Precise Trajectory Tracking Research Articles

Design and implementation of fast terminal sliding mode control with synchronization error for cable-driven parallel robots

Since the cable structure generally leads to lower stiffness, cable-driven parallel robots (CDPRs) currently face some graver control challenges, where the inevitable system uncertainty will have more significant impacts on the control accuracy of CDPRs. To improve this situation, a novel sliding mode surface and the corresponding novel approaching law are defined by investigating the multi-cable synchronization, and then a new fast terminal sliding mode control strategy with synchronization error (FTSMC-SE) is proposed in this paper. Referring to the parallel structure of CDPRs, the synchronous motion of adjacent cables is ensured to obviously improve the control accuracy. Meanwhile, by deeply analyzing the finite-time convergence characteristic of the fast terminal sliding mode control, the defined synchronization error is skillfully integrated with the sliding mode surface and its novel approaching law to achieve further improvement. The Lyapunov theory is then used to analyze the finite-time stability with the error convergence guarantee of the control system. Simulation and experimental results indicate that the more synchronized cable motion and the faster error convergence can be achieved by the proposed FTSMC-SE, which together promotes the final higher precision trajectory tracking.

Precise Trajectory Tracking of Multi-Rotor UAVs Using Wind Disturbance Rejection Approach

Precise Trajectory Tracking of Multi-Rotor UAVs Using Wind Disturbance Rejection Approach

Lightweight Electrohydrostatic Actuator Drive Solution for Exoskeleton Robots

The practical long-term application of power-assisted exoskeleton robots requires lightweight, high-efficient, and high-control precision actuators. Based on the improvement of hardware design and control method, this article proposes a complete drive solution for the joint drive of exoskeleton robots and promotes the research of robot joint drive based on the pump-controlled hydraulic system. Specifically, a compact, backdrivable, and energy-efficient drive unit, lightweight electrohydrostatic actuator (LEHA) with a weight of 2.5 kg and a rated power of 340 W is designed first. Then, by combining the fifth-order high-precision dynamics model of LEHA and virtual decomposition control method, a high-performance controller with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{\infty }$</tex-math></inline-formula> stability is developed to realize the precise position trajectory tracking control of LEHA. Experimental results based on actual exoskeleton robot knee joints show that the proposed solution has high trajectory tracking performance over the frequency range of human body swing phase motion (0.5–1.5 Hz) and different loads (0–20 kg). Moreover, compared with the valve-controlled hydraulic power system with the same exoskeleton robot knee joint and wearer, test results show that the average efficiency increased by 18.13% after using LEHA under the swing phase test.

A Hybrid Visual–Haptic Framework for Motion Synchronization in Human–Robot Cotransporting: A Human Motion Prediction Method

In this article, we propose a hybrid visual–haptic framework enabling a robot to achieve motion synchronization in human–robot cotransporting. Visual sensing is employed in capturing human motion in real time. To deal with the inherent delays between the human’s initiative motion and the robot’s responsive motion in cotransporting, a human motion prediction method is developed to make the robot follow human motion proactively. Motion synchronization is achieved when the robot accurately tracks the filtered and predicted human motion. Force sensing is utilized to regulate interaction forces to ensure compliance when motion error between the human and robot is generated. A neural network (NN)-based control is proposed to achieve precise trajectory tracking. Comparative experimental results show that our proposed framework is effective in such cotransporting tasks.

Model Inversion for Precise Path and Trajectory Tracking in an Underactuated, Non-Minimum Phase, Spatial Overhead Crane

PurposeThis paper proposes a motion planning technique for precise path and trajectory tracking in an underactuated, non-minimum phase, spatial overhead crane. Besides having a number of independent actuators that is smaller than the number of degrees of freedom, tip control on this system presents unstable internal dynamics that leads to divergent solution of the inverse dynamic problem.MethodThe paper exploits the representation of the controlled output as a separable function of the actuated (i.e., the platform translations) and unactuated (i.e., the swing angles) coordinates to easily formulate the internal dynamics, without any approximation, and to study its stability. Then, output redefinition is adopted within the internal dynamics to stabilize it, leading to stable and causal reference commands for the platform translations.ResultsBesides proposing the theoretical formulation of this novel method, the paper includes the numerical validation and the experimental application on a laboratory setup. Comparison with the state-of-the-art input shaping is also proposed.ConclusionThe results, obtained through different reference trajectories, clearly show that almost exact tracking is obtained also in the experiments, by outperforming the benchmarks.

Development of neural‐network‐based stereo bionic compound eyes with fiber bundles

SummaryThe compound eye system has many unique advantages, enabling organisms to quickly and accurately obtain the three‐dimensional spatial information of the target. Therefore, its bionic applications have great potential in object localization, dynamic tracking, and 3D reconstruction. However, the current bionic compound eye systems still have great difficulties in target detection. Most of the bionic compound eye systems only verify the possibility of three‐dimensional (3D) detection, and there is no suitable calibration and detection scheme. In this article, a fiber‐optic stereo bionic compound eye is designed, and a simple and rapid calibration method suitable for this system is selected by comparing two effective optical information. Further, the system quantitatively analyzes the detection performance of the target to achieve precise positioning and dynamic trajectory tracking. In the static detection experiment, the average detection errors of the 3D position at the horizontal angle, the elevation angle and the depth are 0.33°, 0.32° and 1.84 mm, respectively. In the dynamic trajectory tracking experiment, the circle radius errors in the X‐Z plane and Y‐Z plane are 0.04 and 2.20 mm, respectively. The proposed system provides a new perspective to understand the nature of the compound eye.

INDI-based aggressive quadrotor flight control with position and attitude constraints

Recent studies have significantly contributed to the extensive use of quadrotors for delivery, mapping, and inspection. To further increase the versatility of quadrotors under confined environments, we focus on the precise trajectory tracking problem with position and attitude constraints. In tightly constrained scenarios, any slight error will infect flight security, especially in a large attitude maneuver. We utilize the incremental nonlinear dynamic inversion (INDI) method to precisely linearize the nonlinearities in the system and generalize it to the entire rotation space to reach a globally expressed control law. Meanwhile, the thrust alignment is introduced to improve the robustness against the mismatch between actuator dynamics and rotational dynamics, guaranteeing higher tracking accuracy. Improvements over a conventional geometry tracking controller are demonstrated in experiments where the quadrotor flies through an inclined narrow gap with orientation up to 90°. Flight tests also indicate the high disturbance rejection capabilities with the thrust alignment in gap traverse flight.

QPSO-MPC based tracking algorithm for cable-driven continuum robots.

Cable-driven continuum robots (CDCRs) can flexibly travel through narrow space for complex workspace tasks. However, it is challenging to design the trajectory tracking algorithm for CDCRs due to their nonlinear dynamic behaviors and cable hysteresis characteristics. In this contribution, a model predictive control (MPC) tracking algorithm based on quantum particle swarm optimization (QPSO) is designed for CDCRs to realize effective trajectory tracking under constraints. In order to make kinematic analysis of a CDCR, the forward and inverse mapping among actuation space, joint space and work space is analyzed by using the piecewise constant curvature method and the homogeneous coordinate transformation. To improve the performance of conventional MPC for complex tracking tasks, QPSO is adopted in the rolling optimization of MPC for its global optimization performance, robustness and fast convergence. Both simulation and operational experiment results demonstrate that the designed QPSO-MPC presents high control stability and trajectory tracking precision. Compared with MPC and particle swarm optimization (PSO) based MPC, the tracking error of QPSO-MPC is reduced by at least 43 and 24%, respectively.

Improvement of an Adaptive Robot Control by Particle Swarm Optimization-Based Model Identification

Model-based controllers suffer from the effects of modeling imprecisions. The analytical form of the available model often contains only approximate parameters and can be physically incomplete. The consequences of these effects can be compensated by adaptive techniques and by the improvement of the available model. Lyapunov function-based classic methods, which assume exact analytical model forms, guarantee asymptotic stability by cautious and slow parameter tuning. Fixed point iteration-based adaptive controllers can work without the exact model form but immediately yield precise trajectory tracking. They neither identify nor improve the parameters of the available model. However, any amendment of the model can improve the controller’s operation by affecting its range and speed of convergence. It is shown that even very primitive, fast, and simple versions of evolutionary computation-based methods can produce considerable improvement in their operation. Particle swarm optimization (PSO) is an attractive, efficient, and simple tool for model improvement. In this paper, a PSO-based model approximation technique was investigated for use in the control of a three degrees of freedom PUMA-type robot arm via numerical simulations. A fixed point iteration (FPI)-based adaptive controller was used for tracking a nominal trajectory while the PSO attempted to refine the model. It was found that the refined model still had few errors, the effects of which could not be completely neglected in the model-based control. The best practical solution seems to be the application of the same adaptive control with the use of the more precise, PSO-improved model. Apart from a preliminary study, the first attempt to combine PSO with FPI is presented here.

High Tracking Control for a New Independent Metering Valve System Using Velocity-Load Feedforward and Position Feedback Methods

The new configuration of independent metering valve (NIMV) system uses three proportional valves that gave been effectively proven to be energy saving compared with a conventional independent metering valve system in the fixed load condition. However, the variable load condition completely affects the accuracy and energy consumption during the operation of excavators. To improve the motion tracking precision and reduce the energy consumption of the NIMV system, a novel control method based on the coordinated control of the pump and the valve is proposed. In detail, the valve is controlled by considering velocity, load force, and position feedback of the cylinder. Meanwhile, velocity feedforward and position feedback methods are used to control the speed of the pump. In addition, a switching mode for the NIMV system is designed to flexibly select the metering modes based on the load and velocity conditions. To confirm the effectiveness of the proposed control method, the co-simulation model is built by using the AMESim and MATLAB software. From the results, the proposed method not only has high trajectory tracking precision with the displacement error of the cylinder at around 3.6% but also achieves up to 6.4% energy saving.

Iterative Learning Control for Precise Aircraft Trajectory Tracking in Continuous Climb and Descent Operations

This paper presents an iterative learning control method for precise aircraft trajectory tracking. Given a trajectory to be followed by an aircraft with a dynamical model which is assumed to be known, the proposed algorithm improves the system performance in following the trajectory using the spatial and temporal deviations suffered by previous flights to anticipate recurring disturbances and compensate for them proactively by generating a new reference trajectory to be followed, which is the input for the aircraft’s own trajectory tracking controller. The proposed method is tested in a simulated busy terminal maneuvering area in which the time-based separation between aircraft is short enough for similar weather conditions to be expected. The numerical experiments are conducted considering aircraft of the same type, which are assumed to follow the same trajectory in two operations in which precise trajectory tracking is essential: continuous climb and descent operations. The obtained results show a significant reduction of the trajectory tracking error in few iterations, proving the effectiveness of the iterative learning control method applied to commercial aircraft trajectory tracking. Higher precision in trajectory tracking implies higher predictability of aircraft trajectories, which results in an improvement of the efficiency and capacity of the air traffic management system and in reductions of costs and emissions.

Robust tracking for nanopositioning stages using sliding mode control with active disturbance rejection: Design and implementation

This paper presents the design and implementation of a novel sliding mode control integrated with active disturbance rejection (SMCDR) for precise robust trajectory tracking of piezoelectric nanopositioning stages. The model uncertainties, nonlinearity, and external disturbances of the piezoelectric nanopositioning stage are regarded as a lumped disturbance, which is estimated by an extended state observer. The active disturbance rejection control (ADRC) strategy is used to realize a preliminary trajectory tracking, while the sliding mode control is adopted to handle the estimation error and residual uncertainties, and to improve the tracking performance. The exponential stability of the proposed SMCDR is proved using Lyapunov’s direct method. The proposed SMCDR controller combines the strength of both ADRC and sliding mode control, exhibits a simple structure, requires only the position measurements, and does not require any information of model parameters except for an approximate constant gain. Experimental results reveal the robustness of the SMCDR approach in suppressing the hysteresis of piezoelectric actuator, and illustrate the superior performance over conventional ADRC, integral sliding mode controller (ISMC) and PID controller for trajectory tracking control of piezoelectric nanopositioning stages.

Continuous non‐singular terminal sliding‐mode control of permanent magnet spherical actuator for trajectory tracking based on a modified nonlinear disturbance observer

Multi-degree-of-freedom permanent magnet spherical actuators (PMSAs) are highly nonlinear, coupled, and multivariable systems that are subject to different types of disturbances including unknown payloads, unmodelled dynamics, frictions, and other external disturbances, which adversely affect the trajectory tracking performance of a system. In this paper, a disturbance-observer-based continuous non-singular terminal sliding-mode control (NDOB-CNTSMC) strategy is developed for a PMSA to enhance its trajectory tracking performance. Firstly, a nonlinear disturbance observer (NDOB) with a parameter design method is proposed to suppress uncertainty and reject disturbance in a PMSA trajectory tracking control system. Secondly, a continuous non-singular terminal sliding-mode controller (CNTSMC) is presented to compensate for the effect of the disturbance observation error and unobservable disturbances. The stability of the proposed control strategy is proved by the Lyapunov theorem. Both simulation and experimental results have shown that the control strategy proposed in this research can effectively address the issues of the inaccuracy of modelling and various disturbances and improve the trajectory tracking precision of the PMSA.

A Fuzzy-PLOS Guidance Law for Precise Trajectory Tracking of a UAV in the Presence of Wind

A Fuzzy-PLOS Guidance Law for Precise Trajectory Tracking of a UAV in the Presence of Wind

Differentiator‐based time delay control for uncertain robot manipulators

AbstractHigh‐quality acceleration signal plays a significant role in fast and precise trajectory tracking of robot manipulators via time delay control (TDC). This paper proposes a fast transient tracking differentiator (FTD) for obtaining the noise‐less time derivative from a noisy measurement within the framework of tracking differentiator (TD) design methodology. Global asymptotic convergence of the proposed FTD is proven by Lyapunov's direct method and TD theory. The proposed FTD is cascaded to construct an acceleration estimation and is integrated with the commonly used TDC for an improved trajectory tracking of robot manipulators in the presences of parametric uncertainties and bounded disturbances. Numerical simulations and real‐time experimental validation comparisons demonstrate that the proposed approach provides an easy‐going model‐free improved design for fast and accurate trajectory tracking of robot manipulators with position measurement only.

A collaborative excitation method for piezoelectric stick-slip actuator to eliminate rollback and generate precise smooth motion

The actuators with the abilities of precise trajectory tracking in large range are widely needed in many applications. However, nearly all the previous achievements can only accomplish the integration of high precision and long stroke in the point-to-point positioning, but not the trajectory tracking. Hence, this work proposes a collaborative excitation method for the stick–slip driving principle to eliminate the rollback and improve the motion smoothness. A 2-DOF piezoelectric actuator is fabricated to verify the validity, and the theoretical models are derived to explain the driving principle. The experimental results indicate that the rollback is eliminated completely, and the motion smoothness is improved significantly. The unlimited motion range and the motion resolution higher than 3.96 nm are presented. The steady load capability is more than 15.6 times of the self-weight. Furthermore, the close-loop trajectory tracking errors are smaller than 0.13 µm, which are less than 18.9% of the conventional excitation method. Besides, the precise planar tracking is also accomplished. To sum up, the proposed method improves the precise tracking performances of the piezoelectric stick–slip actuator significantly, and it has broad applicability on other actuators as well. Hence, it shows great prospects in the applications requiring precise trajectory tracking.

Improved Performance in Quadrotor Trajectory Tracking Using MIMO PIλ-D Control

This paper aims to develop a fractional control approach for quadrotor trajectory tracking. A fractional-order integrator (PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> ) with a feedback derivative scheme is designed to control each state of the MIMO system. The designed feedback controller stabilizes the initially unstable decoupled states and widens the stability, while PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> provides precise trajectory tracking capabilities. After a successful simulation study, the new PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> -D controller is implemented in the hardware environment. The various performance and load disturbance analyses reveal the effectiveness of the proposed scheme compared with the classical PD/PID controllers. The real-time study also shows that this scheme is a simple yet robust solution.

Data-driven trajectory tracking control for autonomous underwater vehicle based on iterative extended state observer.

In this study, we explore the precise trajectory tracking control problem of autonomous underwater vehicle (AUV) under the disturbance of the underwater environment. First, a model-free adaptive control (MFAC) is designed based on data-driven ideology and a full-form dynamic linearization (FFDL) method is utilized to online estimate time-varying parameter pseudo gradient (PG) to establish an equivalent data model of AUV motion. Second, the iterative extended state observer (IESO) scheme is designed to combine with FFDL-MFAC. Because the proposed novel controller is able to learn from repeated iterations, the proposed novel controller can estimate and compensate the model approximation error produced by external environmental unknown disturbance. Third, three-dimensional motion is decoupled into horizontal and vertical and a multi closed-loop control structure is designed that exhibits faster convergence rate and reduces sensitivity to parameter jumps than single closed-loop system. Finally, two simulation scenarios are designed featuring non external disturbance and Gaussian noise of signal-to-noise ratio of 90 dB. The simulation results reveal the superiority of FFDL. Furthermore, we adpot the technical parameters data of T-SEA I AUV to conduct numerical simulation, aunderwater trajectory as the tracking scenario and set waves to 0.5 m and current to 0.2 m/s to simulate Lv.2 ocean conditions of "International Ocean State Standard". The simulation results demonstrate the effectiveness and robustness of the proposed tracking control algorithm.

Practical tracking control of piezoelectric actuators with time-delay estimation and nonsingular terminal sliding mode

A novel type of nonlinear robust control strategy is proposed in view of uncertain nonlinear factors, such as hysteresis, creep, and high-frequency vibration, of piezoelectric actuators (PEAs). This strategy can be used for the precise trajectory tracking of PEAs. The Bouc–Wen dynamic model is reasonably simplified to facilitate engineering application. The hysteresis term is summarized as an unknown term to avoid its nonlinear parameter identification. The controller robustness is achieved due to the nonsingular terminal sliding mode control, and the online estimation of unknown disturbances is realized because of the delay estimation technology; thus, no prior knowledge of the unknown boundary of the system is required. The precision robust differentiator is used to estimate the speed and acceleration signals in real time on the basis of the obtained displacement signals. The closed-loop stability of the system is proved by the Lyapunov criterion. Experimental results show that the proposed control strategy performs better than the traditional time-delay estimation control in terms of control accuracy and energy conservation. Therefore, the proposed control strategy can play an important role in the micro/nanofield driven by PEAs.

Robust trajectory tracking control of underactuated unmanned surface vehicles with exponential stability: theory and experimental validation

PurposeTrajectory tracking is an important issue to underactuated unmanned surface vehicles (USVs). However, parametric uncertainties and environmental disturbances bring great challenges to the precise trajectory tracking control of USVs. This paper aims to propose a robust trajectory tracking control algorithm with exponential stability for underactuated USVs with parametric uncertainties and unknown environmental disturbances.Design/methodology/approachIn this method, the backstepping method and sliding mode control method are combined to ensure that the underactuated USV can track and maintain the desired trajectory. In addition, a modified switching-gain adaptation algorithm is adopted to enhance the robustness and reduce chattering. Besides, the global exponential stability of the closed-loop system is proved by Lyapunov’s direct method.FindingsThe proposed method in this paper offers a robust trajectory tracking solution to underactuated USVs and it is verified by simulations and experiments. Compared with the traditional proportion-integral-derivative method and several state-of-the-art algorithms, the proposed method has superior performance in simulation and experimental results.Originality/valueThis paper proposes a robust trajectory tracking control algorithm with exponential stability for underactuated USVs. The proposed method achieves exponential stability with better robustness and transient performance.