Desired Motion Trajectory Research Articles

Fixed-Time Formation Tracking Control of Nonlinear Multi-Agent Systems with Directed Topology and Disturbance

In this paper, we study the fixed-time formation (FixF) control problem for the nonlinear second-order multi-agent systems (MASs) with directed graph, where all agents are subject to communication disturbances. To overcome the bounded disturbance of communication and to guarantee the realization of predesignated formation within a fixed-time, a suitable FixF control protocol based on the backstepping method is proposed. Furthermore, to eliminate the dependence of the control parameters on global information, a new adaptive FixF control protocol is provided to combine with some mild conditions of control gain such that the formation with acceptable bounded error of MASs can be achieved within a fixed-time. Finally, the theoretical results are verified by two simulation examples, one of the simulation examples is that we set the desired formation as a regular octagon and the desired formation motion trajectory as a circle, the results show that all agents can form formation motion within a fixed-time.

Deep learning with an attention mechanism for continuous biomechanical motion estimation across varied activities.

Reliable estimation of desired motion trajectories plays a crucial part in the continuous control of lower extremity assistance devices such as prostheses and orthoses. Moreover, reliable estimation methods are also required to predict hard-to-measure biomechanical quantities (e.g., joint contact moment/force) for use in sports injury science. Recognising that human locomotion is an inherently time-sequential and limb-synergetic behaviour, this study investigates models and learning algorithms for predicting the motion of a subject's leg from the motion of complementary limbs. The novel deep learning model architectures proposed are based on the Long Short-Term Memory approach with the addition of an attention mechanism. A dataset comprising Inertial Measurement Unit signals from 21 subjects traversing varied terrains was used, including stair ascent/descent, ramp ascent/descent, stopped, level-ground walking and the transitions between these conditions. Fourier Analysis is deployed to evaluate the model robustness, in addition to assessing time-based prediction errors. The experiment on three unseen test participants suggests that the branched neural network structure is preferred to tackle the multioutput problem, and the inclusion of an attention mechanism demonstrates improved performance in terms of accuracy, robustness and network size. An experimental comparison found that 57% of the model parameters were not needed after adding attention layers meanwhile the prediction error is lower than the LSTM model without attention mechanism. The attention model has errors of 9.06% and 7.64% (normalised root mean square error) for ankle and hip acceleration prediction respectively. Also, less high-frequency noise is present in the attention model predictions. We conclude that the internal structure of the proposed deep learning model is justified, principally the benefit of using an attention mechanism. Experimental results for biomechanical motion estimation are obtained, showing greater accuracy than only with LSTM. The trained attention model can be used throughout despite transitioning between terrain types. Such a model will be useful in, for example, the control of lower-limb prostheses, instead of the need to identify and switch between different trajectory generators for different walking modes.

Study on the Modeling and Compensation Method of Pose Error Analysis for the Fracture Reduction Robot.

Background: In the process of fracture reduction, there are some errors between the actual trajectory and the ideal trajectory due to mechanism errors, which would affect the smooth operation of fracture reduction. To this end, based on self-developed parallel mechanism fracture reduction robot (FRR), a novel method to reduce the pose errors of FRR is proposed. Methods: Firstly, this paper analyzed the pose errors, and built the model of the robot pose errors. Secondly, mechanism errors of FRR were converted into drive bar parameter’s errors, and the influence of each drive bar parameter on the robot pose error were analyzed. Thirdly, combining with Cauchy opposition-based learning and differential evolution algorithm (DE), an improved whale optimization algorithm (CRLWOA-DE) is proposed to compensate the end-effector’s pose errors, which could improve the speed and accuracy of fracture reduction, respectively. Results: The iterative accuracy of CRLWOA-DE is improved by 50.74%, and the optimization speed is improved by 22.62% compared with the whale optimization algorithm (WOA). Meanwhile, compared with particle swarm optimization (PSO) and ant colony optimization (ACO), CRLWOA-DE is proved to be more accurate. Furthermore, SimMechanics in the software of MATLAB was used to reconstruct the fracture reduction robot, and it was verified that the actual motion trajectory of the CRLWOA-DE optimized kinematic stage showed a significant reduction in error in both the x-axis and z-axis directions compared to the desired motion trajectory. Conclusions: This study revealed that the error compensation in FRR reset process had been realized, and the CRLWOA-DE method could be used for reducing the pose error of the fracture reduction robot, which has some significance for the bone fracture and deformity correction.

Intelligent Bus Platoon Lateral and Longitudinal Control Method Based on Finite-Time Sliding Mode.

Considering the rapid convergence of the longitudinal and lateral tracking errors of the platoon, a finite-time tracking control method for the longitudinal and lateral directions of the intelligent bus platoon is proposed. Based on the bus platoon model and desired motion trajectory, a distributed longitudinal and lateral finite-time sliding mode tracking control framework of the platoon is designed. Considering the finite-time convergence of the sliding mode of the system, a nonsingular integral terminal sliding mode (NITSM) is designed. An adaptive power integral reaching law (APIRL) is proposed for the finite-time accessibility of the system approaching mode. Based on NITSM-APIRL, a distributed longitudinal and lateral finite-time sliding mode tracking controller for the bus platoon is designed, and a Lyapunov function is created to analyze the finite-time stability and string stability of the system. Based on the Trucksim/Simulink joint simulation experiment platform, the control performance of the method is contrasted with the existing methods, and the actual vehicle test verification is completed by relying on the National Intelligent Connected Vehicle testing zone, which proves the practicability of the method.

Finite-Time, Robust, and Adaptive Motion Control with State Constraints: Controller Derivation and Real Plant Experiments

The paper refers to one of the most important problems in industrial automation and robotics—effective motion control in the presence of state variable constraints. A new, nonlinear, adaptive, robust, and practically applicable motion controller for a motor-driven servo is proposed. The developed controller guarantees that the transient of the motion is practically finished in a predefined time, and after this moment, the desired motion trajectory is tracked with specified accuracy, inviolable, time-variable constraints imposed on the position and the velocity are preserved, and all these features are robust against disturbances and violations of the system’s parameters. This approach, distinguished by the fact that the settling time and the quasi-steady-state tracking accuracy are explicitly available design parameters, has never been described before. The controller is based on a special type of time-varying barrier Lyapunov function (BLF), responsible for the finite-time tracking and for meeting the constraints. The derivation of the controller is based on Lyapunov stability theory. A mixture of robust adaptive, nonlinear control techniques is applied to prove the system’s stability. Numerous simulations and experiments with a real permanent-magnet motor- driven servo prove the practical applicability and usefulness of the presented approach.

On Active Vibration Absorption in Motion Control of a Quadrotor UAV

Conventional dynamic vibration absorbers are physical control devices designed to be coupled to flexible mechanical structures to be protected against undesirable forced vibrations. In this article, an approach to extend the capabilities of forced vibration suppression of the dynamic vibration absorbers into desired motion trajectory tracking control algorithms for a four-rotor unmanned aerial vehicle (UAV) is introduced. Nevertheless, additional physical control devices for mechanical vibration absorption are unnecessary in the proposed motion profile reference tracking control design perspective. A new dynamic control design approach for efficient tracking of desired motion profiles as well as for simultaneous active harmonic vibration absorption for a quadrotor helicopter is then proposed. In contrast to other control design methods, the presented motion tracking control scheme is based on the synthesis of multiple virtual (nonphysical) dynamic vibration absorbers. The mathematical structure of these physical mechanical devices, known as dynamic vibration absorbers, is properly exploited and extended for control synthesis for underactuated multiple-input multiple-output four-rotor nonlinear aerial dynamic systems. In this fashion, additional capabilities of active suppression of vibrating forces and torques can be achieved in specified motion directions on four-rotor helicopters. Moreover, since the dynamic vibration absorbers are designed to be virtual, these can be directly tuned for diverse operating conditions. In the present study, it is thus demonstrated that the mathematical structure of physical mechanical vibration absorbers can be extended for the design of active vibration control schemes for desired motion trajectory tracking tasks on four-rotor aerial vehicles subjected to adverse harmonic disturbances. The effectiveness of the presented novel design perspective of virtual dynamic vibration absorption schemes is proved by analytical and numerical results. Several operating case studies to stress the advantages to extend the undesirable vibration attenuation capabilities of the dynamic vibration absorbers into trajectory tracking control algorithms for nonlinear four-rotor helicopter systems are presented.

Actuation and Motion Control of Flexible Robots: Small Deformation Problem

AbstractThis paper introduces a new computational approach for the articulated joint/deformation actuation and motion control of robot manipulators with flexible components. Oscillations due to small deformations of relatively stiff robot components which cannot be ignored, are modeled in this study using the finite element (FE) floating frame of reference (FFR) formulation which employs two coupled sets of coordinates: the reference and elastic coordinates. The inverse dynamics, based on the FFR formulation, leads to driving forces associated with the deformation degrees of freedom. Because of the link flexibility, two approaches can be considered to determine the actuation forces required to achieve the desired motion trajectories. These two approaches are the partially constrained inverse dynamics (PCID) and the fully constrained inverse dynamics (FCID). The FCID approach, which will be considered in future investigations and allows for motion and shape control, can be used to achieve the desired motion trajectories and suppress undesirable oscillations. The new small-deformation PCID approach introduced in this study, on the other hand, allows for achieving the desired motion trajectories, determining systematically the actuation forces and moments associated with the robot joint and elastic degrees of freedom, and avoiding deteriorations in the vibration characteristics as measured by the differences between the inverse- and forward-dynamics solutions. A procedure for determining the actuation forces associated with the deformation degrees of freedom is proposed and is exemplified using piezoelectric actuators. The PCID solution is used to define a new set of algebraic equations that can be solved for the piezoelectric actuation voltages required to maintain the forward-dynamics oscillations within their inverse-dynamics limits. A planar two-link flexible-robot manipulator is presented to demonstrate the implementation of the joint/deformation actuation approach. The results obtained show deterioration in the robot precision if the deformation actuation is not considered.

Enhancing Human Mobility Exoskeleton Comfort Using Admittance Controller

Human mobility exoskeletons have been in development for several years and are becoming increasingly efficient. Unfortunately, user comfort was not always a priority design criterion throughout their development. To further improve this technology, exoskeletons should operate and deliver assistance without causing discomfort to the user. For this, improvements are necessary from an ergonomic point of view. The device’s control method is important when endeavoring to enhance user comfort. Exoskeleton or rehabilitation device controllers use methods of control called interaction controls (admittance and impedance controls). This paper proposes an extended version of an admittance controller to enhance user comfort. The control method used consists of adding an inner loop that is controlled by a proportional-integral-derivative (PID) controller. This allows the interaction force to be kept as close as possible to the desired force trajectory. The force-tracking admittance controller modifies the actuation force of the system in order to follow both the desired motion trajectory and the desired relative force between the user and the exoskeleton.

Finite-Time Control of Myringotomy Surgical Device Based on Nonsingular Terminal Sliding Disturbance Observer

This paper presents a disturbance observer-based nonsingular terminal sliding mode control design for a myringotomy surgical device. The methodology is established to control a semi-automated hand-held ear surgical device for the treatment of otitis media with effusion. Otitis media with effusion is the collection of bacterial fluid in the middle ear space which can potentially lead to hearing loss and chronic infections. A finite-time terminal sliding surface is proposed and a nonsingular terminal sliding control is constructed. The control approach fulfils precise tracking of the desired motion trajectory in the presence of disturbances, nonlinearities and uncertainties. The stability of the control approach is analyzed. In addition, the tracking control of the myringotomy surgical device is proven mathematically and the simulation results confirm the applicability and efficiency of the proposed approach and a precise tracking performance following desired motion trajectory is demonstrated in the simulations.

A Force/Motion Control Approach Based on Trajectory Planning for Industrial Robots With Closed Control Architecture

Most industrial robots are provided by the manufacturer with a controller that cannot be modified by the user (e.g. a standard PID). This arrangement is commonly referred to as closed control architecture, since it is not possible to program arbitrary control laws. For the implementation of novel algorithms, it is on the contrary necessary to employ an open control architecture, which allows programming any control scheme. For that reason, it is customary to have testbeds that are made up of robot manipulators specially designed for this goal. Another disadvantage of the closed control architecture is that the controller provided by the manufacturer usually does not include a force control term since it allows only to program desired motion trajectories. To overcome these drawbacks without physically modifying the closed control architecture, this contribution presents a novel approach to simultaneously follow position and force trajectories by employing only motion planning, i.e. only by choosing the desired position trajectory. The approach is especially well suited for DC motor actuators with large gear reduction ratios as those of many industrial robots. The convergence of the manipulator position and applied force depends exclusively on the performance of the controller provided by the manufacturer. The approach is tested on a dual-arm cooperative manipulation system made up of two ABB IRB-2400 industrial robots with closed control architecture.

Integral Nonsingular Terminal Sliding Mode Control of Hydraulic Servo Actuator Based on Extended State Observer

Hydraulic servo actuator always suffers from various disturbance and uncertainties, which makes it difficult to design a higher performance controller. In this paper, an integral nonsingular terminal sliding mode controller based on extended state observer (ESO‐INTSM) is proposed to improve the robust performance of hydraulic servo actuator. The ESO is designed to estimate not only the parametric uncertainties but also the model disturbance. Based on the observed states of ESO, the proposed controllers could enable hydraulic servo actuator to track the desired motion trajectories. The stability of the synthesized controller is proved via Lyapunov analysis, which is very important for high‐accuracy tracking control of hydraulic servo actuator. Simulation and experimental results demonstrate that the proposed control strategy can effectively attenuate the adverse influence caused by the uncertainties and apparently improve the tracking accuracy.

An effort for resolving redundancy of a multi-finger robotic hand in straight-line motions

Multi-finger robotic hands are the main robotic invention for providing assistive movement therapy in hand rehabilitation. In this paper, the concept of task priority is adopted in order to solve the redundancy resolution of a robotic hand. The redundancy parameter has been used to design the inverse kinematic model in order to determine the joint angles when the finger moves to perform the initial subtask of tracing the desired trajectory while considering the secondary subtask of increasing the instantaneous manipulability. Five different human subjects performed the experimentation where the index finger and thumb are allowed to follow the three desired motion trajectories. Markers are placed on the finger joints in order to track the motion and obtain the finger joint angles. Further, the experimental joint angles are compared with those obtained from inverse kinematics. The index finger and thumb behaviour is analysed based on the redundancy resolution scheme. It has been observed that the optimized root-mean-square error remains insignificant of the different subjects performing the motion and the type of motion trajectories adopted for the index finger as well as the thumb. Thereafter, the proposed scheme is applied to a four-finger tendon-actuated robotic hand and it has been observed that the scheme can be applied to solve the redundancies of any robotic hand.

Dynamic trajectory adjustment of lower limb exoskeleton in swing phase based on impedance control strategy

The lower limb exoskeleton provides assistance by following the lower limb joints’ desired motion trajectory. However, angle control is not enough to meet the requirements in some special circumstances such as encountering obstacles. In the swing phase of the attached leg with the exoskeleton, there is a different contact force between the sole and the road surface in different road conditions. Therefore, it is particularly important to control the joint angle and contact force simultaneously, that is, it is not only necessary to follow the desired angle but also to minimize the influence of external contact force. In this article, a novel scheme is proposed to adjust the trajectory dynamically in the swing phase. First of all, the physical model is streamlined and the Lagrangian principle is carried out to dynamic analysis and established a model of lower limb exoskeleton in the swing phase. Furthermore, the angle dynamics equation is transformed into a Cartesian coordinate system to calculate the end contact force for the impedance model. Finally, the impedance control strategy together with a disturbance observer is designed which is suitable for nonlinear and strong coupling characteristics. The simulation result shows that the control system can follow the angle accurately in the condition of minimizing external constraints. Hardware experiment shows that lower extremity exoskeleton can adjust motion trajectory actively when encountering obstacles and complete the movement trajectory tracking at the same time.

Adaptive Fuzzy Sliding Mode Control for High-Precision Motion Tracking of a Multi-DOF Micro/Nano Manipulator

This letter introduces a robust adaptive control methodology for piezo-actuated flexure-based micro/nano manipulation mechanisms. This special control approach is established for tracking of the desired complex motion trajectories with system uncertainties. Further, the control methodology is formulated to accommodate not only the system uncertainties but also nonlinearities including the hysteresis effect and external disturbances in the motion of a 3-degrees-of-freedom (3-DOF) XYZ micro/nano manipulator. Adaptive fuzzy sliding mode control (AFSMC) is developed for the formulation of the control methodology. The fuzzy logic component and adaptation law employed in the controller are used to approximate the system uncertainties and compensate for the effect of nonlinear terms in the system. The resulting control strategy is devised using a sliding mode control scheme. The asymptotic tracking ability of the designed controller is proved by using Lyapunov-based stability analysis. Furthermore, an experimental study is performed on the 3-DOF compliant monolithic parallel micro/nano manipulator and the results confirm that the designed control approach produces high-precision motion tracking and smaller tracking errors compared to a model-free control technique, i.e. Proportional-Integral-Derivative (PID) controller.

Multi-UAV Formation Control Based on a Novel Back-Stepping Approach

This paper addressed a well-documented open problem regarding multiple unmanned aerial vehicles (multi-UAVs) formation keeping. A cooperative guidance control method based on the back-stepping approach is proposed to rapidly form the desired formation and reach the multi-UAV steady state. The UAV formation system consists of four UAVs, forming a regular triangle formation. One of the UAVs is a virtual leader and is located at the center of the triangle; the other three UAVs are located at the vertices of the triangle. The forward speed of leader is used as the forward direction of the formation, and the followers follow the leader in a formation flight. The error dynamics model of each follower is established by using the leader guidance mechanism, and the communication mode between any two UAVs is established based on graph theory. In addition, the guidance control law is obtained via the back-stepping approach. We reasonably construct the Lyapunov function to prove the stability of the proposed cooperative guidance control law in formation aggregation and keeping. Moreover, the proposed method is compared with the model prediction method (MPC) and the Lyapunov method to further verify the effectiveness of the proposed method. The simulation results show that each UAV can converge to the desired motion trajectory and fly in the desired formation with fast convergence speed and small steady-state error.

High-frequency robust position control of a nonlinear piezoelectric bending actuator

Piezoelectric bending actuators have been widely used in a variety of micro- and nano-applications, including atomic force microscopy, micro assembly, cell manipulation, and in general, micro electromechanical systems. However, their control algorithms at low frequencies suffer from nonlinearities such as hysteresis in high voltages and creep in long-time static applications. Also, in high-frequency applications, especially near the actuator natural frequencies, the actuator dynamic is greatly affected by the material nonlinearity. Therefore, the control approaches based on the linear dynamic modeling cannot be effective at high frequencies. Thus, the position control of the foregoing actuators become challenging, and it has been of researchers’ interests in the last decade. In this article, the robust position control of a bimorph piezoelectric bending actuators is investigated. In this regard, based on the nonlinear constitutive equations and the Euler–Bernoulli beam theory, a nonlinear dynamic model is presented. Then, to track a desired motion trajectory, an observer-based robust position control algorithm is proposed. The proposed control methodology is able to accommodate parametric uncertainties and other un-modeled dynamics. Also, it ensures the elimination of the position tracking error in the presence of the estimated states. Finally, the tracking ability of the controller is demonstrated in an experimental study. The experimental results show that the identification of the system is properly conducted with the average error of 5.5%. Also, the efficiency of the robust controller is proved with the error of 3.7% and 4.9% in the position tracking of the actuator inside and outside of the identified region, respectively.

Human-in-the-Loop Control Strategy of Unilateral Exoskeleton Robots for Gait Rehabilitation

In this article, a human-in-the-loop control methodology is proposed for the gait rehabilitation of patients with hemiplegia. It utilizes a unilateral exoskeleton system consisting of a unilateral lower limb exoskeleton and a real-time robot follower, such that the affected legs can be coordinated with the healthy legs with the assistance of the exoskeleton robot. In order to achieve immersive training during the physical therapy, the human-in-the-loop controller is developed. Furthermore, a region-based barrier Lyapunov function (BLF) is designed to separate the task workspace of the exoskeleton into a human region and a robot region, enabling the human leg to follow the desired motion trajectory in a compliant region, and the motion control of the exoskeleton is determined by humans; while in the robot region, the exoskeleton dominates the movement of human subjects. In order to make the motion control transit smoothly between the robot region and the human region, an adaptive controller is exploited to counteract the system’s nonlinear uncertainties. Both the theoretical analysis and experimental results support the effectiveness and practicability on hemiplegic patients of our control strategy.

A New Approach to Decoupled Non-Resonant Polishing.

Two-dimensional vibration-assisted polishing (2D-VAP) is a new polishing approach proposed in recent years, which is considered to be very suitable for the polishing of micro-optical parts and micro-structured surfaces. The advantages of the 2D-VAP approach are as follows: A very high relative velocity can be obtained between the workpiece and the polishing tool; the desired motion trajectory can be formed in one polishing cycle. However, there are still some problems to be solved in the 2D-VAP approach, mainly involving: The vibration frequency of the resonant excitation cannot be regulated, which makes it difficult to adapt to the processing demands of different materials; the theoretical model of removal function has been studied in few papers; and motion coupling occurs easily between the horizontal and vertical directions, which affects the trajectory synthesized at the polishing tool. In order to solve these problems, a new approach to decoupled non-resonant polishing is developed in this paper, and its effectiveness is investigated by the theoretical analysis and polishing experiments. Theoretical studies of removal function show that the vibration frequency, vibration amplitude and loading force are proportional to the removal depth. The comparison of experimental and modeling results of removal function show that they have good coherence, and the correctness of the theoretical model of removal function is verified. In addition, the stability experiments of removal function prove that the polishing approach has better stability and is beneficial to the convergence of workpiece surface.

Motion Control for Piezoelectric-Actuator-Based Surgical Device Using Neural Network and Extended State Observer

This paper presents a robust neural network with an extended state observer control methodology for a piezoelectric-actuator-based surgical device. This control methodology is proposed for tracking of desired motion trajectories in the presence of unknown or uncertain system parameters, nonlinearities including friction, hysteresis, and disturbances in the motion system. In particular, the radial basis function neural network, which serves as a function approximator, aims to create a model for an unknown function to find a relationship between input and output data. An extended state observer is utilized to assist in canceling disturbances and uncertainties of the system dynamically. The stability of the control approach is analyzed. The convergence of position and velocity tracking errors is proven theoretically. Experiments are conducted to demonstrate that the performance with an improved accuracy can be attained by the proposed control scheme. With the motion tracking capability, the control methodology helps the novel surgical device achieve higher success rate in operation, which is also suitable for similar piezoelectric ultrasonic actuator applications.

Adaptive sliding mode enhanced disturbance observer-based control of surgical device

This paper presents an enhanced adaptive robust disturbance observer-based motion tracking control methodology. This control approach is established and investigated for a semi-automated hand-held ear surgical device for the treatment of Otitis Media with Effusion. The proposed control methodology is utilised for tracking a desired motion trajectory in the presence of unknown or uncertain system parameters, nonlinearities including hysteresis, and disturbances in the motion system. The stability of the control approach is analysed. The convergence of position and velocity tracking errors is proven theoretically. A precise tracking performance following desired motion trajectory is demonstrated in the experimental study.