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Dynamics and Control of Complex Systems and Robots

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

Deadline for manuscript submissions: closed (20 October 2024) | Viewed by 11673

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Special Issue Editors

Prof. Dr. Qingdu Li

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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
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Xiaosong Yang

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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
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Dr. Gang Wang

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Guest Editor

Institute of Machine Intelligence, University of Shanghai for Science and Technology, Shanghai 200093, China
Interests: distributed control; adaptive control; robotics
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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

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Keywords

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

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Published Papers (12 papers)

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Research

21 pages, 2468 KiB

Open AccessArticle

Distributed Observer for Linear Systems with Multirate Sampled Outputs Involving Multiple Delays

by Laura-Adriana Galicia-Galicia, Omar Hernández-González, Carlos Daniel Garcia-Beltran, Guillermo Valencia-Palomo and María-Eusebia Guerrero-Sánchez

Mathematics 2024, 12(18), 2943; https://doi.org/10.3390/math12182943 - 22 Sep 2024

Viewed by 474

Abstract

This paper focuses on the design of a continuous distributed observer for linear systems under multirate sampled output measurements involving multiple delays. It is mathematically proved that the continuous distributed observer can achieve estimation in a sensor network environment, where output measurements from each sensor are available at different sampling instants, whether these times are periodic or aperiodic, and despite the presence of multiple time-varying delays. Each sampled and delayed measurement represents a node of the network, necessitating a dedicated observer for each node, which has access to only part of the system’s output and communicates with its neighbors according to a given network graph. The exponential convergence of the error dynamics is ensured by Lyapunov stability analysis, which accounts for the influence of the sampled and delayed measurements at each node. To demonstrate the effectiveness of the proposed observer, simulation tests were conducted on the tracking control of chasing satellites in low Earth orbit (LEO), encompassing both small and large sampling rates and delays. The continuous distributed observer with sampled output measurements exhibited convergence in scenarios with different sampling intervals, even in the presence of time-varying delays, achieving asymptotic omniscience, as demonstrated in the convergence analysis. Full article

(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)

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17 pages, 2924 KiB

Open AccessArticle

Balance and Walking Control for Biped Robot Based on Divergent Component of Motion and Contact Force Optimization

by Shuai Heng, Xizhe Zang, Chao Song, Boyang Chen, Yue Zhang, Yanhe Zhu and Jie Zhao

Mathematics 2024, 12(14), 2188; https://doi.org/10.3390/math12142188 - 12 Jul 2024

Viewed by 960

Abstract

This paper presents a complete planner and controller scheme to achieve balance and walking for a biped robot, which does not need to distinguish the robot’s dynamic model parameters. The high-level planner utilizes model predictive control to optimize both the foothold location and step duration based on the Divergent Component of Motion (DCM) model to enhance the robustness of generated gaits. For low-level control, we use quadratic programming (QP) to optimize the contact force distribution under the contact constraints to achieve the virtual wrench exerted on the base of the robot. Then, the joint torques sent to the robot are derived from three parts: first, the torques mapped from the contact force; second, the swing leg tracking; and third, the stance foot stabilization. The simulation and experiment on BRUCE, a miniature bipedal robot from Westwood Robotics (Los Angeles, CA, USA), testify to the performance of the control scheme, including push recovery, Center of Mass (CoM) tracking, and omnidirectional walking. Full article

(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)

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17 pages, 3595 KiB

Open AccessArticle

Simultaneous Tracking and Stabilization of Nonholonomic Wheeled Mobile Robots under Constrained Velocity and Torque

by Yuan Li, Yuyang Cai, Yong Wang, Wei Li and Gang Wang

Mathematics 2024, 12(13), 1985; https://doi.org/10.3390/math12131985 - 27 Jun 2024

Viewed by 580

Abstract

Currently, most assumptions in nonholonomic mobile robot controllers indicate that the robot velocity can become significantly large and that the robot actuators are able to generate the necessary level of torque input. Based on the sliding mode control theory, this paper develops a new framework to handle the control problem of a wheeled robot dynamics model with constrained velocity and torque. Through rigorous theoretical analysis and extensive simulations, we demonstrate that the proposed controller guarantees asymptotic convergence of tracking or stabilization errors and boundedness of closed-loop signals. The advantages of the developed controller include the ability to simultaneously achieve tracking and stabilization control of nonholonomic mobile robots and the ability to ensure that the prescribed velocity and torque constraints are not breached by simply tuning the design parameters a priori, even in the presence of uncertain disturbances. Full article

(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)

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11 pages, 1473 KiB

Open AccessArticle

Design, Modeling, and Experimental Validation of a Vision-Based Table Tennis Juggling Robot

by Yunfeng Ji, Bangsen Zhang, Yue Mao, Han Wang, Xiaoyi Hu and Lingling Zhang

Mathematics 2024, 12(11), 1634; https://doi.org/10.3390/math12111634 - 23 May 2024

Viewed by 933

Abstract

This paper develops a new vision-based robot customized for table tennis juggling tasks. Specifically, the robot is equipped with two industrial cameras operating as a sensing system. An image-processing algorithm is proposed that allows the robot to balance a table tennis ball while controlling its bounce height. The robot adopts a parallel structure design, and the end effector employs three ball joints to increase the degree of freedom (DOF) of the parallel mechanism. In addition, we design a control scheme explicitly customized for this robotic system. Extensive real-time experiments are performed to show the effectiveness of the juggling robot at different jumping heights. Furthermore, the ability to consistently maintain a fixed preset bounce height is demonstrated. These experimental results confirm the efficacy of the developed robotic system. Full article

(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)

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21 pages, 502 KiB

Open AccessArticle

Quadratic Tracking Control of Linear Stochastic Systems with Unknown Dynamics Using Average Off-Policy Q-Learning Method

by Longyan Hao, Chaoli Wang and Yibo Shi

Mathematics 2024, 12(10), 1533; https://doi.org/10.3390/math12101533 - 14 May 2024

Cited by 1 | Viewed by 583

Abstract

This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy Q-learning algorithm avoids the assumption of an initial stability control. First, a pole placement strategy is used to design an initial stable control for systems with unknown dynamics. Second, the initial stable control is used to design a data-based average off-policy Q-learning algorithm. Then, this algorithm is used to solve the stochastic linear quadratic tracking (LQT) problem, and a convergence proof of the algorithm is provided. Finally, numerical examples show that this algorithm outperforms other algorithms in a simulation. Full article

(This article belongs to the Special Issue Dynamics and Control of Complex Systems and Robots)

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16 pages, 2508 KiB

Open AccessArticle

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

Cited by 1 | Viewed by 801

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 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

Open AccessArticle

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 793

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 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

M R R @ 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

Open AccessArticle

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 - 8 Apr 2024

Cited by 1 | Viewed by 883

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 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

Open AccessArticle

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

Cited by 1 | Viewed by 1017

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 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

Open AccessArticle

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 690

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 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

Open AccessArticle

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 1668

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 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

Open AccessArticle

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 1266

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. 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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