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Mathematics
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Dynamics and Control of Complex Systems and Robots
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Dynamics and Control of Complex Systems and Robots

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

Deadline for manuscript submissions: 20 October 2024 | Viewed by 3728

Special Issue Editors

Prof. Dr. Qingdu Li

E-Mail Website
Guest Editor
Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai 200093, China
Interests: biped robots; dynamic walking; nonlinear circuits; complex systems
Prof. Dr. Xiaosong Yang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Interests: nonlinear system; asymptotic stability; dynamics analysis; bifurcation and chaos
Special Issues, Collections and Topics in MDPI journals
Dr. Gang Wang

E-Mail Website
Guest Editor
Institute of Machine Intelligence, College of Health Sciences and Engineering, University of Shanghai for Science and Technology, Shanghai, China
Interests: distributed control; adaptive control; consensus control; nonlinear systems; nonholonomic robots; robotics

Special Issue Information

Dear Colleagues,

This Special Issue showcases the latest research on the use of mathematical models and methods in the analysis and control of complex systems and robots.

These articles explore a range of topics, including nonlinear dynamics, adaptive control, optimal control, distributed control, and learning control. They present new theoretical results and practical applications that demonstrate the dynamics and control of complex systems and robots.

Specific applications of these techniques in different complex systems and robotic domains are addressed. The topics include:

  • The modelling and control of nonlinear systems using differential geometry and Lie group methods;
  • Designing adaptive controllers for uncertain systems using Lyapunov stability theory and sliding mode control techniques;
  • Robotic system using optimal control theory and numerical optimization methods;
  • Learning control policies for autonomous robots using machine learning algorithms and reinforcement learning techniques;
  • Learning cross-domain knowledge for robotic interaction and comprehension using machine learning algorithms and large pretrained language models.

We hope this Special Issue will serve as a valuable resource for researchers and practitioners interested in this field. The articles provide a glimpse into the diverse range of mathematical techniques that can be applied to these fields, while also highlighting the importance of collaboration between mathematicians and engineers in addressing real-world challenges.

Prof. Dr. Qingdu Li
Prof. Dr. Xiaosong Yang
Dr. Gang Wang
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

  • modeling and control of nonlinear systems
  • machine learning algorithms
  • complex systems and stability analysis

Published Papers (7 papers)

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Research

16 pages, 2508 KiB  
Article
Instance Segmentation of Sparse Point Clouds with Spatio-Temporal Coding for Autonomous Robot
by Na Liu, Ye Yuan, Sai Zhang, Guodong Wu, Jie Leng and Lihong Wan
Mathematics 2024, 12(8), 1200; https://doi.org/10.3390/math12081200 - 17 Apr 2024
Viewed by 306
Abstract
In the study of Simultaneous Localization and Mapping (SLAM), the existence of dynamic obstacles will have a great impact on it, and when there are many dynamic obstacles, it will lead to great challenges in mapping. Therefore, segmenting dynamic objects in the environment [...] Read more.
In the study of Simultaneous Localization and Mapping (SLAM), the existence of dynamic obstacles will have a great impact on it, and when there are many dynamic obstacles, it will lead to great challenges in mapping. Therefore, segmenting dynamic objects in the environment is particularly important. The common data format in the field of autonomous robots is point clouds. How to use point clouds to segment dynamic objects is the focus of this study. The existing point clouds instance segmentation methods are mostly based on dense point clouds. In our application scenario, we use 16-line LiDAR (sparse point clouds) and propose a sparse point clouds instance segmentation method based on spatio-temporal encoding and decoding for autonomous robots in dynamic environments. Compared with other point clouds instance segmentation methods, the proposed algorithm has significantly improved average percision and average recall on instance segmentation of our point clouds dataset. In addition, the annotation of point clouds is time-consuming and laborious, and the existing dataset for point clouds instance segmentation is also very limited. Thus, we propose an autonomous point clouds annotation algorithm that integrates object tracking, segmentation, and point clouds to 2D mapping methods, the resulting data can then be used for training robust model. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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16 pages, 1066 KiB  
Article
Spatio-Temporal Contrastive Heterogeneous Graph Attention Networks for Session-Based Recommendation
by Fan Yang and Dunlu Peng
Mathematics 2024, 12(8), 1193; https://doi.org/10.3390/math12081193 - 16 Apr 2024
Viewed by 281
Abstract
The main goal of session-based recommendation (SBR) is to analyze the list of possible next interaction items through the user’s historical interaction sequence. The existing session recommendation models directly model the session sequence as a graph, and only consider the aggregation of neighbor [...] Read more.
The main goal of session-based recommendation (SBR) is to analyze the list of possible next interaction items through the user’s historical interaction sequence. The existing session recommendation models directly model the session sequence as a graph, and only consider the aggregation of neighbor items based on spatial structure information, ignoring the time information of items. The sparsity of interaction sequences also affects the accuracy of recommendation. This paper proposes a spatio-temporal contrastive heterogeneous graph attention network model (STC-HGAT). The session sequence is built as a spatial heterogeneous hypergraph, a latent Dirichlet allocation (LDA) algorithm is used to construct the category nodes of the items to enhance the contextual semantic information of the hypergraph, and the hypergraph attention network is employed to capture the spatial structure information of the session. The temporal heterogeneous graph is constructed to aggregate the temporal information of the item. Then, the spatial and temporal information are fused by sumpooling. Meanwhile, a modulation factor is added to the cross-entropy loss function to construct the adaptive weight (AW) loss function. Contrastive learning (CL) is used as an auxiliary task to further enhance the modeling, so as to alleviate the sparsity of data. A large number of experiments on real public datasets show that the STC-HGAT model proposed in this paper is superior to the baseline models in metrics such as P@20 and MRR@20, improving the recommendation performance to a certain extent. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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12 pages, 9015 KiB  
Article
Robust Control for Underactuated Fixed-Wing Unmanned Aerial Vehicles
by Tianyi Wang, Luxin Zhang and Zhihua Chen
Mathematics 2024, 12(7), 1118; https://doi.org/10.3390/math12071118 - 08 Apr 2024
Viewed by 402
Abstract
Dynamic surface control (DSC) is a recognized nonlinear control approach for high-order systems. However, as the complexity of the system increases and the first-order filter (FOF) is introduced, there exists a singularity problem, i.e., the control input will reach infinity. This limits the [...] Read more.
Dynamic surface control (DSC) is a recognized nonlinear control approach for high-order systems. However, as the complexity of the system increases and the first-order filter (FOF) is introduced, there exists a singularity problem, i.e., the control input will reach infinity. This limits the application of the DSC algorithm to a class of real-world systems with complex dynamics. To address the problem of singularity, we present a novel DSC approach called nonsingular dynamic surface control (NDSC), which completely avoids the singularity problem and significantly improves the overall control performance. NDSC includes a nonsingular hypersurface, which is constructed by the error between system states and virtual control inputs. Then the nonsingular hypersurface will be applied to derive the corresponding control law with the aid of the DSC approach to ensure the output of the system can track arbitrary desired trajectories. NDSC has the following novel features: (1) finite time asymptotic stabilization can be guaranteed; (2) the performance of NDSC is insensitive to the FOF’s parameter variation once the maximum tracking error of FOF is bounded, which significantly reduces reliance on the control sampling frequency. We thoroughly evaluate the proposed NDSC algorithm in an unmanned aerial vehicle (UAV) system with an underactuated nature. Finally, the simulation results illustrate and highlight the effectiveness and superiority of the proposed control algorithm. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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21 pages, 6864 KiB  
Article
Integrated the Artificial Potential Field with the Leader–Follower Approach for Unmanned Aerial Vehicles Cooperative Obstacle Avoidance
by Yingxue Zhang, Jinbao Chen, Meng Chen, Chuanzhi Chen, Zeyu Zhang and Xiaokang Deng
Mathematics 2024, 12(7), 954; https://doi.org/10.3390/math12070954 - 23 Mar 2024
Viewed by 485
Abstract
For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory [...] Read more.
For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader’s attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient “few controlling many” paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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11 pages, 3922 KiB  
Article
Event-Triggered Consensus Control in Euler–Lagrange Systems Subject to Communication Delays and Intermittent Information Exchange
by Yunfeng Ji, Wei Li and Gang Wang
Mathematics 2024, 12(7), 942; https://doi.org/10.3390/math12070942 - 22 Mar 2024
Viewed by 352
Abstract
In this paper, we investigate the consensus control problem of Euler–Lagrange systems which can be used to describe the motion of various mechanical systems such as manipulators and quadcopters. We focus on consensus control strategies, which are important for achieving coordinated behavior in [...] Read more.
In this paper, we investigate the consensus control problem of Euler–Lagrange systems which can be used to describe the motion of various mechanical systems such as manipulators and quadcopters. We focus on consensus control strategies, which are important for achieving coordinated behavior in multi-agent systems. The paper considers the key challenges posed by random communication delays and packet losses that are increasingly common in networked control systems. In addition, it is assumed that each system receives information from neighboring agents intermittently. Addressing these challenges is critical to ensure the reliability and efficiency of such systems in real-world applications. Communication delay is time-varying and can be very large, but should be smaller than some bounded constant. To decrease the frequency of control input updates, we implement an event-triggered scheme that regulates the controller’s updates for each agent. Specifically, it does not update control inputs at traditional fixed intervals, but responds to predefined conditions and introduces a dynamic consensus item to handle information irregularities caused by communication delays and intermittent information exchange. The consensus can be achieved if the communication graph of agents contains a spanning tree with the desired velocity as the root node. That is, all Euler–Lagrange systems need to obtain the desired velocity, directly or indirectly (via neighbors), to reach consensus. We establish that the Zeno behavior can be avoided, ensuring a positive minimum duration between successive event-triggered instances. Finally, we provide simulation results to show the performance of our proposed algorithm. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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23 pages, 15167 KiB  
Article
High Dynamic Bipedal Robot with Underactuated Telescopic Straight Legs
by Haiming Mou, Jun Tang, Jian Liu, Wenqiong Xu, Yunfeng Hou and Jianwei Zhang
Mathematics 2024, 12(4), 600; https://doi.org/10.3390/math12040600 - 17 Feb 2024
Viewed by 766
Abstract
Bipedal robots have long been a focal point of robotics research with an unwavering emphasis on platform stability. Achieving stability necessitates meticulous design considerations at every stage, encompassing resilience against environmental disturbances and the inevitable wear associated with various tasks. In pursuit of [...] Read more.
Bipedal robots have long been a focal point of robotics research with an unwavering emphasis on platform stability. Achieving stability necessitates meticulous design considerations at every stage, encompassing resilience against environmental disturbances and the inevitable wear associated with various tasks. In pursuit of these objectives, here, the bipedal L04 Robot is introduced. The L04 Robot employs a groundbreaking approach by compactly enclosing the hip joints in all directions and employing a coupled joint design. This innovative approach allows the robot to attain the traditional 6 degrees of freedom in the hip joint while using only four motors. This design not only enhances energy efficiency and battery life but also safeguards all vulnerable motor reducers. Moreover, the double-slider leg design enables the robot to simulate knee bending and leg height adjustment through leg extension. This simulation can be mathematically modeled as a linear inverted pendulum (LIP), rendering the L04 Robot a versatile platform for research into bipedal robot motion control. A dynamic analysis of the bipedal robot based on this structural innovation is conducted accordingly. The design of motion control laws for forward, backward, and lateral movements are also presented. Both simulation and physical experiments corroborate the excellent bipedal walking performance, affirming the stability and superior walking capabilities of the L04 Robot. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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18 pages, 13348 KiB  
Article
A Low-Inertia and High-Stiffness Cable-Driven Biped Robot: Design, Modeling, and Control
by Jun Tang, Haiming Mou, Yunfeng Hou, Yudi Zhu, Jian Liu and Jianwei Zhang
Mathematics 2024, 12(4), 559; https://doi.org/10.3390/math12040559 - 13 Feb 2024
Viewed by 652
Abstract
In this paper, a biped robot system for dynamic walking is presented. It has two 2-degree-of-freedom (DOF) lightweight legs and a 6-DOF hip. All the joint pulleys of the legs are driven by motors that are placed at the hip using steel cables. [...] Read more.
In this paper, a biped robot system for dynamic walking is presented. It has two 2-degree-of-freedom (DOF) lightweight legs and a 6-DOF hip. All the joint pulleys of the legs are driven by motors that are placed at the hip using steel cables. Since all the heavy motors are mounted at the hip, the biped robot has remarkably low-mass legs beyond the hip, which guarantees low inertia during walking at high speeds. Utilizing cable-amplification mechanisms, high stiffness and strength are achieved, resulting in better control performance compared to conventional direct-driven methods. Techniques are developed to estimate joint-angle errors caused by the elastic deformation of the cables. To achieve smooth control, we introduce the concept of a virtual leg, which is an imaginary leg connecting the hip joint and the ankle joint. A robust control approach based on the “virtual leg” is presented, which considers the variances of the virtual leg length during walking. Experiments are conducted to validate the effectiveness of the mechanical design and the proposed control approach. Full article
(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)
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