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Mathematics
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Robotics and Intelligent Systems: New Mathematical Challenges and Algorithmic Innovations
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Robotics and Intelligent Systems: New Mathematical Challenges and Algorithmic Innovations

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

Deadline for manuscript submissions: 30 June 2026 | Viewed by 2147

Special Issue Editor

Dr. Ming Xie

E-Mail Website
Guest Editor
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
Interests: humanoid robotics; autonomous vehicles; machine vision; artificial intelligence

Special Issue Information

Dear Colleagues,

In the current era, we are witnessing the transition from mastering automation toward achieving autonomy. The mastery of automation has a foundation rooted in the mathematical theories underlying the control of dynamical systems. Certainly, the achievement of autonomy depends on whether we will be able to build solid mathematical principles underlying the design of artificial intelligence or artificial minds inside the advanced robots of the future.

This Special Issue seeks papers within its scope, which encompasses the new mathematical challenges and algorithmic innovations faced by intelligent robots that can autonomously undertake various tasks in a real environment in real time. Among these challenges, the biggest one is discovering the mathematical principles underlying the pipeline of transformations from visual sensory signals to visual knowledge (i.e., geometry, topology, kinematics, and dynamics), from existing knowledge about the physical space to new knowledge about the same physical space, and from the knowledge about tasks to be performed in a real environment to motor signals which can be performed by a robot’s body or mechanism.

If your research can contribute partially to the above areas of study, please indicate your interest to me as soon as possible. Among the potential contributors, five of them will be granted the full waiver of publication/processing fees. I hope that you will be among these five authors in this exciting Special Issue.

Dr. Ming Xie
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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

  • mathematical principles underlying advanced robot’s perception
  • mathematical principles underlying advanced robot’s thinking
  • mathematical principles underlying advanced robot’s planning
  • mathematical principles underlying advanced robot’s composition
  • mathematical principles underlying advanced robot’s control
  • mathematical principles underlying advanced robot’s communication

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

54 pages, 5015 KB  
Article
Reliability in Robotics and Intelligent Systems: Mathematical Modeling and Algorithmic Innovations
by Madina Issametova, Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Elizaveta E. Kuleshova and Denis V. Valuev
Mathematics 2026, 14(3), 580; https://doi.org/10.3390/math14030580 - 6 Feb 2026
Cited by 1 | Viewed by 810
Abstract
The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the [...] Read more.
The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the probability of the end-effector falling into a given area of permissible poses. The proposed framework integrates a deterministic kinematic model, a stochastic representation of Denavit–Hartenberg parameters and control variables, analytical methods for estimating probabilities, and numerical modeling using the Monte Carlo method. The methodology has been tested on the widely used industrial robot FANUC LR Mate 200iD/7L. The results demonstrate a significant dependence of geometric reliability on the kinematic configuration of the manipulator, with maximum reliability in compact poses and a significant reduction in elongated configurations near singularities. Comprehensive validation was carried out, including numerical experiments on a planar prototype, high-precision physical measurements on a real robot and analysis of operational data, which confirmed the adequacy of the proposed model. The developed approach provides a powerful tool for designing, optimizing and predicting the reliability of robotic cells in high-precision automation environments. Full article
(This article belongs to the Special Issue Robotics and Intelligent Systems: New Mathematical Challenges and Algorithmic Innovations)
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24 pages, 84138 KB  
Article
A Hybrid Strategy for Achieving Robust Matching Inside the Binocular Vision of a Humanoid Robot
by Ming Xie, Xiaohui Wang and Jianghao Li
Mathematics 2025, 13(21), 3488; https://doi.org/10.3390/math13213488 - 1 Nov 2025
Cited by 1 | Viewed by 744
Abstract
Binocular vision is a core module in humanoid robots, and stereo matching is one of the key challenges in binocular vision, relying on template matching techniques and mathematical optimization methods to achieve precise image matching. However, occlusion significantly affects matching accuracy and robustness [...] Read more.
Binocular vision is a core module in humanoid robots, and stereo matching is one of the key challenges in binocular vision, relying on template matching techniques and mathematical optimization methods to achieve precise image matching. However, occlusion significantly affects matching accuracy and robustness in practical applications. To address this issue, we propose a novel hybrid matching strategy. This method does not require network training and has high computational efficiency, effectively addressing occlusion issues. First, we propose the Inverse Template Matching Mathematical Method (ITM), which is based on optimization theory. This method generates multiple new templates from the image to be matched using mathematical segmentation techniques and then matches them with the original template through an inverse optimization process, thereby effectively improving matching accuracy under mild occlusion conditions. Second, we propose the Iterative Matching Mathematical Method (IMM), which repeatedly executes ITM combined with optimization strategies to continuously refine the size of matching templates, thereby further improving matching accuracy under complex occlusion conditions. Concurrently, we adopt a local region selection strategy to selectively target areas related to occlusion regions for inverse optimization matching, significantly enhancing matching efficiency. Experimental results show that under severe occlusion conditions, the proposed method achieves a 93% improvement in accuracy compared to traditional template matching methods and a 37% improvement compared to methods based on convolutional neural networks (CNNs), reaching the current state of the art in the field. Our method introduces a reverse optimization paradigm into the field of template matching and provides an innovative mathematical solution to address occlusion issues. Full article
(This article belongs to the Special Issue Robotics and Intelligent Systems: New Mathematical Challenges and Algorithmic Innovations)
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