Applications of Fractional-Order Calculus in Robotics

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 15 June 2024 | Viewed by 15190

Special Issue Editors


E-Mail Website
Guest Editor
Department of Mechanical Engineering and Technology Management, Faculty of Science and Technology, Norwegian University of Life Sciences (NMBU), 1430 Ås, Norway
Interests: fractional calculus; fractional control; fractional modeling; robotics; manipulators

E-Mail Website
Guest Editor
Department of Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia
Interests: fractional calculus; fractional-order neural networks; forecasting and prediction

Special Issue Information

Dear Colleagues,

In the last few decades, fractional calculus has frequently been chosen by researchers as an alternative method for modeling and controlling dynamical systems. The fractional-order approach could provide a more precise analysis of a robotic system than its integer counterpart. This Special Issue is devoted to advancements in the modeling and control of robotic systems utilizing fractional calculus.

This issue aims to introduce new concepts in the field of fractional-order modeling and control and provide a platform for researchers to report these concepts. This Special Issue welcomes contributions from fellow researchers, academics, industry experts, and engineering students working on a similar topic.

The following are examples of possible areas of interest, but they are not exhaustive:

  • Fractional Order Control;
  • Developments in the tuning of fractional controllers applied to Robotics;
  • Fractional control strategies for different Robotic systems;
  • Fractional Calculus applied to UAVs;
  • Adaptive Fractional Order Control of Robotic Systems;
  • Developments of optimized control algorithms for fractional control Factional Order modeling;
  • Fractional-order behavior modeling of Robotic Systems;
  • Fractional calculus applied to underactuated Robotic Systems;
  • Developments of optimized algorithms for fractional modeling 

Dr. Abhaya Pal Singh
Dr. Kishore Bingi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional calculus
  • fractional control
  • fractional modeling
  • robotics
  • manipulators fractal

Published Papers (9 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Jump to: Review

19 pages, 11261 KiB  
Article
Smooth and Efficient Path Planning for Car-like Mobile Robot Using Improved Ant Colony Optimization in Narrow and Large-Size Scenes
by Likun Li, Liyu Jiang, Wenzhang Tu, Liquan Jiang and Ruhan He
Fractal Fract. 2024, 8(3), 157; https://doi.org/10.3390/fractalfract8030157 - 10 Mar 2024
Cited by 1 | Viewed by 1060
Abstract
Car-like mobile robots (CLMRs) are extensively utilized in various intricate scenarios owing to their exceptional maneuverability, stability, and adaptability, in which path planning is an important technical basis for their autonomous navigation. However, path planning methods are prone to inefficiently generate unsmooth paths [...] Read more.
Car-like mobile robots (CLMRs) are extensively utilized in various intricate scenarios owing to their exceptional maneuverability, stability, and adaptability, in which path planning is an important technical basis for their autonomous navigation. However, path planning methods are prone to inefficiently generate unsmooth paths in narrow and large-size scenes, especially considering the chassis model complexity of CLMRs with suspension. To this end, instead of traditional path planning based on an integer order model, this paper proposes fractional-order enhanced path planning using an improved Ant Colony Optimization (ACO) for CLMRs with suspension, which can obtain smooth and efficient paths in narrow and large-size scenes. On one hand, to improve the accuracy of the kinematic model construction of CLMRs with suspension, an accurate fractional-order-based kinematic modelling method is proposed, which considers the dynamic adjustment of the angle constraints. On the other hand, an improved ACO-based path planning method using fractional-order models is introduced by adopting a global multifactorial heuristic function with dynamic angle constraints, adaptive pheromone adjustment, and fractional-order state-transfer models, which avoids easily falling into a local optimum and unsmooth problem in a narrow space while increasing the search speed and success rate in large-scale scenes. Finally, the proposed method’s effectiveness is validated in both large-scale and narrow scenes, confirming its capability to handle various challenging scenarios. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

25 pages, 2779 KiB  
Article
Hybrid LSTM-Based Fractional-Order Neural Network for Jeju Island’s Wind Farm Power Forecasting
by Bhukya Ramadevi, Venkata Ramana Kasi and Kishore Bingi
Fractal Fract. 2024, 8(3), 149; https://doi.org/10.3390/fractalfract8030149 - 5 Mar 2024
Cited by 1 | Viewed by 1134
Abstract
Efficient integration of wind energy requires accurate wind power forecasting. This prediction is critical in optimising grid operation, energy trading, and effectively harnessing renewable resources. However, the wind’s complex and variable nature poses considerable challenges to achieving accurate forecasts. In this context, the [...] Read more.
Efficient integration of wind energy requires accurate wind power forecasting. This prediction is critical in optimising grid operation, energy trading, and effectively harnessing renewable resources. However, the wind’s complex and variable nature poses considerable challenges to achieving accurate forecasts. In this context, the accuracy of wind parameter forecasts, including wind speed and direction, is essential to enhancing the precision of wind power predictions. The presence of missing data in these parameters further complicates the forecasting process. These missing values could result from sensor malfunctions, communication issues, or other technical constraints. Addressing this issue is essential to ensuring the reliability of wind power predictions and the stability of the power grid. This paper proposes a long short-term memory (LSTM) model to forecast missing wind speed and direction data to tackle these issues. A fractional-order neural network (FONN) with a fractional arctan activation function is also developed to enhance generated wind power prediction. The predictive efficacy of the FONN model is demonstrated through two comprehensive case studies. In the first case, wind direction and forecast wind speed data are used, while in the second case, wind speed and forecast wind direction data are used for predicting power. The proposed hybrid neural network model improves wind power forecasting accuracy and addresses data gaps. The model’s performance is measured using mean errors and R2 values. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

31 pages, 9287 KiB  
Article
Fuzzy Fractional Order PID Tuned via PSO for a Pneumatic Actuator with Ball Beam (PABB) System
by Mohamed Naji Muftah, Ahmad Athif Mohd Faudzi, Shafishuhaza Sahlan and Shahrol Mohamaddan
Fractal Fract. 2023, 7(6), 416; https://doi.org/10.3390/fractalfract7060416 - 23 May 2023
Cited by 1 | Viewed by 1328
Abstract
This study aims to improve the performance of a pneumatic positioning system by designing a control system based on Fuzzy Fractional Order Proportional Integral Derivative (Fuzzy FOPID) controllers. The pneumatic system’s mathematical model was obtained using a system identification approach, and the Fuzzy [...] Read more.
This study aims to improve the performance of a pneumatic positioning system by designing a control system based on Fuzzy Fractional Order Proportional Integral Derivative (Fuzzy FOPID) controllers. The pneumatic system’s mathematical model was obtained using a system identification approach, and the Fuzzy FOPID controller was optimized using a PSO algorithm to achieve a balance between performance and robustness. The control system’s performance was compared to that of a Fuzzy PID controller through real-time experimental results, which showed that the former provided better rapidity, stability, and precision. The proposed control system was applied to a pneumatically actuated ball and beam (PABB) system, where a Fuzzy FOPID controller was used for the inner loop and another Fuzzy FOPID controller was used for the outer loop. The results demonstrated that the intelligent pneumatic actuator, when coupled with a Fuzzy FOPID controller, can accurately and robustly control the positioning of the ball and beam system. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

22 pages, 6940 KiB  
Article
Robust Trajectory Tracking Control for Serial Robotic Manipulators Using Fractional Order-Based PTID Controller
by Banu Ataşlar-Ayyıldız
Fractal Fract. 2023, 7(3), 250; https://doi.org/10.3390/fractalfract7030250 - 9 Mar 2023
Cited by 6 | Viewed by 1378
Abstract
The design of advanced robust control is crucial for serial robotic manipulators under various uncertainties and disturbances in case of the forceful performance needs of industrial robotic applications. Therefore, this work has proposed the design and implementation of a fractional order proportional tilt [...] Read more.
The design of advanced robust control is crucial for serial robotic manipulators under various uncertainties and disturbances in case of the forceful performance needs of industrial robotic applications. Therefore, this work has proposed the design and implementation of a fractional order proportional tilt integral derivative (FOPTID) controller in joint space for a 3-DOF serial robotic manipulator. The proposed controller has been designed based on the fractional calculus concept to fulfill trajectory tracking with high accuracy and also reduce effects from disturbances and uncertainties. The parameters of the controller have been optimized with a GWO–PSO algorithm, which is a hybrid tuning method, by considering the time integral performance criterion. The superior and contribution of the GWO–PSO-based FOPTID controller has been demonstrated by comparing the results with those offered by PID, FOPID and PTID control strategies tuned by the GWO–PSO. The examination of the results showed that the proposed controller, which is based on the GWO–PSO algorithm, demonstrates better trajectory tracking performance and increased robustness against various trajectories, external disturbances, and joint frictions as compared to other controllers under the same operating conditions. In terms of the trajectory tracking performance for robustness, the superiority of the proposed controllers tuned by GWO–PSO has been confirmed by 20.2% to 44.5% reductions in the joint tracking errors. Moreover, for assessing the energy consumption of the tuned controllers, the total energy consumption of the proposed controller for all joints has been remarkably reduced by 2.45% as compared to others. Consequently, the results illustrated that the proposed controller is robust and stable and sustains against the continuous disturbance. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

16 pages, 3201 KiB  
Article
Digital-Twin-Based Real-Time Optimization for a Fractional Order Controller for Industrial Robots
by Xuan Liu, He Gan, Ying Luo, Yangquan Chen and Liang Gao
Fractal Fract. 2023, 7(2), 167; https://doi.org/10.3390/fractalfract7020167 - 7 Feb 2023
Cited by 6 | Viewed by 1745
Abstract
Digital twins are applied in smart manufacturing towards a smarter cyber-physical manufacturing system for effective analysis, fault diagnosis, and system optimization of a physical system. In this paper, a framework applying a digital twin to industrial robots is proposed and realizes the real-time [...] Read more.
Digital twins are applied in smart manufacturing towards a smarter cyber-physical manufacturing system for effective analysis, fault diagnosis, and system optimization of a physical system. In this paper, a framework applying a digital twin to industrial robots is proposed and realizes the real-time monitoring and performance optimization of industrial robots. This framework includes multi-domain modeling, behavioral matching, control optimization, and parameter updating. The properties of the industrial robot are first modeled in a digital environment to realize the strong interactive and all-around 3D visual monitoring. Then, behavioral matching is performed to map the virtual system to the physical system in real time. Furthermore, the control performance of the system is improved by using a fractional order controller based on the improved particle swarm optimization algorithm. This framework is applied to the experimental verification of real-time control optimization on an industrial robot. The time-domain performance is improved in the simulation and experimental results, where the overshoot is promoted at least 42%, the peak time is promoted at least 32%, and the settling time is promoted at least 33%. The simulation and experimental results demonstrate the effectiveness of the proposed framework for a digital twin combined with fractional order control (FOC). Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

17 pages, 4266 KiB  
Article
Cascade Control for Two-Axis Position Mechatronic Systems
by Dora Morar, Vlad Mihaly, Mircea Şuşcă and Petru Dobra
Fractal Fract. 2023, 7(2), 122; https://doi.org/10.3390/fractalfract7020122 - 28 Jan 2023
Cited by 1 | Viewed by 1285
Abstract
The current paper proposes an extension for two controller design procedures for a two-axis positioning mechatronic system, followed by a comparison between them. As such, the first method consists in formulating an optimization problem in terms of linear matrix inequalities (LMIs) in order [...] Read more.
The current paper proposes an extension for two controller design procedures for a two-axis positioning mechatronic system, followed by a comparison between them. As such, the first method consists in formulating an optimization problem in terms of linear matrix inequalities (LMIs) in order to impose the location of the closed-loop poles, considering an uncertain model of such a system. The uncertain model is treated using various forms of linear differential inclusions (LDIs), namely, polytopic LDI (PLDI) and diagonal norm-bound LDI (DNLDI). Additionally, the problem regarding the command signal constraints is characterized in terms of LMIs. The imposed structure of the controller is a cascade one, with a PI controller for the position loop and a P controller for the velocity loop, having an additional feedforward term. On the other hand, the second method consists in designing a cascade controller with an inner P controller, as in the previous method, the outer controller being a fractional-order IλIDλD (FOID) controller. In terms of degrees of freedom, both methods present four degrees of freedom for each axis. The presented controller design procedures will be applied for a numerical example of such a positioning system, and a comparison of the obtained performance metrics will be performed. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

14 pages, 2562 KiB  
Article
Using a Fully Fractional Generalised Maxwell Model for Describing the Time Dependent Sinusoidal Creep of a Dielectric Elastomer Actuator
by Timi Karner, Rok Belšak and Janez Gotlih
Fractal Fract. 2022, 6(12), 720; https://doi.org/10.3390/fractalfract6120720 - 4 Dec 2022
Cited by 2 | Viewed by 1201
Abstract
Actuators made of dielectric elastomers are used in soft robotics for a variety of applications. However, due to their mechanical properties, they exhibit viscoelastic behaviour, especially in the initial phase of their performance, which can be observed in the first cycles of dynamic [...] Read more.
Actuators made of dielectric elastomers are used in soft robotics for a variety of applications. However, due to their mechanical properties, they exhibit viscoelastic behaviour, especially in the initial phase of their performance, which can be observed in the first cycles of dynamic excitation. A fully fractional generalised Maxwell model was derived and used for the first time to capture the viscoelastic effect of dielectric elastomer actuators. The Laplace transform was used to derive the fully fractional generalised Maxwell model. The Laplace transform has proven to be very useful and practical in deriving fractional viscoelastic constitutive models. Using the global optimisation procedure called Pattern Search, the optimal parameters, as well as the number of branches of the fully fractional generalised Maxwell model, were derived from the experimental results. For the fully fractional generalised Maxwell model, the optimal number of branches was determined considering the derivation order of each element of the branch. The derived model can readily be implemented in the simulation of a dielectric elastomer actuator control, and can also easily be used for different viscoelastic materials. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

15 pages, 6303 KiB  
Article
Fractional-Order Impedance Control for Robot Manipulator
by Yixiao Ding, Xiaolian Liu, Pengchong Chen, Xin Luo and Ying Luo
Fractal Fract. 2022, 6(11), 684; https://doi.org/10.3390/fractalfract6110684 - 18 Nov 2022
Cited by 6 | Viewed by 1614
Abstract
Impedance control is an important method in robot–environment interaction. In traditional impedance control, the damping force is regarded as a linear viscoelastic model, which limits the description of the dynamic model of the impedance system to a certain extent. For the robot manipulator, [...] Read more.
Impedance control is an important method in robot–environment interaction. In traditional impedance control, the damping force is regarded as a linear viscoelastic model, which limits the description of the dynamic model of the impedance system to a certain extent. For the robot manipulator, the optimal impedance parameters of the impedance controller are the key to improve the performance. In this paper, the damping force is described more accurately by fractional calculus than the traditional viscoelastic model, and a fractional-order impedance controller for the robot manipulator is proposed. A practical and systematic tuning procedure based on the frequency design method is developed for the proposed fractional-order impedance controller. The fairness of comparison between the fractional-order impedance controller and the integer-order impedance controller is addressed under the same specifications. Fair comparisons of the two controllers via the simulation and experiment tests show that, in the step response, the fractional-order impedance controller has a better integral time square error (ITSE) result, smaller overshoot and less settling time than the integer-order impedance controller. In terms of anti-disturbance, the fractional-order impedance controller can achieve stability with less recovering time and better ITSE index than integer order impedance controller. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

Review

Jump to: Research

29 pages, 800 KiB  
Review
A Review on Fractional-Order Modelling and Control of Robotic Manipulators
by Kishore Bingi, B Rajanarayan Prusty and Abhaya Pal Singh
Fractal Fract. 2023, 7(1), 77; https://doi.org/10.3390/fractalfract7010077 - 10 Jan 2023
Cited by 14 | Viewed by 2542
Abstract
Robot manipulators are widely used in many fields and play a vital role in the assembly, maintenance, and servicing of future complex in-orbit infrastructures. They are also helpful in areas where it is undesirable for humans to go, for instance, during undersea exploration, [...] Read more.
Robot manipulators are widely used in many fields and play a vital role in the assembly, maintenance, and servicing of future complex in-orbit infrastructures. They are also helpful in areas where it is undesirable for humans to go, for instance, during undersea exploration, in radioactive surroundings, and other hazardous places. Robotic manipulators are highly coupled and non-linear multivariable mechanical systems designed to perform one of these specific tasks. Further, the time-varying constraints and uncertainties of robotic manipulators will adversely affect the characteristics and response of these systems. Therefore, these systems require effective modelling and robust controllers to handle such complexities, which is challenging for control engineers. To solve this problem, many researchers have used the fractional-order concept in the modelling and control of robotic manipulators; yet it remains a challenge. This review paper presents comprehensive and significant research on state-of-the-art fractional-order modelling and control strategies for robotic manipulators. It also aims to provide a control engineering community for better understanding and up-to-date knowledge of fractional-order modelling, control trends, and future directions. The main table summarises around 95 works closely related to the mentioned issue. Key areas focused on include modelling, fractional-order modelling type, model order, fractional-order control, controller parameters, comparison controllers, tuning techniques, objective function, fractional-order definitions and approximation techniques, simulation tools and validation type. Trends for existing research have been broadly studied and depicted graphically. Further, future perspective and research gaps have also been discussed comprehensively. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Calculus in Robotics)
Show Figures

Figure 1

Back to TopTop