scholarly journals Analysis of servo-constraint problems for underactuated multibody systems

2013 ◽  
Vol 4 (1) ◽  
pp. 113-129 ◽  
Author(s):  
R. Seifried ◽  
W. Blajer
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Feedforward Control ◽  
Underactuated Mechanical Systems ◽  
Trajectory Tracking Control ◽  
Model Inversion ◽  
Flat Systems ◽  
First Results ◽  
Servo Constraints ◽  
Constraint Approach

Abstract. Underactuated multibody systems have fewer control inputs than degrees of freedom. In trajectory tracking control of such systems an accurate and efficient feedforward control is often necessary. For multibody systems feedforward control by model inversion can be designed using servo-constraints. So far servo-constraints have been mostly applied to differentially flat underactuated mechanical systems. Differentially flat systems can be inverted purely by algebraic manipulations and using a finite number of differentiations of the desired output trajectory. However, such algebraic solutions are often hard to find and therefore the servo-constraint approach provides an efficient and practical solution method. Recently first results on servo-constraint problems of non-flat underactuated multibody systems have been reported. Hereby additional dynamics arise, so-called internal dynamics, yielding a dynamical system as inverse model. In this paper the servo-constraint problem is analyzed for both, differentially flat and non-flat systems. Different arising important phenomena are demonstrated using two illustrative examples. Also strategies for the numerical solution of servo-constraint problems are discussed.

Stabilization of Internal Dynamics of Underactuated Systems by Periodic Servo-Constraints

2017 ◽  
Vol 17 (05) ◽  
pp. 1740004 ◽  
Author(s):  
László Bencsik ◽  
László L. Kovács ◽  
Ambrus Zelei
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Algorithmic Approach ◽  
Servo Constraints ◽  
And Control ◽  
Dependent Coordinates

The model-based motion control of underactuated, multiple degree-of-freedom, complex multibody systems is in focus. Underactuated mechanical systems possess less number of independent control inputs than degrees-of-freedom. The main difficulty in their control is caused by the dynamics of the uncontrolled part of the system. The complexity of multibody systems makes the dynamical and control formulation difficult. The direct application of traditional control techniques available in the literature can lead to unstable dynamic behavior in many cases. In order to avoid instability, these general methods are usually adapted for specific problems in an intuitive way. Here, we present a direct, more algorithmic approach, and propose the use of periodic servo-constraints to overcome stability problems and enhance the dynamic behavior. An exact, stability analysis-based method is also proposed for tuning the control parameters. A stability analysis procedure is developed which is directly applicable for investigating the dynamics of mechanical systems described by dependent coordinates and mathematically formulated as a set of algebraic differential equations.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Thomas Gorius ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Tracking Control ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Feedforward Control ◽  
Flexible Multibody Systems ◽  
Flexible Manipulator ◽  
End Effector ◽  
Nonminimum Phase ◽  
Flexible Multibody

In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.

Diversity of Servo-Constraint Problems for Underactuated Mechanical Systems: A Case Study Illustration

2013 ◽  
Vol 198 ◽  
pp. 473-482 ◽  
Author(s):  
Wojciech Blajer ◽  
Robert Seifried ◽  
Krzysztof Kołodziejczyk
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
Underactuated System ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Internal Dynamics ◽  
Mass System ◽  
Flat Systems

Underactuated mechanical systems are systems with fewer control inputs than degrees of freedom. Determination of an input control strategy that forces an underactuated system to complete specified in time outputs (servo-constraints), whose number is equal to the number of inputs, can be a challenging task. Diversity of the servo-constraint problems is discussed here using a simple spring-mass system mounted on a carriage (two degrees of freedom, one control input, and one specified in time output). A formulation of underactuated system dynamics which includes the output coordinates is motivated, with the governing equations arising either as ODEs (ordinary differential equations) or DAEs (differential-algebraic equations). Solutions to the servo-constraint problem are then discussed with reference to so-called non-flat systems (with internal dynamics) and differentially flat systems (no internal dynamics). Some computational issues related to the ODE and DAE formulations are finally discussed, and relevant simulation results for the sample case study are reported.

scholarly journals A 4-DOF Upper Limb Exoskeleton for Physical Assistance: Design, Modeling, Control and Performance Evaluation

2021 ◽  
Vol 11 (13) ◽  
pp. 5865
Author(s):  
Muhammad Ahsan Gull ◽  
Mikkel Thoegersen ◽  
Stefan Hein Bengtson ◽  
Mostafa Mohammadi ◽  
Lotte N. S. Andreasen Struijk ◽  
...  
Keyword(s):  
Upper Limb ◽  
Tracking Control ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Mechanical Design ◽  
Trajectory Tracking Control ◽  
Upper Limb Exoskeleton ◽  
And Performance ◽  
Physically Disabled People ◽  
Human Upper Limb

Wheelchair mounted upper limb exoskeletons offer an alternative way to support disabled individuals in their activities of daily living (ADL). Key challenges in exoskeleton technology include innovative mechanical design and implementation of a control method that can assure a safe and comfortable interaction between the human upper limb and exoskeleton. In this article, we present a mechanical design of a four degrees of freedom (DOF) wheelchair mounted upper limb exoskeleton. The design takes advantage of non-backdrivable mechanism that can hold the output position without energy consumption and provide assistance to the completely paralyzed users. Moreover, a PD-based trajectory tracking control is implemented to enhance the performance of human exoskeleton system for two different tasks. Preliminary results are provided to show the effectiveness and reliability of using the proposed design for physically disabled people.

A hierarchical constraint approach for dynamic modeling and trajectory tracking control of a mobile robot

2021 ◽  
pp. 107754632199918
Author(s):  
Rongrong Yu ◽  
Shuhui Ding ◽  
Heqiang Tian ◽  
Ye-Hwa Chen
Keyword(s):  
Mobile Robot ◽  
Dynamic Modeling ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Wheeled Mobile Robot ◽  
Structural Constraints ◽  
Control Force ◽  
Trajectory Tracking Control ◽  
Motion Constraints ◽  
Constraint Approach

The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out.

scholarly journals Dead-Time Compensation for the First-Order Dead-Time Processes: Towards a Broader Overview

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1519
Author(s):  
Mikulas Huba ◽  
Pavol Bistak ◽  
Damir Vrancic ◽  
Katarina Zakova
Keyword(s):  
Degrees Of Freedom ◽  
Dead Time ◽  
Feedforward Control ◽  
Structural Instability ◽  
Smith Predictor ◽  
Actual Process ◽  
Delayed Systems ◽  
First Order ◽  
Plant Modelling ◽  
Dead Time Compensation

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control of stable, integrating, and unstable first-order dead-time processes including simple diagnostics of the model used and focusing on the possibility of simplified but reliable plant modelling. The first approach, based on the first historically known dead-time compensator (DTC) with possible dead-beat performance, is based on the reconstruction of the actual process variables and the compensation of input disturbances by an extended state observer (ESO). Such solutions play an important role both in a disturbance observer (DOB) based control and in an active disturbance rejection control (ADRC). The second approach considered comes from the Smith predictor with two degrees of freedom, which combines feedforward control with output disturbance reconstruction and compensation by the parallel plant model. It is shown that these two approaches offer advantageous properties in the case of actuator limitations, in contrast to the commonly used PID controllers. However, when applied to integrating and unstable first-order systems, the unconstrained and possibly unobservable output disturbance signal of the second solution must be eliminated from the control loop, due to the hidden structural instability of the Smith predictor-like solutions. The modified solutions, usually referred to as filtered Smith predictor (FSP), then no longer provide a disturbance signal and thus no longer fully fit into the concept of Industry 4.0, which is focused on further optimization, predictive maintenance in dynamic systems, diagnosis, fault detection and fault identification of dynamic processes and forms the basis for the digitalization of smart production. Nevertheless, the detailed analysis of the elimination of the unstable disturbance response mode is also worth mentioning in terms of other possible solutions. The application of both approaches to the control of a thermal process shows almost equivalent quality, but with different dependencies on the tuning parameters used. It is confirmed that a more detailed identification of the controlled process and the resulting higher complexity of the control algorithms does not necessarily lead to an increase in the resulting quality of the transients, which underlines the importance of the simplified plant modelling for practice.

scholarly journals Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

2021 ◽  
pp. 014233122110313
Author(s):  
Afef Hfaiedh ◽  
Ahmed Chemori ◽  
Afef Abdelkrim
Keyword(s):  
Real Time ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Class I ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Control Scheme ◽  
And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

scholarly journals Flatness-Based Control of a Two Degrees-of-Freedom Platform With Pneumatic Artificial Muscles

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
David Bou Saba ◽  
Paolo Massioni ◽  
Eric Bideaux ◽  
Xavier Brun
Keyword(s):  
Degrees Of Freedom ◽  
Control Method ◽  
Sliding Mode ◽  
Feedforward Control ◽  
Volume Ratio ◽  
Open Loop ◽  
Control Technique ◽  
Artificial Muscles ◽  
Two Degrees Of Freedom ◽  
Pneumatic Artificial Muscles

Pneumatic artificial muscles (PAMs) are an interesting type of actuators as they provide high power-to-weight and power-to-volume ratio. However, their efficient use requires very accurate control methods taking into account their complex and nonlinear dynamics. This paper considers a two degrees-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves. An overactuation is present as three muscles are controlled for only two degrees-of-freedom. The contribution of this work is twofold. First, whereas most of the literature approaches the control of systems of similar nature with sliding mode control, we show that the platform can be controlled with the flatness-based approach. This method is a nonlinear open-loop controller. In addition, this approach is model-based, and it can be applied thanks to the accurate models of the muscles, the platform and the servovalves, experimentally developed. In addition to the flatness-based controller, which is mainly a feedforward control, a proportional-integral (PI) controller is added in order to overcome the modeling errors and to improve the control robustness. Second, we solve the overactuation of the platform by an adequate choice for the range of the efforts applied by the muscles. In this paper, we recall the basics of this control technique and then show how it is applied to the proposed experimental platform. At the end of the paper, the proposed approach is compared to the most commonly used control method, and its effectiveness is shown by means of experimental results.

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