Dynamics Compensation Research Articles

Two-Stage Robot Controller Auto-Tuning Methodology for Trajectory Tracking Applications

Autonomy is increasingly demanded of industrial manipulators. Robots have to be capable of regulating their behavior to different operational conditions, without requiring high time/resource-consuming human intervention. Achieving an automated tuning of the control parameters of a manipulator is still a challenging task. This paper addresses the problem of automated tuning of the manipulator controller for trajectory tracking. A Bayesian optimization algorithm is proposed to tune firstly the low-level controller parameters (i.e., robot dynamics compensation), then the high-level controller parameters (i.e., the joint PID gains), providing a two-stage robot controller auto-tuning methodology. In both the optimization phases, the algorithm adapts the control parameters through a data-driven procedure, optimizing a user-defined trajectory tracking cost. Safety constraints ensuring, e.g., closed-loop stability and bounds on the maximum joint position errors, are also included. The performance of the proposed approach is demonstrated on a torque-controlled 7-degree-of-freedom FRANKA Emika robot manipulator. The 4 robot dynamics parameters (i.e., 4 link-mass parameters) are tuned in 40 iterations, while the robot control parameters (i.e., 21 PID gains) are tuned in 90 iterations. Comparable trajectory tracking-errors results with respect to the FRANKA Emika embedded position controller are achieved.

Depth control of ROV in nuclear power plant based on fuzzy PID and dynamics compensation

Depth control is very important for underwater robot in nuclear power plant, especially when the robot needs to perform special tasks at specific depths under the water. Aiming to realize the depth control for the nuclear environment, the paper proposes a depth control strategy combining fuzzy PID with dynamics compensation based on the fact that the water in the reactor pool is very calm. Firstly, we conducted the hydrodynamics analysis of the developed remotly operated vehilcle (ROV) using ANSYS FLUENT software to get the relationship between moving velocity and water resistance in heave direction. Then, field experiments were conducted to compensate the dynamics errors using least square method according to the real-time depth values collected by depth gauge. After that, the fuzzy PID controller was designed to tune the PID parameters using fuzzy rules based on the compensated relationship between outputs of propellers and depth values. Experiments were conducted with results showing that accuracy of the depth control strategy combing fuzzy PID with dynamics compensation can reach within 3 cm, which can fully meet the requirements of practical application in the reactor pool. The highlight of the paper is that we combine the fuzzy PID algorithm with compensated dynamics equation, which is very suitable to realize the depth control for ROV in nuclear power plant.

High Precision Adaptive Robust Neural Network Control of a Servo Pneumatic System

In this paper, an adaptive robust neural network controller (ARNNC) is synthesized for a single-rod pneumatic actuator to achieve high tracking accuracy without knowing the bounds of the parameters and disturbances. The ARNNC control framework integrates adaptive control, robust control, and neural network control intelligently. Adaptive control improves the precision of dynamic compensation with parametric estimation, and robust control attenuates the effect of unmodeled dynamics and unknown disturbances. In reality, the unmodeled dynamics of the complicated pneumatic systems and unpredictable disturbances in working conditions affect the tracking precision. However, these cannot be expressed as an exact formula. Therefore, the real-time learning radial basis function (RBF) neural network component is considered for better compensation of unmodeled dynamics, random disturbances, and estimation errors of the adaptive control. Although the bounds of the parameters and disturbances for the pneumatic systems are unknown, the prescribed transient performance and final tracking accuracy of the proposed method can be still achieved with fictitious bounds. Asymptotic tracking performance can be acquired under the provided circumstance. The comparative experiments with a pneumatic cylinder driven by proportional direction valve illustrate the effectiveness of the proposed ARNNC as shown by a high tracking accuracy is achieved.

Decoupled Torque Control of Series Elastic Actuator With Adaptive Robust Compensation of Time-Varying Load-Side Dynamics

Modern robots are increasingly being designed to collaborate with human, and the safety of human-robot interaction has become more significant than ever. Series elastic actuator (SEA) is a potential actuator system in force control for various robotic applications with inherent safe property. However, achieving the good performances of SEA torque control especially with unknown load-side dynamics is still challenging. In this article, a high performance decoupled torque controller is proposed to control the SEA as an ideal torque source that is suitable for various application scenarios. A more general decoupled dynamics of the SEA system is first established to fit the various scenarios by considering the large parametric uncertainties, nonlinearities, and unmodeled uncertainties. The adaptive robust control algorithm with an effective compensation mechanism is then developed to attenuate the uncertainties. Theoretically, the proposed approach guarantees the stability and high performance of the SEA system. Comparative experiments are carried out on a SEA testbed, and the experimental results demonstrate that the proposed approach has significant performance improvements over previous approaches.

Cutting force modeling and accurate measurement in milling of flexible workpieces

Abstract This paper presents the cutting force modeling and the experimental verification for the model with the accurate measurement of the milling forces through the dynamic compensation of the workpiece-dynamometer assembly dynamics in the milling of the flexible workpieces. To this end, time domain simulation containing both the tool and workpiece dynamics in two directions and a mechanistic force model are used to numerically estimate the cutting forces. Single and two degree of freedom flexure stages, which represent the workpiece flexibility, were designed and constructed to perform the experimental validation. For the accurate measurement of the cutting forces, inverse-based filtering compensation method is employed. It has been found that the measured cutting forces are significantly distorted by the workpiece flexibility and they can not provide reliable information about the milling mechanics and dynamics. However, by the use of the inverse-based filtering approach, the actual cutting forces acting on the tool/workpiece have been accurately obtained and they are in reasonable agreement with the computed ones. Furthermore, it has been observed that the variation in the workpiece dynamics due to the material removal in the milling plays a crucial role for the accurate cutting force compensation.

Synthesis of the Robotic Tool Motion-Controlling Algorithm Using Method of Correction Dynamics and Pertubations Compensation

The task of controlling the manipulation robot movement in one direction has been considered. Such task appears at cutting, welding, painting and other similar operations, when the robot instrument performs a program motion along the working surface and at the same time, it is necessary to keep a definite distance from this instrument to the surface automatically without excessive correction. A new algorithm of controlling the linear object of the second order of the general form has been obtained by dynamics and perturbations compensation method, which takes precedence over well-known decisions. The algorithm provides a zero static error of the system regulation and movement in acquisition of external effects within the accuracy of standard filters of the second order that is convenient for practical use. The first filter indicates movements of the system during the task performing; the second one provides perturbations compensation on state variables. A step-by-step procedure of the algorithm synthesis has been represented for the second order controlled object of the general form. Formulae for calculating regulator coefficients have been obtained. The obtained equations defining processes in a closed control system allow performing the analysis of the control quality and the dynamics of control changes depending on external influences. A method of equations identification of the robot motion in conditions when we know the maximum speed of its instrument movement and a dynamic error of the robot servosystem regulating has been developed. By this method, the robot equations are brought up to the Vyshnegradskiy’s form and then on the computer model a fundamental frequency and a decay factor can be easily chosen. The application of the obtained algorithm has been reviewed to create a system of automatic regulation of the robot instrument position. It has been clarified that defining free coefficients of these filters on position of filter fundamental frequency equation and a controlled object provides the given system operation speed at moderate amplitude of controlling actions. A mathematical modeling method has shown the advantages of regulation program quality, parametric and structural robustness of the obtained control system.

Finite-time composite guidance law with input constraint and dynamics compensation

Guidance laws are proposed for a near space interceptor with on–off type thrust as output. The target-interceptor engagement kinematics is integrated with the first-order dynamics of thruster to design guidance laws. The bang-bang type guidance law with linear sliding mode is proposed to deal with thruster dynamics, and the sufficient condition for finite time convergence is rigorously proved based on the finite-time convergence theory. According to the sufficient condition, a sliding mode guidance law with hysteresis-band switching is introduced to reduce the switching frequency of thruster. Then two guidance laws are combined into a composite guidance law to improve the guidance performance. Simulation results show that the line-of-sight angular rate can converge to a neighborhood of the equilibrium point before the final time of the guidance process, and the composite guidance law has better performance than typical guidance laws.

A new method for assessing anisotropy in fused deposition modeled parts using computed tomography data

Voids in fused deposition modeled (FDM) parts are assumed to be a key driver for their anisotropic behavior. However, these assumptions are based on investigations of voids using only 2D data (microscopy images). This paper presents a new method to measure such voids by analyzing 3D-data of from X-ray computed tomography (CT), and application of this data for assessment of mechanical parameters. The article is divided into three parts, where the first part elaborates on a proposed method to assess and characterize the void geometry throughout uniaxial printed FDM parts using CT-data. The second part presents an investigation of the void configurations in samples manufactured using different process parameters, aiming to understand how variation in extrusion rate and compensation for non-linear dynamic extrusion behavior affects the void sizes. The third part displays how the information regarding void sizes could be further related to global mechanical properties, using a multiscale finite element approach. The present method of CT-data analysis gives a clear overview of the spatial variation of the void geometry, and findings from the investigated samples suggest that the size of voids have a large non-random spatial variation, highly dependent on the turning points of the toolpaths, and also significantly affected by accumulation of excess material. Printing at a low extrusion rate increases the void sizes considerably, while implementation of an extrusion dynamics compensation algorithm was found to have low impact on the void sizes. The multiscale finite element approach predicts anisotropic elastic behavior, significantly more compliant in the vertical and transversal direction, relative to the printing direction of the infill. It also predicts a non-isotropic strain energy density throughout the specimen, where the location and magnitude of the most energy dense locations vary significantly for different directions of loading, which implicates an anisotropic behavior in terms of failure, in accordance with literature.

Model-based control for exoskeletons with series elastic actuators evaluated on sit-to-stand movements

BackgroundCurrently, control of exoskeletons in rehabilitation focuses on imposing desired trajectories to promote relearning of motions. Furthermore, assistance is often provided by imposing these desired trajectories using impedance controllers. However, lower-limb exoskeletons are also a promising solution for mobility problems of individuals in daily life. To develop an assistive exoskeleton which allows the user to be autonomous, i.e. in control of his motions, remains a challenge. This paper presents a model-based control method to tackle this challenge.MethodsThe model-based control method utilizes a dynamic model of the exoskeleton to compensate for its own dynamics. After this compensation of the exoskeleton dynamics, the exoskeleton can provide a desired assistance to the user. While dynamic models of exoskeletons used in the literature focus on gravity compensation only, the need for modelling and monitoring of the ground contact impedes their widespread use. The control strategy proposed here relies on modelling of the full exoskeleton dynamics and of the contacts with the environment. A modelling strategy and general control scheme are introduced.ResultsValidation of the control method on 15 non-disabled adults performing sit-to-stand motions shows that muscle effort and joint torques are similar in the conditions with dynamically compensated exoskeleton and without exoskeleton. The condition with exoskeleton in which the compensating controller was not active showed a significant increase in human joint torques and muscle effort at the knee and hip. Motor saturation occurred during the assisted condition, which limited the assistance the exoskeleton could deliver.ConclusionsThis work presents the modelling steps and controller design to compensate the exoskeleton dynamics. The validation seems to indicate that the presented model-based controller is able to compensate the exoskeleton.

Robust actuator dynamics compensation method for real-time hybrid simulation

Abstract Real-time hybrid simulation (RTHS) is a practical, cost-effective, and versatile experimental technique to evaluate structural performance under dynamic excitation. The simulated structure is commonly split into a physically tested rate-dependent substructure (PS) and a numerically simulated substructure (NS). A transfer system such as a servo-hydraulic actuator is used to impose boundary conditions on the PS. Consequently, efficient actuator control is necessary to guarantee reliable simulation results. However, time delay and uncertainties exist due to the dynamics of the actuator, which adversely influence the accuracy and stability of RTHS. Therefore, an innovative robust actuator dynamics compensation method is proposed in this study comprising three components, namely a mixed sensitivity-based robust H∞ controller to stabilize the actuator–specimen dynamics, a polynomial extrapolation module to further cancel the actuator delay, and an adaptive filter for displacement reconstruction of the actuator–specimen system. A detailed design procedure of the proposed strategy is presented. The efficacy of the proposed strategy is validated through a series of virtual tests on the benchmark problem for RTHS. Results show that the proposed method exhibits excellent tracking performance and robustness. In particular, the maximum values of the calculated time delay (TD), root mean square of the tracking error (RMSE), and peak tracking error (PE) are 0 ms, 2.56%, and 2.12%, respectively, whereas the maximum values of the standard deviation of TD, RMSE, and PE are 0 ms, 0.25%, and 0.33%, respectively.

A general framework for solving inverse dynamics problems in multi-axis motion control

An inverse dynamics compensation (IDC) scheme for the execution of curvilinear paths by multi-axis motion controllers is proposed. For a path specified by a parametric curve r(ξ), the IDC scheme computes a real-time path correction Δr(ξ) that (theoretically) eliminates path deviations incurred by the inertia and damping of the machine axes. To exploit the linear time-invariant nature of the dynamic equations, the correction term is computed as a function of elapsed time t, and the corresponding curve parameter values ξ are only determined as the final step of the IDC scheme, through a real-time interpolator algorithm. It is shown that, in general, the correction term for P, PI, and PID controllers consists of derivative, natural, and integral terms (the integrand of the latter involving only the path r(ξ), and not its derivatives). The use of lead segments to minimize transient effects associated with the initial conditions is also discussed, and the performance of the method is illustrated by simulation results. The IDC scheme is expressed in terms of a linear differential operator formalism to provide a clear, general, and systematic development, amenable to further adaptations and extensions.

Spatial force measurement using a rigid hexapod-based end-effector with structure-integrated force sensors in a hexapod machine tool

In machine tools, in-process force measurement is required by many manufacturing applications, where a particular demand for spatial measurements in up to 6 degrees of freedom (DoF) is growing. Beside expensive commercial 6 DoF force/torque sensors or vague drive current evaluation, sensor integration as part of machine components or joints has been discussed for a long time. The approach presented here, integrates 6 cost-efficient commercial 1 DoF force sensors in hexapod structures and kinematics, that are particularly suitable for sensor integration due to the absence of friction, the presence of mainly longitudinal forces and the availability of 6 DoF. These sensors can be placed at different positions, whereby this article focuses on a rigid hexapod-based end-effector. As the end-effector is not an independent measuring system, but part of a machine, that moves dynamically through the workspace and carries workpieces or tools, a suitable measurement model is necessary that addresses all those influences. After a brief literature overview and introduction to the approach, this work presents the dynamic measurement model including sensor and quasi-static error parameters, aspects about optimal framework design and several steps of validation and evaluation of the new measuring system. These include application of static loads, workspace analysis, dynamic transfer behaviour, rigid body dynamics compensation and, finally, process force measurement during a milling process.

The Influence of the Electronic Structure Method on Intersystem Crossing Dynamics. The Case of Thioformaldehyde.

The ability of different electronic structure methods to correctly describe intersystem crossing dynamics is evaluated, using thioformaldehyde as a test case. Mischievously, all methods considered-ranging from the multireference methods MRCISD, MS-CASPT2, or SA-CASSCF, to the single-reference methods ADC(2), CC2, and TDDFT in different flavors-provide the same state ordering and energies of the low-lying singlet and triplet electronic excited states within an acceptable error of 0.2-0.3 eV. However, the outcome of the nonadiabatic simulations after excitation to the lowest S1 (1 nπ*) state are dramatically different. While MS-CASPT2, ADC(2), BP86, and PBE do not transfer population to the triplet states within 500 fs-consistent with experimental evidence-SA-CASSCF, B3LYP, and BHHLYP predict intersystem crossing yields between 3% and 21% within the same time. The different excited state dynamics can be rationalized by inspecting potential energy profiles along the C-S bond stretch mode and single-triplet energy gaps. It is found that already at a C-S bond length of 1.9 Å, all the single-reference methods struggle to describe the correct asymptotic behavior of the potentials. Moreover, some methods, including SA-CASSCF, obtain incorrect 1 nπ*-3 ππ* energy gaps, leading to compensation of errors (ADC(2), BP86, PBE), or wrong dynamics (SA-CASSCF, B3LYP, BHHLYP). Only the accurate MRCISD and MS-CASPT2 methods are able to describe the C-S bond correctly and thus able to deliver the correct potential energy surfaces and dynamics for the right reason. A correlation with the amount of Hartree-Fock exchange in the density functional and the ease to access the 3 ππ* state from the 1 nπ* are able to explain the different behavior observed for GGA and hybrid functionals. It is thus illustrated that even in the case of a simple molecule, like CH2S, the sole assessment of vertical excitation energies as reliability predictors for nonadiabatic dynamics is inadequate. The reason is that ISC does not occur at the FC geometry, but rather at distorted geometries where the singlet-triplet gaps become small. Hence, a characterization of the potential energy surfaces beyond the Franck-Condon region is mandatory.

Stable Gaussian process based tracking control of Euler–Lagrange systems

Perfect tracking control for real-world Euler–Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows to maintain good tracking performance at low feedback gains. However, accurate models are often difficult to obtain.In this article, we address the problem of stable high-performance tracking control for unknown Euler–Lagrange systems. In particular, we employ Gaussian Process regression to obtain a data-driven model that is used for the feed-forward compensation of unknown dynamics of the system. The model fidelity is used to adapt the feedback gains allowing low feedback gains in state space regions of high model confidence. The proposed control law guarantees a globally bounded tracking error with a specific probability. Simulation studies demonstrate the superiority over state of the art tracking control approaches.

Data-based feedback controller tuning utilizing collocated and non-collocated sensors

In motion control applications, such as machine tools and high-precision positioning stages for the semiconductor or flat panel industries, it is becoming common to place sensors on not only the motor side (collocated side) but also the load side (non-collocated side). The load side information enables compensation of transmission dynamics, such as friction or backlash. However, due to the phase lag of the load side frequency characteristics, it is difficult to increase the feedback bandwidth. To address this problem, this paper proposes a feedback controller design method based on frequency response data that utilizes both collocated and non-collocated sensor information. Experimental results show that the proposed method effectively suppresses the input disturbance. Furthermore, the proposed optimization requires less calculation time compared with nonlinear optimization with random initial values and exhibits better performance.

Adaptive Neural Control of a Kinematically Redundant Exoskeleton Robot Using Brain-Machine Interfaces.

In this paper, a closed-loop control has been developed for the exoskeleton robot system based on brain-machine interface (BMI). Adaptive controllers in joint space, a redundancy resolution method at the velocity level, and commands that generated from BMI in task space have been integrated effectively to make the robot perform manipulation tasks controlled by human operator's electroencephalogram. By extracting the features from neural activity, the proposed intention decoding algorithm can generate the commands to control the exoskeleton robot. To achieve optimal motion, a redundancy resolution at the velocity level has been implemented through neural dynamics optimization. Considering human-robot interaction force as well as coupled dynamics during the exoskeleton operation, an adaptive controller with redundancy resolution has been designed to drive the exoskeleton tracking the planned trajectory in human brain and to offer a convenient method of dynamics compensation with minimal knowledge of the dynamics parameters of the exoskeleton robot. Extensive experiments which employed a few subjects have been carried out. In the experiments, subjects successfully fulfilled the given manipulation tasks with convergence of tracking errors, which verified that the proposed brain-controlled exoskeleton robot system is effective.

Gradient extremum seeking for static maps with actuation dynamics governed by diffusion PDEs

We design and analyze the scalar gradient extremum seeking control feedback for static maps with actuation dynamics governed by diffusion PDEs. Conceptually, a non-model based online optimization control scheme is paired with actuation dynamics which occur in chemistry, biology and economics. A learning-based adaptive control approach with known actuation dynamics is considered in this paper. In the design part, we first compensate the actuation dynamics in the dither signals. Secondly, we introduce an average-based actuation dynamics compensation controller via a backstepping transformation, which is fed by the perturbation-based gradient and Hessian estimates of the static map. The stability analysis of the error-dynamics is based on using Lyapunov’s method and applying averaging for infinite-dimensional systems to capture the infinite-dimensional state of the actuator model. Local exponential convergence to a small neighborhood of the optimal point is proven and illustrated by numerical simulations.

On superposition of Hammerstein systems: Application to simultaneous hysteresis‐dynamics compensation

SummarySuperposition principle (SP)—the response (output) of a linear system to a weighted combination of inputs equals to the combination of the outputs with the same weights and each corresponding to the individual input, respectively—is one of the most fundamental properties of linear systems, and has been exploited for controls, for example, in the development of model predictive control. Extension of the superposition principle beyond linear systems, however, is largely limited. In this paper, the almost superposition of Hammerstein systems (ASHS) and its application to precision control of hysteresis‐Hammerstein systems is studied. We first show, under some minor conditions, the existence of a nonstrict form ASHS, and under one further condition, the strict‐form ASHS. We then present one application of the ASHS—simultaneous hysteresis and dynamics compensation in output tracking of hysteresis‐Hammerstein systems, where offline iterative learning control to track the output elements is integrated with online synthesis of the control input via an inverse Preisach modeling. The proposed ASHS‐based technique is further enhanced through two online optimization schemes, and then illustrated through a simulation example on piezoelectric actuators model.

Model-based tracking control design, implementation of embedded digital controller and testing of a biomechatronic device for robotic rehabilitation

In this paper, the tracking control problem of a biomimetic exoskeleton powered by a pair of pneumatic artificial muscles is considered. The antagonistic configuration of the pair of pneumatic muscles, which is biologically inspired, enables safe and reliable actuation in applications of orthopaedic rehabilitation. However, during the inflation-deflation process, the pneumatic muscles introduce nonlinearity and hysteresis which deteriorate the control performance. A model of the antagonistic artificial muscles is adopted to develop a computed-torque control for feedforward compensation of the nonlinear dynamics of the actuated joint. A PID control action is used in combination with the feedforward compensation to achieve fast and accurate tracking control performance. The model, which possesses a reduced set of parameters as functions of the inflation/deflation phase, enables efficient nonlinear compensation. The experimental tests on the biomechatronic device, compared with other state-of-the-art approaches for controlling pneumatic artificial muscles, show better tracking performance in terms of convergence rate and robustness, justifying the convenience of using the proposed control methodology in the design of tracking controllers for exoskeletal biomechatronic devices.

Data-Driven PID Controller and Its Application to Pulp Neutralization Process

The pulp neutralization process is a complex industrial process with strong nonlinearity and time-varying dynamics. In general, this kind of process is hardly controlled by using traditional control techniques such as the proportional-integral-derivative (PID) controller. To resolve this problem, a novel PID control scheme is proposed by integrating a data-driven compensation of unmodeled dynamics and a multistep ahead of optimal control strategy. Essential difference from the classical PID controller lies in the use of unmodeled dynamics, the measured data from the pulp neutralization process is used directly for building the nonlinear PID controller, which plays an important role in control system design. Based on multistep ahead prediction optimal control theory, the controller parameters can be obtained through optimizing a cost function. Some theoretical results on the stability and convergence of the closed-loop system are established. To demonstrate the effectiveness of the proposed control techniques, a simulation model and a cobalt nickel hydroxide pulp neutralization process are employed. Simulations were carried out using data extracted from an actual pulp neutralization process, followed by some industrial experiments. Results from both simulations and experiments indicate that our proposed controller can effectively control the pH value of the pulp neutralization process with promising control performance.