Applied Mathematics in Robotics: Theory, Methods and Applications

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

Title: The Application of Gröbner Bases to Robotic Problems
Authors: Ulrike Thomas
Affiliation: Chemnitz University of Technology, Robotics and Human-Machine Interaction Lab, Germany
Abstract: Gröbner-Bases and the Buchberger-Algorithm help to solve robotic problems. But unfortunately, they have not yet been widely used. Only few applications are in robotics are known where the Gröbner-Bases have been applied. Reasons often lie in the inaccuracy and discretization of such robotic problems and also the usage of trigonometric equations, which makes the application of Gröbner-Bases challenging. Thus, this article shows how the Gröbner-Bases can be applied to robotic problems. Solutions will be given for a few kinematic and control problems. The resulted Gröbner-Bases are described, and a generic way is presented how to solve similar problems.