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Mathematics
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Mathematical Modeling in Nonlinear Control and Robotics
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Mathematical Modeling in Nonlinear Control and Robotics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 July 2024) | Viewed by 7085

Special Issue Editors

Dr. Jianqing Peng

E-Mail Website
Guest Editor
School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518055, China
Interests: robotic control; computer vision; parameter estimation; image processing
Dr. Lei Yan

E-Mail Website
Guest Editor
School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Interests: dexterous manipulation; novel techniques and algorithms developed in several areas including motion planning, trajectory optimization and model-based control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to invite you to submit your latest research in the area of nonlinear modeling and control to this upcoming Special Issue of Mathematics, entitled “Mathematical Modeling in Nonlinear Control and Robotics”. There are many nonlinear characteristics in the robot control process that are difficult to approximate linearly, especially for some new robots. Therefore, the study of nonlinear control modeling has great theoretical significance and application value.

This Special Issue aims to promote the advancement of research in the areas of mathematical modeling, nonlinear control, and robotics. This journal will provide a platform for researchers to publish their latest findings and insights in these areas in order to to advance the understanding of complex and dynamic systems.

We invite authors to submit original research articles and reviews to this Special Issue. Research areas may include (but are not limited to) the following topic:

  1. Mathematical modeling of nonlinear systems.
  2. Nonlinear control theory and design, including advanced control methods for nonlinear systems and their applications.
  3. Robotics and automation, including kinematics, dynamics, motion planning.
  4. Applications of mathematical modeling and control to various engineering fields, such as aerospace, automotive, and chemical processing.

We look forward to receiving your contributions.

Dr. Jianqing Peng
Dr. Lei Yan
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • nonlinear systems
  • mathematical modeling
  • robotics
  • control methods
  • cable-driven robots
  • artificial intelligence
  • aerospace control
  • optimal control
  • motion planning
  • automation

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Published Papers (5 papers)

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Research

14 pages, 5376 KiB  
Article
Event-Triggered Tracking Control for Nonlinear Systems with Mismatched Disturbances: A Non-Recursive Design Approach
by Gaofeng Dong and Xin Zhao
Mathematics 2024, 12(11), 1716; https://doi.org/10.3390/math12111716 - 31 May 2024
Viewed by 537
Abstract
Considering the situation of limited resources in practical applications, it is significant to design control algorithms with high resource utilization rates for a class of nonlinear systems subject to mismatched disturbances. In contrast to common recursive methods, this paper proposes a novel event-triggered [...] Read more.
Considering the situation of limited resources in practical applications, it is significant to design control algorithms with high resource utilization rates for a class of nonlinear systems subject to mismatched disturbances. In contrast to common recursive methods, this paper proposes a novel event-triggered tracking control approach by co-designing the triggering event and the controller within a non-recursive design framework that combines disturbance estimation techniques and feedforward compensation strategies. Through rigorous Lyapunov stability analysis, the global boundedness of each state in the closed-loop system is demonstrated, and the absence of the Zeno phenomenon is further verified. A representative numerical simulation and a practical implementation for speed regulation of permanent magnet synchronous motor (PMSM) system confirm the effectiveness and simplicity of the proposed control strategy. Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
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25 pages, 4515 KiB  
Article
Modeling, Analysis and Evaluation of a Novel Compact 6-DoF 3-RRRS Needle Biopsy Robot
by Jiangnan Wang, Ruiqi Xiang, Jindong Xiang, Baichuan Wang, Xiyun Wu, Mingzhen Cai, Zhijie Pan, Mengtang Li and Xun Li
Mathematics 2024, 12(10), 1461; https://doi.org/10.3390/math12101461 - 8 May 2024
Cited by 1 | Viewed by 865
Abstract
Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed [...] Read more.
Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed designed for specific application scenarios, and only position-level kinematics are derived, preventing advanced speed control or singularity analysis. As a step forward, this paper aims to design a universal needle biopsy robot platform which features 6 DoF 3-RRRS (Revolute–Revolute–Revolute–Spherical) parallel structure. The analytical solutions to its nonlinear kinematic problems, including forward kinematics, inverse kinematics, and differential kinematics are derived, allowing fast and accurate feedback control calculations. A multibody simulation platform and a first-generation prototype are established next to provide comprehensive verifications for the derived robotic model. Finally, simulated puncture experiments are carried out to illustrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
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27 pages, 2878 KiB  
Article
Toward Optimal Robot Machining Considering the Workpiece Surface Geometry in a Task-Oriented Approach
by Aleš Hace
Mathematics 2024, 12(2), 257; https://doi.org/10.3390/math12020257 - 12 Jan 2024
Cited by 1 | Viewed by 1323
Abstract
Robot workpiece machining is interesting in industry as it offers some advantages, such as higher flexibility in comparison with the conventional approach based on CNC technology. However, in recent years, we have been facing a strong progressive shift to custom-based manufacturing and low-volume/high-mix [...] Read more.
Robot workpiece machining is interesting in industry as it offers some advantages, such as higher flexibility in comparison with the conventional approach based on CNC technology. However, in recent years, we have been facing a strong progressive shift to custom-based manufacturing and low-volume/high-mix production, which require a novel approach to automation via the employment of collaborative robotics. However, collaborative robots feature only limited motion capability to provide safety in cooperation with human workers. Thus, it is highly necessary to perform more detailed robot task planning to ensure its feasibility and optimal performance. In this paper, we deal with the problem of studying kinematic robot performance in the case of such manufacturing tasks, where the robot tool is constrained to follow the machining path embedded on the workpiece surface at a prescribed orientation. The presented approach is based on the well-known concept of manipulability, although the latter suffers from physical inconsistency due to mixing different units of linear and angular velocity in a general 6 DOF task case. Therefore, we introduce the workpiece surface constraint in the robot kinematic analysis, which enables an evaluation of its available velocity capability in a reduced dimension space. Such constrained robot kinematics transform the robot’s task space to a two-dimensional surface tangent plane, and the manipulability analysis may be limited to the space of linear velocity only. Thus, the problem of physical inconsistency is avoided effectively. We show the theoretical derivation of the proposed method, which was verified by numerical experiments. Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
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19 pages, 6023 KiB  
Article
Efficient Trajectory Planning for Optimizing Energy Consumption and Completion Time in UAV-Assisted IoT Networks
by Mengtang Li, Guoku Jia, Xun Li and Hao Qiu
Mathematics 2023, 11(20), 4399; https://doi.org/10.3390/math11204399 - 23 Oct 2023
Cited by 3 | Viewed by 1680
Abstract
Quadrotor unmanned aerial vehicles (UAVs) have emerged as ubiquitous and agile robots and data carriers within the framework of the future Internet of Things (IoT) and mobile wireless networks. Yet, the insufficient onboard battery necessitates the optimization of energy consumption for both the [...] Read more.
Quadrotor unmanned aerial vehicles (UAVs) have emerged as ubiquitous and agile robots and data carriers within the framework of the future Internet of Things (IoT) and mobile wireless networks. Yet, the insufficient onboard battery necessitates the optimization of energy consumption for both the UAV and IoT devices while ensuring that communication requirements are met. This paper therefore proposes a more accurate and mathematically tractable model for characterizing a UAV’s energy consumption concerning desired trajectories. This nonlinear model takes into account the UAV’s dynamics, brushless direct current (BLDC) motor dynamics, and aerodynamics. To optimize the communication time between IoT devices and the UAV, IoT devices are clustered using a modified GAK-means algorithm, with dynamically optimized communication coverage radii. Subsequently, a fly–circle–communicate (FCC) trajectory design algorithm is introduced and derived to conserve energy and save mission time. Under the FCC approach, the UAV sequentially visits the cluster centers and performs circular flight and communication. Transitions between cluster centers are smoothed via 3D Dubins curves, which provide physically achievable trajectories. Comprehensive numerical studies indicate that the proposed trajectory planning method reduces overall communication time and preserves UAV battery energy compared to other benchmark schemes. Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
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23 pages, 21736 KiB  
Article
Stiffness Modeling and Dynamics Co-Modeling for Space Cable-Driven Linkage Continuous Manipulators
by Hejie Xu, Xinliang Li, Yanan Li, Deshan Meng and Xueqian Wang
Mathematics 2023, 11(8), 1874; https://doi.org/10.3390/math11081874 - 15 Apr 2023
Cited by 1 | Viewed by 1748
Abstract
The space cable-driven continuous manipulator (SCCM) has a slender structure, ultra-high degrees of freedom, and a low mass, which make it suitable for equipment inspection and maintenance operations in an unstructured and limited space environment. In this paper, the SCCM including the cable [...] Read more.
The space cable-driven continuous manipulator (SCCM) has a slender structure, ultra-high degrees of freedom, and a low mass, which make it suitable for equipment inspection and maintenance operations in an unstructured and limited space environment. In this paper, the SCCM including the cable network and plenty of joint links was deeply modeled. Firstly, the mapping relationship between the cable-driving space, joint space, and task space of the SCCM was studied, and the complete kinematic relationship of the SCCM was established. Secondly, the stiffness components of the SCCM are discussed, and the stiffness modeling method of each part is given. Finally, the Cartesian space equivalent stiffness model of the end was established. Then, a dynamic co-modeling method of Matlab + Adams is proposed, which greatly improved the modeling efficiency while ensuring the modeling accuracy. Finally, based on the stiffness model, the end stiffness characteristics of a specific configuration were analyzed, and the influence of the cable tension on the stiffness and frequency of the manipulator was analyzed. Based on the dynamic co-modeling, the task trajectory dynamics’ simulation analysis and space slit crossing experiment were carried out, which verified that the designed SCCM can meet the needs of slit crossing. Full article
(This article belongs to the Special Issue Mathematical Modeling in Nonlinear Control and Robotics)
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