Applied Mathematics in Robotics: Theory, Methods and Applications

A special issue of AppliedMath (ISSN 2673-9909).

Deadline for manuscript submissions: closed (31 December 2024) | Viewed by 8753

Special Issue Editors


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Guest Editor
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
Interests: GNSS; GNSS-RTK; GNSS NLOS/multipath mitigation in urban canyons LiDAR-aided GNSS positioning; perception-aided GNSS positioning; LiDAR SLAM in challenging dynamic scenes; navigation; autonomous driving; robotics
Special Issues, Collections and Topics in MDPI journals
Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China
Interests: optimization; symbolic computation; robotics; navigation; optimal filtering; orbit determination; hybridization theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Robotics is the study and application of intelligent systems that can sense, think, and act. It has broad and promising applications in various fields, such as industry, the military, education, and entertainment. It also depends on the theories and methods of applied mathematics, such as optimization, statistics, probability, logic, graph theory, complex networks, and machine learning. Applied mathematics gives robotics a solid mathematical foundation and also provides tools and ideas for innovation and improvement. This Special Issue collects and showcases the latest advances of applied mathematics in robotics, in terms of theory, methods, and applications. We invite research on different types of robots, such as manipulators, walking robots, soft robots, haptic robots, microrobots, and swarm robots, and on different tasks, such as grasping, manipulation, motion, navigation, collaboration, and interaction. The goal of this Special Issue is to enhance the communication and collaboration between applied mathematics and robotics and to foster the development and application of robotic technology.

Dr. Chengxi Zhang
Dr. Weisong Wen
Dr. Jin Wu
Guest Editors

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Keywords

  • navigation and multi-sensor fusion
  • machine vision and 3D reconstruction
  • space engineering, planning and control
  • mechanics and dynamics
  • GNSS, NLOS/multipath mitigation
  • LiDAR SLAM

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Published Papers (2 papers)

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Research

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32 pages, 2630 KiB  
Article
Autonomous Drifting like Professional Racing Drivers: A Survey
by Yang Liu, Fulong Ma, Xiaodong Mei, Bohuan Xue, Jin Wu and Chengxi Zhang
AppliedMath 2025, 5(2), 33; https://doi.org/10.3390/appliedmath5020033 - 26 Mar 2025
Viewed by 212
Abstract
Autonomous drifting is an advanced technique that enhances vehicle maneuverability beyond conventional driving limits. This survey provides a comprehensive, systematic review of autonomous drifting research published between 2005 and early 2025, analyzing approximately 80 peer-reviewed studies. We employed a modified PRISMA approach to [...] Read more.
Autonomous drifting is an advanced technique that enhances vehicle maneuverability beyond conventional driving limits. This survey provides a comprehensive, systematic review of autonomous drifting research published between 2005 and early 2025, analyzing approximately 80 peer-reviewed studies. We employed a modified PRISMA approach to categorize and evaluate research across two main methodological frameworks: dynamical model-based approaches and deep learning techniques. Our analysis reveals that while dynamical methods offer precise control when accurately modeled, they often struggle with generalization to unknown environments. In contrast, deep learning approaches demonstrate better adaptability but face challenges in safety verification and sample efficiency. We comprehensively examine experimental platforms used in the field—from high-fidelity simulators to full-scale vehicles—along with their sensor configurations and computational requirements. This review uniquely identifies critical research gaps, including real-time performance limitations, environmental generalization challenges, safety validation concerns, and integration issues with broader autonomous systems. Our findings suggest that hybrid approaches combining model-based knowledge with data-driven learning may offer the most promising path forward for robust autonomous drifting capabilities in diverse applications ranging from motorsports to emergency collision avoidance in production vehicles. Full article
(This article belongs to the Special Issue Applied Mathematics in Robotics: Theory, Methods and Applications)
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Review

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19 pages, 351 KiB  
Review
Swarm Intelligence-Based Multi-Robotics: A Comprehensive Review
by Luong Vuong Nguyen
AppliedMath 2024, 4(4), 1192-1210; https://doi.org/10.3390/appliedmath4040064 - 2 Oct 2024
Cited by 3 | Viewed by 6647
Abstract
Swarm Intelligence (SI) represents a paradigm shift in artificial intelligence, leveraging the collective behavior of decentralized, self-organized systems to solve complex problems. This study provides a comprehensive review of SI, focusing on its application to multi-robot systems. We explore foundational concepts, diverse SI [...] Read more.
Swarm Intelligence (SI) represents a paradigm shift in artificial intelligence, leveraging the collective behavior of decentralized, self-organized systems to solve complex problems. This study provides a comprehensive review of SI, focusing on its application to multi-robot systems. We explore foundational concepts, diverse SI algorithms, and their practical implementations by synthesizing insights from various reputable sources. The review highlights how principles derived from natural swarms, such as those of ants, bees, and birds, can be harnessed to enhance the efficiency, robustness, and scalability of multi-robot systems. We explore key advancements, ongoing challenges, and potential future directions. Through this extensive examination, we aim to provide a foundational understanding and a detailed taxonomy of SI research, paving the way for further innovation and development in theoretical and applied contexts. Full article
(This article belongs to the Special Issue Applied Mathematics in Robotics: Theory, Methods and Applications)
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