Robot Joint Research Articles

A Kinematically Constrained Kalman Filter for Sensor Fusion in a Wearable Origami Robot

AbstractSensing for wearable robots is an ongoing challenge, especially given the recent trend of soft and compliant robots. Recently, a wearable origami exoshell has been designed to sense the user’s torso motion and provide mobility assistance. The materials of the exoshell contribute to a lightweight design with compliant joints, which are ideal characteristics for a wearable device. Common sensors are not ideal for the exoshell as they compromise these design characteristics. Rotary encoders are often rigid metal devices that add considerable weight and compromise the flexibility of the joints. Inertial measurement unit sensors are affected by environments with variable electromagnetic fields and therefore not ideal for wearable applications. Hall effect sensors and gyroscopes are utilized as alternative compatible sensors, which introduce their own set of challenges: noisy measurements and drift due to sensor bias. To mitigate this, we designed the Kinematically Constrained Kalman filter for sensor fusion of gyroscopes and Hall effect sensors, with the goal of estimating the human’s torso and robot joint angles. We augmented the states to consider bias related to the torso angle in order to compensate for drift. The forward kinematics of the robot is incorporated into the Kalman filter as state constraints to address the unobservability of the torso angle and its related bias. The proposed algorithm improved the estimation performance of the torso angle and its bias, compared to the individual sensors and the standard Kalman filter, as demonstrated through bench tests and experiments with a human user.

A Self-Aligning Upper-Limb Exoskeleton Preserving Natural Shoulder Movements: Kinematic Compatibility Analysis.

NESM- γ is an upper-limb exoskeleton to train motor functions of post-stroke patients. Based on the kinesiology of the upper limb, the NESM- γ includes a four degrees-of-freedom (DOF) active kinematic chain for the shoulder and elbow, along with a passive chain for self-aligning robotic joint axes with the glenohumeral (GH) joint's center of rotation. The passive chain accounts for scapulohumeral rhythm and trunk rotations. To assess self-aligning performance, we analyzed the kinematic and electromyographic data of the shoulder in eight healthy subjects performing reaching tasks under three experimental conditions: moving without the exoskeleton (baseline), moving while wearing the exoskeleton with the passive DOFs properly functioning, i.e., unlocked (human-in-the-loop(HIL)-unlocked), and with the passive DOFs locked (HIL-locked). Comparison of baseline and HIL-unlocked conditions showed nearly unchanged anatomical movement patterns, with a root-mean-square error of shoulder angle lower than 5 deg and median deviations of the GH center of rotation below 20 mm. Peak muscle activations showed no significant differences. In contrast, the HIL-locked condition deviated significantly from the baseline, as observed by the trunk and GH trajectory deviations up to 50 mm, accompanied by increased peak muscle activations in the Deltoid and Upper Trapezius muscles. These findings highlight the need for kinematic solutions in shoulder exoskeletons that can accommodate the movements of the entire shoulder complex and trunk to achieve kinematic compatibility.

Compliance control method for robot joint with variable stiffness

Compliance control method for robot joint with variable stiffness

Velocity Estimation of Robot Manipulators: An Experimental Comparison

Accurate velocity information is often essential to the control of robot manipulators, especially for precise tracking of fast trajectories. However, joint velocities are rarely directly measured and instead estimated to save costs. While many approaches have been proposed for the velocity estimation of robot joints, no comprehensive experimental evaluation exists, making it difficult to choose the appropriate method. This paper compares multiple estimation methods running on a six degrees-of-freedom manipulator. We evaluate: 1) the estimation error using a ground-truth signal, 2) the closed-loop tracking error, 3) convergence behavior, 4) sensor fault tolerance, 5) implementation and tuning effort. To ensure a fair comparison, we optimally tune the estimators using a genetic algorithm. All estimation methods have a similar estimation error and similar closed-loop tracking performance, except for the nonlinear high-gain observer, which is not accurate enough. Sliding-mode observers can provide a precise velocity estimation despite sensor faults.

Reduced-Order Observer Design for Robot Manipulators

This letter investigates the design of reduced-order observers for robot manipulators. Observer stability conditions are obtained based on a Lyapunov analysis. The proposed observer is enhanced with a hybrid scheme that may adjust the gains to cope with possible unbounded velocities of the robot joints. Thanks to such hybrid strategy, the observer works accurately both for robots driven by open-loop controllers and by output feedback controllers. Numerical simulations illustrate the efficacy of the reduced-order observer in several scenarios, including a comparison with the performance of a classical full-order observer.

Accurate TCP Position and Orientation Trajectory Generation in 6DOF Robotic Manipulators and CNC Machine Tools using FIR Filtering and Haversine Synchronisation

The use of robotics in manufacturing is rapidly growing. One promising application in particular is the use of robots as machining platforms. Robotic machining offers many advantages such as large operating envelopes, flexibility in operations and low installation and running costs. Robotic machining platforms much like computer numerically controlled (CNC) machine tools are commanded by numerical controllers (NCs) using the well established G-code part programming language (ISO-6983). Toolpaths are defined in the work piece coordinate system (WCS) as a series of discrete tool centre point (TCP) positions and tool orientations. The role of the NC is to generate smooth feed drive or robot joint commands such that the tool or end effector travels along the commanded toolpath whilst satisfying TCP position and orientation tolerances and robot/machine tool kinematic constraints. Interpolating tool orientations directly in the WCS requires complex real-time spherical interpolation computations. Overcoming this challenge, this paper introduces a C4 continuous tool path trajectory generation method for 6DOF motion. The tool centre point position is smoothed in the WCS, however, the tool orientation is smoothed directly in the rotary coordinate system without the requirement for spherical interpolation. The interpolated tool orientation trajectory follows the path of the great circle arc using the modified Haversine method eliminating non-linear interpolation errors present in linear interpolation of rotary axis positions (machine coordinate system interpolation). The proposed method is validated by simulation of a 6DOF robotic manipulator.

Multi-Objective Redundancy Optimization of Continuous-Point Robot Milling Path in Shipbuilding

The 6-DOF manipulator provides a new option for traditional shipbuilding for its advantages of vast working space, low power consumption, and excellent flexibility. However, the rotation of the end effector along the tool axis is functionally redundant when using a robotic arm for five-axis machining. In the process of ship construction, the performance of the parts’ protective coating needs to be machined to meet the Performance Standard of Protective Coatings (PSPC). The arbitrary redundancy configuration in path planning will result in drastic fluctuations in the robot joint angle, greatly reducing machining quality and efficiency. There have been some studies on singleobjective optimization of redundant variables, However, the quality and efficiency of milling are not affected by a single factor, it is usually influenced by several factors, such as the manipulator stiffness, the joint motion smoothness, and the energy consumption. To solve this problem, this paper proposed a new path optimization method for the industrial robot when it is used for five-axis machining. The path smoothness performance index and the energy consumption index are established based on the joint acceleration and the joint velocity, respectively. The path planning issue is formulated as a constrained multi-objective optimization problem by taking into account the constraints of joint limits and singularity avoidance. Then, the path is split into multiple segments for optimization to avoid the slow convergence rate caused by the high dimension. An algorithm combining the non-dominated sorting genetic algorithm (NSGA-II) and the differential evolution (DE) algorithm is employed to solve the above optimization problem. The simulations validate the effectiveness of the algorithm, showing the improvement of smoothness and the reduction of energy consumption.

Passivity-Based Motion and Force Tracking Control for Constrained Elastic Joint Robots

In the past, several motion and force controls were successfully implemented on rigid-joint robots with constraints. With the invention of mechanically compliant robots, the focus on designing controllers for elastic joint robots with constraints is increasing, especially involving the complexity of the joint elasticity in control. Aiming to bridge the gap between the control schemes of rigid- and elastic-joint robots, this letter presents a controller consisting of a PD+ task-space tracking and integral force control, while the intrinsic inertial and elastic properties of the system are fully preserved. We provide a passivity analysis and prove uniform asymptotic stability of the equilibrium. Simulations on a planar two-armed benchmark system with constraints validate the proposed control law.

Safe Learning-Based Control of Elastic Joint Robots via Control Barrier Functions

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

Model-Based Fault Diagnosis Algorithms for Robotic Systems

In this paper, three model-based fault diagnosis algorithms for robotic systems are designed, compared, simulated, and implemented. The first algorithm is based on a nonlinear adaptive observer (NLAO), where a sufficient condition for the convergence of the estimator is derived in terms of linear matrix inequality (LMI) under persistence of excitation condition. The second algorithm is based on an adaptive extended Kalman filter (AEKF). Unlike traditional approaches, where the fault parameters are considered as augmented state variables, the AEKF directly estimates the fault parameters from measurement data. The third algorithm is based on a cascade of a nonlinear observer (NLO) and a linearized adaptive Kalman filter (LAKF), called the adaptive exogenous Kalman filter (AXKF). The pros and cons for each algorithm are discussed. The performance of the algorithms is compared in a single-link joint robot system. Furthermore, the algorithms are implemented in a ball-balancing robot to detect and estimate the magnitude of the actuator faults.

On Tracking Control of Robot Manipulator with Flexible Joints in Operational Space

In this paper, an adaptive control framework and a command-filtered control framework are proposed for flexible joint robot manipulators to track a desired trajectory in the workspace. First, we present an adaptive control algorithm which ensures that the output (the end-effector) of the uncertain manipulator with flexible joints tracks a desired trajectory in the operational space. Subsequently, a control algorithm is synthesized with the command-filtered technique to eliminate the requirements of the joint-jerk feedback and the third-order derivative of system models. The advantages of the proposed control frameworks are guaranteeing the tracking performance in the workspace and scaling down the complexity of the controller. Therefore, the proposed approaches can be applied to heterogeneous robotic systems and are easier to implement. The stability and convergence of the closed-loop systems are analyzed based on Lyapunov technique. Simulation results are provided to show the efficiency of the proposed control frameworks.

Design and dynamic transmission error analysis of a new type of cycloidal-pin reducer with a rotatable output-pin mechanism

A new type of one-stage precision cycloidal-pin reducer is designed and explored in this study. The design innovatively replaces the fixed output-pin mechanism of conventional cycloidal-pin reducers with a rotatable output-pin mechanism, thereby transforming the sliding contact between the output-pin and the output-hole into a rolling contact. This new structural design is found to significantly improve the transmission efficiency of the reducer. To evaluate the dynamic transmission error (DTE) characteristics of the proposed reducer, a general dynamic model of the cycloidal-pin transmission system considering the influences of multi-source error factors on the geometry of the main components is established. The geometric error of the component is determined by taking random values within a given design-tolerance zone. The geometric error distribution introduced using this method can well match the actual machining situation. Finally, the DTEs of the new reducers with three different tolerance designs are analyzed numerically and tested experimentally. The results show that the new reducer with a reasonable tolerance design can achieve high transmission accuracy and has the potential for application in the joints of industrial robots.

Design and Analysis of a Novel Variable Stiffness Joint for Robot

The variable stiffness of robot joints plays an important role in improving the robot’s compliance, safety, and energy efficiency. In this paper, a novel type of variable stiffness joint based on a rack and pinion structure (VSJ-RP) is proposed. The structure and the variable stiffness principle of the joint are described in detail. The theoretical stiffness calculation and the dynamic model of the joint are established, and the correctness of the model is validated by simulation. The compliance, safety, energy storage, and release characteristics of the joint are validated by position, bearing capacity, hitting ball, and safety detection experiments, respectively. These experimental results show that the joint stiffness can be adjusted from 14.74 Nm/rad to 726.58 Nm/rad, and the overshoot of the position response is about 5.56–0.5%. The larger the stiffness of the joint, the faster the adjustment response, the smaller the fluctuation, and the more stable the operation are. The maximum output torque of the joint is about 20 Nm, and the torque difference between the minimum and the maximum stiffness of the joint is about 10%. The energy conversion efficiency of the joint is 17.56%~89.86%, and the deformation angle range is 2.66°~4.37°. These phenomena reflect the safety, energy storage, and release capacity of the joint. An effective exploration is performed regarding the miniaturization, safety, and energy utilization of robot variable stiffness joints.

Workspace Description and Evaluation of Master-Slave Dual Hydraulic Manipulators

Nuclear power plant emergency robots are robots used to respond to significant public safety incidents, such as uncontrolled radioactive sources and nuclear catastrophe leaks. However, there are no standardized evaluation criteria for the optimal design of the robots. We offer a quantitative analytic algorithm for optimizing nuclear power plant emergency robots to address this issue. The method optimizes the structural parameters of the robot in accordance with the workspace by analyzing, comparing, and evaluating the workspace. The approach comprises constructing a kinematic model of the mechanical arm and proposing an optimization algorithm based on the alpha shape to accurately describe the manipulator workspace; employing the proposed convex hull algorithm to quantitatively analyze and evaluate the workspace generated by different solutions in terms of area, volume, task demand, Structural Length Index and Global Conditioning Index; and determining the robotic arm joint parameters by selecting the optimum workspace design solution. Using the suggested algorithm, we optimize the design of the master and slave robotic arms of the nuclear power plant emergency robots. Theoretical calculations and simulation results demonstrate that the method is an effective and practical evaluation technique that not only accurately describes the workspace but also optimizes the design of the nuclear power plant emergency robots.

Practically Robust Fixed-Time Convergent Sliding Mode Control for Underactuated Aerial Flexible JointRobots Manipulators

The control of an aerial flexible joint robot (FJR) manipulator system with underactuation is a difficult task due to unavoidable factors, including, coupling, underactuation, nonlinearities, unmodeled uncertainties, and unpredictable external disturbances. To mitigate those issues, a new robust fixed-time sliding mode control (FxTSMC) is proposed by using a fixed-time sliding mode observer (FxTSMO) for the trajectory tracking problem of the FJR attached to the drones system. First, the underactuated FJR is comprehensively modeled and converted to a canonical model by employing two state transformations for ease of the control design. Then, based on the availability of the measured states, a cascaded FxTSMO (CFxTSMO) is constructed to estimate the unmeasurable variables and lumped disturbances simultaneously in fixed-time, and to effectively reduce the estimation noise. Finally, the FxTSMC scheme for a high-order underactuated FJR system is designed to guarantee that the system tracking error approaches to zero within a fixed-time that is independent of the initial conditions. The fixed-time stability of the closed-loop system of the FJR dynamics is mathematically proven by the Lyapunov theorem. Simulation investigations and hardware tests are performed to demonstrate the efficiency of the proposed controller scheme. Furthermore, the control technique developed in this research could be implemented to the various underactuated mechanical systems (UMSs), like drones, in a promising way.

CALIBRATION OF THE ROBOTIC ARM WITH CORRECTIONS USING LOCAL LINEAR NEURO-FUZZY MODELS

The paper deals with the enhancement of the robotic arm calibration using corrections based on local linear neuro-fuzzy models. After the standard calibration of the geometric parameters in the robot's kinematic model, there are still residual errors between the measured positions and the positions predicted by the model. The source of these errors are various non-geometric parameters and nonlinear phenomena that traditional kinematic calibration models do not include. The neuro-fuzzy model based on a locally linear model tree can approximate the residual error as a function of the robot's joint angles. Adding this approximation to the output of the calibrated robot model significantly increases the accuracy of the endeffector position. The results of the described method were verified and compared with other approaches on a simulation model of a flexible planar two-link mechanism. Experimental verification was performed on an industrial robot Stäubli TX200 with data measured by Leica laser tracking device.

A Two-Step Method for Dynamic Parameter Identification of Indy7 Collaborative Robot Manipulator.

Accurate dynamic model is critical for collaborative robots to achieve satisfactory performance in model-based control or other applications such as dynamic simulation and external torque estimation. Such dynamic models are frequently restricted to identifying important system parameters and compensating for nonlinear terms. Friction, as a primary nonlinear element in robotics, has a significant impact on model accuracy. In this paper, a reliable dynamic friction model, which incorporates the influence of temperature fluctuation on the robot joint friction, is utilized to increase the accuracy of identified dynamic parameters. First, robot joint friction is investigated. Extensive test series are performed in the full velocity operating range at temperatures ranging from 19 °C to 51 °C to investigate friction dependency on joint module temperature. Then, dynamic parameter identification is performed using an inverse dynamics identification model and weighted least squares regression constrained to the feasible space, guaranteeing the optimal solution. Using the identified friction model parameters, the friction torque is computed for measured robot joint velocity and temperature. Friction torque is subtracted from the measured torque, and a non-friction torque is used to identify dynamic parameters. Finally, the proposed notion is validated experimentally on the Indy7 collaborative robot manipulator, and the results show that the dynamic model with parameters identified using the proposed method outperforms the dynamic model with parameters identified using the conventional method in tracking measured torque, with a relative improvement of up to 70.37%.

Structural design and stiffness matching control of bionic variable stiffness joint for human–robot collaboration

The physical compliance of interaction is an important requirement for safe and efficient collaboration between robots and humans, and the realization of human–robot compliance requires robot joints with variable stiffness similar to those of human joints. In this study, based on the tissue structure and driving principle of the human arm muscle ligament, a robot joint with variable stiffness is designed, consisting of an elastic belt and serial elastic actuator in parallel. The variable stiffness of the joint is realized by adjusting the tension length of the elastic belt. Surface electromyography (sEMG) signals of the human arm are used as the characterization quantity of joint stiffness to establish the pseudo-stiffness model of the elbow joint. The stiffness of the robot joints is adjusted in real-time to match the human arm stiffness based on the changes in sEMG signals of the human arm during operation. Real-time compliant interaction of human–robot collaboration is realized based on an end stiffness matching strategy. Additionally, to verify the effectiveness of the human joint stiffness matching-based compliance control strategy, a human–robot cooperative lifting experiment was designed. The bionic variable stiffness joint shows good stiffness adjustment, and the human–robot joint stiffness matching strategy based on human sEMG signals can improve the effectiveness and comfort of human–robot collaboration.

Operational Impact Excitation Method for Milling Robot End Frequency Response Function Identification Under Movement State and Pose-Dependent Dynamic Compliance Analysis

Abstract Robot milling has become an important means of machining large structural parts, and the dynamic compliance of the robot end is the key factor affecting machining quality and efficiency. The dynamic characteristics of the milling robot end are different in movement state and static state and have significant pose dependence. In order to effectively evaluate the dynamic compliance of the robot end in the workspace under the movement state, the operational impact excitation method for robot joint relative frequency response function (FRF) identification based on operational modal analysis (OMA) used in machine tool is established, the inertial force generated by the joint acceleration and deceleration movements is used as the excitation force, the robot end relative dynamic compliance index (RERDCI) is proposed to evaluate the dynamic compliance of robot end in different poses, and verified by cutting experiments. Based on RERDCI, the effect of the robot pose on end dynamic compliance is analyzed, and some theoretical guidance for improvement of dynamic performance to resist vibration in milling is given.

Measurements on the external load acting on aquatic resistance fins during flexion/extension movements using a robotic joint.

Aquatic resistance training has been proven to be beneficial to many people, in particular those struggling with degenerative joint diseases or recovering from other musculoskeletal issues as the reaction forces acting on the joints become lower, but without compromising the cardiovascular and neuromuscular benefit of the movement. Little has been written on the load produced by or measurements of the devices used in aquatic resistance training. Therefore, uncertainties exist regarding details of how much load can be applied onto the foot when performing the movements and how to quantify progression. In this study, an instrumented robotic arm was designed, built, and used to measure the load acting on the three different types of fins during a simulated flexion/extension movement of a knee. The angular velocities of the knee ranged from 25°/s to 150°/s, which represent the physiological range of in vivo movements. The results demonstrated that the load followed a second-order polynomial with the angular velocities. The load is therefore a function of the angular velocity, the surface area of the fins, and the location of the fins away from the joint center rotation. We modeled the progression of speeds at maximal voluntary movements based on previous studies. The maximum loads measured between 11kg and 13kg in extension and 6kg and 9kg in flexion at 150°/s rotational velocity.