots.

A novel adaptive trajectory tracking control for complex environments based on accelerated back-propagation neural network

This work addresses the issue of trajectory tracking accuracy degradation for vehicle dynamics parameters and road conditions changing, an adaptive trajectory tracking controller is designed for the intelligent vehicle. Based on the yaw dynamics model, a model predictive controller (MPC) is developed for the trajectory tracking process. Meanwhile, the impacts of different control parameters on trajectory tracking at various speeds are compared. And the change rule between optimal control parameter values and reference speeds is determined by cubic polynomial fitting to ensure minimal error during the trajectory following process. Then, an estimator for vehicle tire cornering stiffness and road adhesion coefficient is designed and tested based on the accelerated back-propagation neural network (ABPNN) model, with its estimation values being compared to those obtained through recursive least square method. Last, a co-simulation platform combining MATLAB/Simulink and CarSim software is established to conduct the trajectory tracking experiment under variable working conditions. Experimental results show that the proposed adaptive controller not only exhibits high accuracy in trajectory tracking but also demonstrates excellent stability and adaptability under medium to low speed conditions, particularly when encountering changing road conditions.

Friction compensation control method for a typical excavator system based on the accurate friction model

Traditional identification methods make it difficult to accurately determine the parameters of the friction model. Based on the LuGre friction model, a hybrid optimization algorithm (HO) is presented to address such aspects. This algorithm combines the genetic algorithm (GA) and particle swarm optimization algorithm (PSO) to obtain the globally optimal solutions. It incorporates three main improvements: introducing selection and crossover operations into the PSO algorithm, utilizing a variable inertia weight coefficient, and applying variable learning coefficients for enhanced performance. Compared to the static optimal solutions of the GA and PSO algorithms, the HO algorithm can improve the optimal solution by 40.68 % and 35.89 % respectively. The HO algorithm can achieve the highest model accuracy: the maximum identified friction error with the HO algorithm is only 1.70 kN, compared to 3.69 kN with the GA method and 8.52 kN with the PSO algorithm. Furthermore, a novel adaptive friction compensation controller (AC) is introduced based on the identification results to improve the stability and accuracy of the electro-hydraulic proportional systems of a 23-ton robotic excavator. Comparisons with existing proportional integral differential (PID) and feedforward compensation controllers (FC) highlight the superiority of the proposed adaptive controller in terms of trajectory accuracy and robustness. In sinusoidal trajectory tracking experiments, the AC method can achieve the highest tracking performance among the three controllers, and the maximum tracking error is only 11.56 mm. Compared to the FC controller, the control accuracy with the AC controller can be improved by 43.38 %. Experiments and simulations have shown that the friction compensation controller can effectively mitigate friction and other disturbances. As a result, the phenomena of crawling and flat peak phenomena can be eliminated.

A Lightweight and Affordable Wearable Haptic Controller for Robot-Assisted Microsurgery.

In robot-assisted microsurgery (RAMS), surgeons often face the challenge of operating with minimal feedback, particularly lacking in haptic feedback. However, most traditional desktop haptic devices have restricted operational areas and limited dexterity. This report describes a novel, lightweight, and low-budget wearable haptic controller for teleoperated microsurgical robotic systems. We designed a wearable haptic interface entirely made using off-the-shelf material-PolyJet Photopolymer, fabricated using liquid and solid hybrid 3D co-printing technology. This interface was designed to resemble human soft tissues and can be wrapped around the fingertips, offering direct contact feedback to the operator. We also demonstrated that the device can be easily integrated with our motion tracking system for remote microsurgery. Two motion tracking methods, marker-based and marker-less, were compared in trajectory-tracking experiments at different depths to find the most effective motion tracking method for our RAMS system. The results indicate that within the 4 to 8 cm tracking range, the marker-based method achieved exceptional detection rates. Furthermore, the performance of three fusion algorithms was compared to establish the unscented Kalman filter as the most accurate and reliable. The effectiveness of the wearable haptic controller was evaluated through user studies focusing on the usefulness of haptic feedback. The results revealed that haptic feedback significantly enhances depth perception for operators during teleoperated RAMS.

Anti-delay Kalman filter fusion algorithm for inter-vehicle sensor network with finite-step convergence

Intelligent vehicle applications in autonomous driving and obstacle avoidance commonly require the precise relative state of vehicles. Accordingly, this study focuses on the coordinate fusion of vehicle state problem experienced by an inter-vehicle sensor network with time-varying transmission delays. Using the ingeniously designed low-complexity integration with a consensus strategy and buffer technology, an anti-delay distributed Kalman filter (DKF) with finite-step convergence is proposed. By introducing an appropriate weight matrix to assess local estimates, the optimal fusion state result is available as a linear minimum variance. In addition, to accommodate practical engineering in intelligent vehicles, the communication weight coefficient and directed topology with unidirectional transmission are considered. From a theoretical perspective, the proof of error covariances’ upper bounds with different communication topologies with delays are presented. Furthermore, the maximum allowable delays of inter-vehicle sensor network are derived backwards. Simulations verify that while considering the various non-ideal factors presented above, the proposed DFK algorithm produces more accurate and robust fusion estimation state results than those of the existing algorithms, making it more valuable in practical applications. Moreover, a mobile car trajectory tracking experiment is conducted, which further verifies the feasibility of the proposed algorithm.

Design of a new Robot Operating System-MATLAB-based autonomous robot system and trajectory tracking experiment

The trajectory tracking performance of an actual robot is usually used as an important standard to evaluate a nonlinear controller algorithm. The aim of this article is to design a new experimental robot system based on the Robot Operating System-MATLAB framework. To validate the performance, a nonlinear tracking controller includes the following features. Firstly, the surface robot model is in Lie algebra [Formula: see text] format, which keeps the potential of cooperation control between space vehicles. Secondly, the nonlinear controller has good robustness under unknown disturbances. Thirdly, the control algorithm focuses on the practical robot, Turtlebot2. The robot system experimental results demonstrate the effectiveness of the proposed controller for trajectory tracking under unknown disturbance. The controller’s potential applications include autonomous robots for indoor examination, extreme condition rescuing, and cooperation between unmanned aerial vehicle and unmanned surface vehicle autodrives.

Design and motion control of exoskeleton robot for paralyzed lower limb rehabilitation.

Patients suffering from limb movement disorders require more complete rehabilitation treatment, and there is a huge demand for rehabilitation exoskeleton robots. Flexible and reliable motion control of exoskeleton robots is very important for patient rehabilitation. This paper proposes a novel exoskeleton robotic system for lower limb rehabilitation. The designed lower limb rehabilitation exoskeleton robot mechanism is mainly composed of the hip joint mechanism, the knee joint mechanism and the ankle joint mechanism. The forces and motion of the exoskeleton robot were analyzed in detail to determine its design parameters. The robot control system was developed to implement closed-loop position control and trajectory planning control of each joint mechanism. Multiple experiments and tests were carried out to verify robot's performance and practicality. In the robot angular response experiments, the joint mechanism could quickly adjust to different desired angles, including 15°, 30°, 45°, and 60°. In the trajectory tracking experiments, the exoskeleton robot could complete tracking movements of typical actions such as walking, standing up, sitting down, go upstairs and go downstairs, with a maximum tracking error of ±5°. Robotic wearing tests on normal people were performed to verify the assistive effects of the lower limb rehabilitation exoskeleton at different stages. The experimental results indicated that the exoskeleton robot has excellent reliability and practicality. The application of this exoskeleton robotic system will help paralyzed patients perform some daily movements and sports.

Development of a Minimally Invasive Surgical Robot Using Self-Helix Twisted Artificial Muscles

In the field of surgery, minimally invasive surgical robots (MISRs) have emerged as the persistent pursuit of physicians to minimize harm and perform precise surgery. The structure of newly proposed MISRs tends to change form rigid to flexible, which poses a challenge to precise control. In this work, a MISR actuated by self-helix twisted artificial muscles (SHTAMs) with large bending angle and high precision is developed. The configuration and operation principle of the MISR are illustrated. Then, the physical model of SHTAM and the kinematics model of the end effector are established. The contraction ratio of SHTAM reaches 27.5%, and the output force is 5424.2 mN. Besides, the maximum bending angle (about 92°) of MISR is measured to verify the kinematic analysis. Moreover, in the point positioning control experiments, the steady-state error is less than 0.11°. Subsequently, the trajectory tracking tests on sinusoidal trajectories with different frequencies and amplitudes are carried out, and the circular trajectory tracking experiment is also performed with a maximum error of 1.8° in cold gel environment. The experimental results indicate that the proposed MISR has a large bending angle and can achieve accurate trajectory control, which exhibits excellent prospect in precision minimally invasive surgery.

A design of pneumatic-driven translational pyramidal manipulator and its actively disturbance rejection tracking control

In this study, we have undertaken the design and implementation of a pneumatic-driven translational pyramidal manipulator (PTPM) with the primary objective of achieving reliable and precise motion control, even under conditions where the PTPM may be exposed to disturbances arising from coupling effects and internal uncertainties. To achieve this purpose, the ALADRC, an adaptive controller that integrates a linear active disturbance rejection controller (LADRC) with a reduced-order linear extended state observer (RLESO) and a radial basis function neural network optimizer (RFNNO), is presented in this paper. This ALADRC has the following advantages in the view of practical applications: (1) it rejects total disturbances and coupling effect, (2) it reduces the order of the extended state observer, (3) it selects observer gains according to system frequencies, and (4) it optimizes controller gains in real time. Two trajectory tracking experiments and three disturbance rejection experiments were conducted to verify the trajectory tracking and disturbance compensation performance of the designed PTPM, respectively. The experimental results indicated that the PTPM controlled using the ALADRC increased the robustness in external disturbance rejection and provided accurate trajectory tracking.

A Novel Electromagnetic Driving System for 5-DOF Manipulation in Intraocular Microsurgery.

This work presents a novel electromagnetic driving system that consists of eight optimized electromagnets arranged in an optimal configuration and employs a control framework based on an active disturbance rejection controller (ADRC) and virtual boundary. The optimal system configuration enhances the system's compatibility with other ophthalmic surgical instruments, while also improving its capacity to generate magnetic force in the vertical direction. Besides, the optimal electromagnet parameters provide a superior comprehensive performance on magnetic field generation capacity and thermal power. Hence, the presented design achieves a stronger capacity for sustained work. Furthermore, the ADRC controller effectively monitors and further compensates the total disturbance as well as gravity to enhance the system's robustness. Meanwhile, the implementation of virtual boundaries substantially enhances interactive security via collision avoidance. The magnetic and thermal performance tests have been performed on the electromagnet to verify the design optimization. The proposed electromagnet can generate a superior magnetic field of 2.071 mT at a distance of 65 mm with an applied current of 1 A. Moreover, it demonstrates minimal temperature elevation from room temperature (25 °C) to 46 °C through natural heat dissipation in 3 h, thereby effectively supporting prolonged magnetic manipulation of intraocular microsurgery. Furthermore, trajectory tracking experiments with disturbances have been performed in a liquid environment similar to the practical ophthalmic surgery scenarios, to verify the robustness and security of the presented control framework. The maximum root mean square (RMS) error of performance tests in different operation modes remains 35.8 μm, providing stable support for intraocular microsurgery.

Whole Body Control of an Autonomous Mobile Manipulator Using Series Elastic Actuators

The flexible joint robot has superior attractive features because of its high mobility, high load ratiohigh torque fidelity, robustness for external disturbance, task adaptability, and safety. In this paper, an autonomous mobile manipulator driven by the designed series elastic actuators (SEAs) is developed. A complete dynamic model of nonholonomic mobile manipulator including a mobile platform and manipulator with joint flexibility operating simultaneously is proposed. An integrated whole body trajectory control framework is proposed for such robot to perform mobile manipulation tasks. Considering the nonholonomic and holonomic constraints in the mobile manipulation, the whole-body dynamics is formulated and reduced. To address the highly nonlinear of the dynamics and model uncertainty, a novel integral Lyapunov function (ILF)-based adaptive neural network control for task tracking under uncertainties of the flexible joint robot model is proposed. Compared with existing methods, the proposed method provides an alternative for controlling flexible joint robots. The feasibility of the proposed method is verified by the extensive trajectory tracking experiment results in our developed flexible joint manipulator.

Soft Lightweight Small-Scale Parallel Robot With High-Precision Positioning

Small-scale (from centimeters down to micrometers) parallel robots with high precision are widely utilized in various industrial and biomedical settings, while such superiorities remain challenges for soft parallel robots (SPRs). In this work, we propose an integrated design and fabrication strategy to make up a soft lightweight (3.5 g) small-scale ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi 60\times$</tex-math></inline-formula> 40 mm) parallel robot based on the dielectric elastomer actuator. Then, a hybrid model is established to describe the mapping between driving space and workspace, taking advantage of the robustness and security of the model-based method and the strong nonlinear fitting ability of the data-driven neural network method. The stiffness and workspace of the robot are analyzed. The results of trajectory tracking experiments demonstrate the accuracy and robustness of the proposed hybrid model. The average positioning error of the different trajectories is 13.4–16.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\,\mu\mathrm{m}$</tex-math></inline-formula> . Finally, the zebrafish embryo puncture experiment is carried out to show the ability of micromanipulation. This research paves a new avenue for designing and controlling high-positioning SPRs, which is expected to be applied in the micromanipulation field.

Disturbance observer–based backstepping sliding mode cascade control of 2–degrees of freedom hydraulic tunneling robot

For the 2–degrees of freedom position tracking problem of the robotized hydraulic-driven roadheader with high nonlinearities and strong uncertainties, a practical disturbance observer–based backstepping sliding cascade control method together with an adaptive compensator is proposed and investigated. The presented methodology mainly includes a continuous nonsingular fast terminal sliding mode with the backstepping technique and the power reaching law with time-varying coefficients used to achieve satisfactory performance against the multi-source disturbances, two disturbance observers used to approximately estimate the unknown dynamics in the mechanical and hydraulic subsystem, respectively. Simultaneously, a continuous robustifying term is also utilized to compensate for the residual disturbances and enhance the robustness. The presented control method doesn’t need the precise model thanks to the auxiliary disturbance observer, and can ensure fast convergence and small tracking error thanks to the backstepping sliding cascade control and the adaptive robust compensator. Based on Lyapunov theory, stability of the overall closed-loop system is proved rigorously, and asymptotically bounded tracking performance of the robotic manipulator is guaranteed. Finally, 2–degrees of freedom trajectory tracking experiments are conducted, and comparative results effectively verify the superiorities of the proposed method.

Optimized Trajectory Tracking for Robot Manipulators with Uncertain Dynamics: A Composite Position Predictive Control Approach

This study addresses the trajectory tracking control challenges of robot manipulators with uncertain dynamics. The aim is to achieve precise and smooth trajectory regulation through a novel composite position predictive control (PPC) scheme that integrates motion profile and disturbance preview techniques. First, we perform offline dynamics identification and feedforward compensation alongside a pre-defined motion profile. To handle the disturbances arising from uncertain dynamics, a super-twisting disturbance observer is designed, resulting in a dynamically compensated prediction model. Furthermore, the receding optimization operations for PPC are executed by solving an optimal solution associated with a joint angle tracking error. The combination of feedforward and feedback control improves the robot manipulator’s absolute positioning accuracy as opposed to the conventional model predictive control method, especially when dealing with uncertain dynamics. The effectiveness of the proposed control method is confirmed through trajectory tracking experiments conducted on a six-degree-of-freedom robot platform with varying end-effector loads. The experimental results demonstrate that the proposed PPC method enhances tracking accuracy by approximately 45% and 25% when compared to the traditional inverse dynamic control (IDC) and the robust IDC approaches, respectively.

Master-slave Control Strategy of Surgical Robots for Gastrointestinal Surgery

The precise construction of the master-slave control strategy is a fundamental requirement for robot-assisted surgery. In this study, we propose a master-slave control strategy for gastrointestinal surgical robots based on the natural orifice transluminal endoscopic surgery surgical robot developed by Tianjin University. The forward and inverse kinematics of the continuum mechanism at the slave manipulator are investigated. A master-slave coordinate mapping system for surgical robots is established by analyzing the kinematic characteristics of the master and slave manipulators. Additionally, an intuitive mapping algorithm and a control flowchart for the robot are developed. The proportional control and incremental control strategies tailored for natural orifice transluminal endoscopic surgery procedures are proposed based on intuitive mapping control. Finally, a master-slave trajectory tracking experiment is performed to validate the feasibility of the proposed master-slave control strategy.