Abstract This paper presents a novel task-space adaptive controller designed to accurately track the trajectory of the end effector in redundant robot manipulators. The developed controller effectively mitigates disruptions caused by input delay while also coping with parametric uncertainties and unknown time-varying additive disturbances within the system dynamics. The designed controller distinguishes itself from traditional joint space controllers by eliminating the need for solving position-level inverse kinematics at each sampling interval, as it employs a novel error dynamics. Furthermore, the controller differs from predictor-based approaches by incorporating a developed auxiliary error signal derived from integrating the input signal over a defined time window from the current to the delayed time, thereby removing the need for future state predictions. The designed controller guarantees the semiglobal uniform ultimate boundedness of the tracking error using a novel Lyapunov-based stability analysis. Numerical simulations conducted on a two-degree-of-freedom planar robot manipulator model validate the effectiveness of the proposed method.

Purpose This paper proposes a novel fractional variable-order super-twisting sliding mode controller (FVO-STSMC) for robust trajectory tracking in robotic manipulators affected by random disturbances and parameter uncertainties. This paper aims to address issues of chattering and adaptability in conventional sliding mode controllers, particularly in stochastic multi-input multi-output systems. Design/methodology/approach The FVO-STSMC uses a variable-order fractional derivative, where the order is dynamically adjusted using a hyperbolic tangent function of the tracking error combined with a time-dependent sinusoidal term. The controller is analyzed theoretically and validated through simulations on a three-degree-of-freedom (DOF) planar robotic manipulator under Gaussian noise and parameter uncertainties. Findings Theoretical analysis confirms mean-square boundedness of tracking errors in the presence of stochastic disturbances and parameter variations. Simulation results demonstrate that the FVO-STSMC achieves lower tracking errors than both fixed-order fractional and standard super-twisting controllers, highlighting its superior robustness and precision. Originality/value This paper presents the first use of a variable-order fractional super-twisting sliding mode controller with dynamic order adjustment for robotic manipulators. The proposed method significantly advances adaptability, precision and robustness, providing valuable contributions to the field of advanced control systems.

The accuracy of planar parallel manipulators (PPMs) is heavily affected by the clearances present in their joints. Wear is inevitable in the joint during the operation of the manipulators, which results in non-uniform clearances. Previous research has been confined to examining the precision of planar parallel manipulators under the assumption of consistent joint clearances. Therefore, this research undertakes a kinematic reliability assessment of planar parallel manipulators, considering the presence of non-uniform clearances in their joints. Initially, the non-uniform clearances are characterized using a B-spline curve for their parametric representation. Then, the position error model of a planar parallel manipulator is established considering non-uniform joint clearances, uncertainty of input data, and errors of linkage dimensions. The matrix of the mean and covariance of the distribution of the position error are analytically derived. The probability density function (PDF) of the distribution of position error is calculated using the central limit theorem. Subsequently, the kinematic reliability in the workspace can be calculated by a direct integral over the obtained PDF. The proposed method is available for a mechanism with any irregular joint clearance when wear occurs. The efficacy and precision of proposed method are confirmed through a comparison against Monte Carlo simulation.

While networked multi-agent systems have been widely explored, the challenges introduced by underactuation still impede safety-critical cooperative control of multiple underactuated manipulators. This paper introduces a distributed framework for end-effector formation control and obstacle avoidance in planar n-link manipulators with a passive first joint and active remaining joints—termed PAn−1 manipulators. By exploiting the integrability of each PAn−1 manipulator’s second-order nonholonomic constraint, we reformulate the dynamics into a cascaded structure and derive a reduced-order model driven solely by active joint velocities. Building on this reduced-order model, we design safety-critical distributed formation control laws for the reduced-order dynamics, which serve as the manipulators’ desired active joint velocities. Then, we employ the backstepping method to obtain control inputs for the full-order dynamics. To guarantee safety, we treat backstepping tracking errors as matched disturbances and address them within a robust control barrier function framework. Numerical simulations and comparative studies confirm the effectiveness of the proposed approach.

The primary objective of this study is to enable the end effector of robot manipulators driven by brushless DC motors (BLDC), subjected to model uncertainties, to track the desired trajectory. Direct control in task space, with the primary goal of minimizing the tracking error of the end effector, is favored. Besides, incorporating actuator dynamics (AD)actuator dynamics (AD) into control synthesis and stability analysis is intended to enhance the sensitivity in terms of positioning and the reliability of robot manipulators. Consideration is given to uncertainties in both the robot manipulator and AD to achieve enhanced tracking performance. In order to improve the efficiency of the closed-loop control system, uncertainties in the dynamic model and AD were estimated using a self-organized adaptive fuzzy logic (AFL)adaptive fuzzy logic (AFL) framework, and the obtained estimates were applied to the control torque input. In the employed AFL framework, the means and variances of the membership functions (MFs)membership functions (MFs) are updated online in each iteration, enabling a more accurate estimation of uncertainties. The use of the newly created Lyapunov function demonstrates that the closed-loop system is uniformly ultimately bound. Experimental comparisons were conducted on a two-degree-of-freedom planar robot manipulator driven by a BLDC motor to test the applicability of the presented controller.

ABSTRACT A generalized formulation of evolution equations, which contains gradient and Hamiltonian systems, has been recently discussed in the context of systematic energy‐preserving spatial discretization and time integration using a Galerkin and Petrov–Galerkin ansatz, respectively. Among the examples from different physical domains, mechanical systems with holonomic constraints, described in terms of non‐minimal configuration variables and velocities, fit into the formulation. The models feature only the derived constraints on velocity level, and they can be numerically integrated, preserving energy and constraints without drift‐off. In this contribution, we set up this formulation for ‐link planar manipulators with mono‐ or multi‐articular elastic couplings in redundant Cartesian coordinates and velocities. Before sketching the recursive construction of the model, we recall the variational principle the model is derived from. A three‐link configuration is used as a simulation example to display the numerical conservation of constraints and energy. Finally, we discuss the extension of the model by joint torque inputs and perspectives regarding control design.

Abstract A design methodology for the high level analysis of inherently force balanced manipulators is presented. It is applied for the analysis and comparison of three closed chain, two degree of freedom, planar robotic manipulator concepts. These designs are based on four bar and five bar linkages, and modeled at an abstracted component level in terms of an extendable link profile, counter masses, and additional attachments with mass/inertia. The methodology optimizes the balanced design counter masses within attachment position constraints. Different geometric parameter combinations for each concept in terms of workspace and total mass with balancing modifications are assessed. The balanced and unbalanced designs for the optimal parameters for each concept are then simulated using multibody dynamics software for different trajectories, with measurement of the reactions forces/moments and joint torques. Through this analysis, the various factors and tradeoffs that influence the design and balance optimization aspects for these force balanced robot manipulator concepts are demonstrated.

Underactuated robotic systems are appealing for industrial use due to their reduced actuator number, which lowers energy consumption and system complexity. Underactuated systems are, however, often affected by residual vibrations. This paper addresses the challenge of generating energy-optimal trajectories while imposing theoretical null residual (and yet practical low) vibration in underactuated systems. The trajectory planning problem is cast as a constrained optimal control problem (OCP) for a two-degree-of-freedom revolute–revolute planar manipulator. The proposed method produces energy-efficient motion while limiting residual vibrations under motor torque limitations. Experiments compare the proposed trajectories to input shaping techniques (ZV, ZVD, NZV, NZVD). Results show energy savings that range from 12% to 69% with comparable and negligible residual oscillations.

A robust controller formulation for the precise end effector tracking of robot manipulators having uncertainties throughout its entire mechanical and actuator subsystems is presented. The formulated robust controller achieves practical end effector tracking, even in the presence of uncertainties in the kinematic and dynamic parameters of the mechanical subsystem and the electrical parameters of the actuator subsystem. Specifically, a robust backstepping type controller formulation that makes use of the nominal values of the system parameters is designed to ensure an exponentially convergent, practical end effector tracking result. The stability and global convergence of the controller formulation are ensured via Lyapunov type arguments and extensive experimental studies conducted on custom–built planar robotic manipulator demonstrate the feasibility of the proposed method.

Abstract Detrimental dendrite growth and water‐involved surface corrosion on Zn anode significantly hinder the aqueous Zn batteries implementation. Herein, Triacetoxy(vinyl)silane (VTSE) is employed as an etchant and a protective layer for Zn metal anode. Owing to the preferential adsorption of VTSE on Zn (002) and (101) planes, the treated Zn anode exhibits highly exposure of (100) facet with VTSE coverage. Such VTSE layer with strong Zn─Si─O interaction guides homogeneous Zn2+ deposition with a good inheritance of (100) plane orientation, further bringing about a reduced nucleation overpotential and accelerated desolvation process. Meanwhile, the dense VTSE layer inhibits the water penetration and suppresses hydrogen evolution corrosion. As expected, the Zn||Cu half cell exhibits prolonged lifespan over 1000 h at 1 mA cm−2 for 1 mAh cm−2.In the Zn||NVO full cell, a remarkable capacity retention of 73.1% can be reached after 2,000 cycles at 1 A g−1. This work offers new insights on the crystal plane manipulation engineering for aqueous Zn anode protection.

Designing manipulation systems with predetermined initial and final positions of the gripper is an important field in modern robotics. The objective is to move the payload along a non-imposed trajectory between two given positions while allowing periodic position changes. This study proposes advanced design concepts for planar 5R parallel manipulators. The proposed design principle focuses on interconnecting the two links of the manipulator, ensuring the gripper’s initial and final positions. The mechanical system employs only one actuator, leading to simplified control and minimal energy expenditure. Consequently, the operational reliability is improved, and the overall cost is reduced. Two different design concepts are discussed: one involves the addition of gears, and the other employs the synthesis of a four-bar linkage with adjustable link lengths. Numerical simulations are conducted to demonstrate and validate the effectiveness of the proposed design concepts. This work presents a novel scientific contribution by introducing a new design concept: it explores the field of fixed-sequence manipulators built on the base of planar 5R parallel mechanisms. A design concept that has hitherto remained unexplored. Furthermore, the significance of this achievement is underscored by the attainment of an explicit mathematical solution, making it more attractive. This approach widens the scope of designing methods for fast manipulation systems, thereby expanding their practical applications in robotics.

Abstract In the case of manipulators actuated by unidirectional pneumatic artificial muscles (PAMs) and passive restoring springs, the system parameters and spring stiffness affect the reachable workspace and the dynamic manipulability. A two-link planar manipulator actuated by PAMs and passive springs was designed and fabricated to analyze the limitations of its dynamic manipulability. Kinematic analysis and forward dynamics simulations show the influence of parameters of passive springs, such as spring stiffness and spring prestretch, on workspace and trajectory tracking performance. Simulation results prove the limitations on the dynamic motion ability of a manipulator with passive springs in certain regions of its workspace as compared to that of bidirectional actuated manipulators. These motion limitations cannot be improved by optimizing the controller. Experimental results show the trajectory tracking performance similar to those obtained in the simulations, thus validating the simulations and the dynamic manipulability analysis. Consequently, we propose a task-based optimization formulation for determining the system parameters, such as stiffness and prestretch of passive springs, to track a given trajectory accurately.

Due to edge feature defects of markers, the visual measurements for the servo control of planar manipulators often exhibit systematically distributed errors even after conventional distortion correction and camera calibration. Then, the measurement errors of visual servo system have strongly limited the absolute positioning accuracy for the feedback control of the planar manipulators. In this paper, a monocular visual measurement error prediction and feedback control method is proposed for a planar manipulator. First, the monocular vision captures markers and extracts pixel information regarding the manipulator's endpoint, while the data from the laser tracker is converted into the same coordinate system to compare and compensate the visual measurement errors. Second, the visual measurement errors of the entire workspace are obtained using visual measurement error prediction based on radial basis function neural network spatial interpolation. The measurement accuracy of the visual measurement system was improved by 91.1%. Finally, the visual measurement error prediction-based feedback controls are conducted for the positioning of planar manipulator. The experiments demonstrate that the positioning accuracy of the planar manipulator is significantly improved via the applications of the proposed method. Its positioning accuracy can reach ±0.2 mm.

The possibilities of using a planar parallel manipulator with two end-effectors for moving workpieces are considered. Parallel manipulators are known for their high accuracy and rigidity, which makes them ideal for tasks requiring precise positioning and manipulation of objects. The introduction of a second end-effector can significantly increase the productivity and efficiency of the process, providing the ability to simultaneously perform several operations. The study includes the synthesis of the manipulator, modeling its operation for moving light-weight workpieces. Particular attention is paid to the issues of synchronization of the movements of the end-effectors and optimization of their motion trajectories to minimize time costs and energy consumption. The results of the work demonstrate the promise of using such manipulators in automated production systems, especially in operations related to processing and moving workpieces.

Compared with conventional dynamic nonlinear equation systems, a hybrid double-deck dynamic nonlinear equation system (H3DNES) not only has multiple layers describing more different tasks in practice, but also has a hybrid nonlinear structure of solution and its derivative describing their nonlinear constraints. Its characteristics lead to the ability to describe more complicated problems involving multiple constraints, and strong nonlinear and dynamic features, such as robot manipulator tracking control. Besides, noises are inevitable in practice and thus strong robustness of models solving H3DNES is also necessary. In this work, a multilayered noise-tolerant zeroing neural network (MNTZNN) model is proposed for solving H3DNES. MNTZNN model has strong robustness and it solves H3DNES successfully even when noises exist in both the two layers of H3DNES. In order to develop the MNTZNN model, a new zeroing neural network (ZNN) design formula is proposed. It not only enables equations with respect to solutions to become equations with respect to the second-order derivatives of solutions but also makes the corresponding model have strong robustness. The robustness of the MNTZNN model is proved when parameters in the model satisfy a loose constraint and the error bounds are programmable via setting appropriate parameter values. Finally, the MNTZNN model is applied to the tracking control of the six-link planar robot manipulator and PUMA560 robot manipulator with hybrid nonlinear constraints of joint angle and velocity.

Redundant manipulators (RMs) are widely used in various fields due to their flexibility and versatility, but challenges remain in adjusting their inverse kinematics (IK) solutions. Adjustable IK solutions are crucial as they not only avoid joint limits but also enable the manipulability of the manipulator to be regulated. To address this issue, this paper proposes an IK optimization method. First, a performance metric for adjustable IK solutions is developed by introducing the motion-level factor. By setting the desired joint motion level, the IK solutions can be adjusted accordingly. Furthermore, a two-stage optimization algorithm is proposed to obtain the adjustable IK solutions. In the first stage, a modified gradient projection method is used to optimize the performance metric, generating a set of initial optimal solutions. However, cumulative errors may arise during this stage. To counteract this, the forward and backward reaching inverse kinematics algorithm is employed in the second stage to enhance the accuracy of the initial solutions. Finally, the effectiveness of the proposed method is validated through simulations and experiments using a planar cable-driven redundant manipulator. The results demonstrate that the IK solutions can be adjusted by modifying the motion-level factors. The proposed two-stage optimization algorithm integrates the advantages of the gradient projection method and the forward and backward reaching inverse kinematics algorithm, yielding a set of accurate and optimal IK solutions. Furthermore, the adjustable IK solutions facilitate the regulation of the RM’s manipulability, enhancing its adaptability and flexibility.

This paper examines the influence of the eight assembling modes of the 3-RRR planar manipulator on its workspace. The workspace is analyzed considering both first-type and second-type singularities. Understanding these issues is crucial in the process of designing such manipulators to avoid unfavorable cases. Additionally, a modular platform concept, suitable for experimental testing and informed by the numerical results presented here, is proposed. The outcomes of the experimental tests will be addressed in future work.

Soft robotics has recently attracted increasing attention due to its inherent softness and compliance. However, to fully realize their potential, it often requires numerous soft components and actuators. One major challenge for a large‐scale system is integration and miniaturization. In addition, for pneumatically controlled actuators, multiplexing is essential to reduce the tubing from the control valves. A miniaturized soft pneumatic actuator matrix (SPAM) with multiplexing control of crossing points by only control signals was realized by embedding two layers of interactive channels () in a soft material (PDMS) to form actuators () by cumulating both strokes and forces at the channel crossings, unlike piston‐based serially coupled gas‐springs that yield constant force. A SPAM prototype of actuators with control signals was studied. A SPAM was demonstrated in a tilting matrix and two coupled SPAMs were used in a pneumatic soft conveyor for planar manipulation. Its simplicity and size allow for future large‐scale integration in soft robotics.

Atmospheric water harvesting (AWH) has been extensively researched as a sustainable solution to current freshwater scarcity. Various bioinspired AWH surfaces have been developed to enhance water-harvesting performance, yet challenges remain in optimizing their structures. In this work, we report a dual-biomimetic AWH surface that combines beetle-inspired heterogeneous wettability with leaf-skeleton-based hierarchical microstructures on a rigid substrate. An authentic leaf skeleton innovatively serves as the mask during photolithography complemented by O2-plasma treatment, enabling precise design of superhydrophilic SiO2 structures with a hierarchy of vein orders forming reticulate meshes on a hydrophobic Si substrate. This design facilitates enhanced water collection through intricate reticulate meshes and directional droplet transport along the abundant multi-order veins. Such AWH surface shows a water-harvesting efficiency of 172 mg cm−2 h−1, increasing up to 62% and 58% over the pristine SiO2/Si wafer and Si wafer, respectively. Additionally, the role of structure orientation in the open-surface droplet transport is explored while the AWH surface is vertically placed during the water-harvesting process. This work highlights the potential of using meticulous natural designs, like leaf skeletons, to improve AWH surfaces, with broad applications in compact devices, such as on-chip evaporative cooling and planar microfluidics manipulation.

The existence of clearance in the joint causes positional deviation and reduces the accuracy of robotics, in which nonlinear factors such as friction and lubrication inside the joint seriously affect its dynamic behaviors. On the other hand, the effectiveness of control algorithms is largely dependent on the dynamic complexity of the robotics, while its complexity analysis is an important prerequisite for achieving high‐performance control. In this paper, we provide a method for analyzing the dynamic complexity of a planar manipulator with clearance and lubrication in joints based on a nonlinearity measure. The influences of joint parameters such as friction coefficient, lubricant viscosity, and gap radius are quantified on the dynamic complexity of the kinetics, which can identify the collision state of the joints effectively in the robot’s motion. First, a dynamical model of a planar manipulator is established by integrating the contact‐separation model and the force model at the joint, and a method for calculating the dynamic complexity based on the nonlinearity measure is proposed. Second, the effects of different joint parameters on the dynamic behaviors of the robotic system are analyzed, and the relationships between the lubricant viscosity, gap radius, and the dynamic complexity under different friction coefficients are established to analyze the impacts of the joint parameters on the dynamic complexities. The results show that the dynamic complexity of the robotic system can be decreased significantly by using the small gap radius and high viscosity of the lubricant, which can help to realize the better control performance. Especially, this method is more sensitive to state changes such as the collision state of the joint relative to the sample entropy method.