Mathematical analysis
Related papers: 20
About
Mathematical analysis is a branch of mathematics concerned with rigorous treatment of limits, continuity, differentiation, integration, and the behavior of functions and equations. In robotics and AI, it provides the foundational tools used to model, analyze, and control complex systems — encompassing differential equations for dynamics, calculus for optimization, linear algebra for coordinate transformations, and numerical methods for real-time computation. Applications span kinematic modeling of robot manipulators, singularity analysis, trajectory planning, nonholonomic motion planning, finite-time control design, and state estimation through filters like the extended Kalman filter. Techniques such as Filippov's differential inclusions handle discontinuous control laws, while polynomial system solvers address inverse kinematics. Mathematical analysis matters because it transforms physical intuition into provable, quantifiable results — enabling engineers to guarantee stability, predict system behavior, optimize performance, and handle edge cases like singularities or impacts with confidence. Without this rigorous foundation, designing reliable autonomous systems capable of operating safely in complex real-world environments would be impossible.
Top Researchers
Top Cited Papers
Fractional Differential Equations
Igor Podlubný
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Fractional Brownian Motions, Fractional Noises and Applications
Benoît B. Mandelbrot, John W. Van Ness
Citations: 7678 • 1968
Closed-form solution of absolute orientation using unit quaternions
Berthold K. P. Horn
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A unified approach for motion and force control of robot manipulators: The operational space formulation
Oussama Khatib
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Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
Robert J. Webster, Bryan A. Jones
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Singularity analysis of closed-loop kinematic chains
Clément Gosselin, Jorge Angeles
Citations: 1719 • 1990
On-Line Computational Scheme for Mechanical Manipulators
J.Y.S. Luh, Michael Walker, Richard P. Paul
Citations: 1574 • 1980
Introduction to robotics: Mechanics and control
M.G. Rodd
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Closed-form solution of absolute orientation using orthonormal matrices
Berthold K. P. Horn, Hugh M. Hilden, S. Negahdaripour
Citations: 1147 • 1988
Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control
Yoshihiko Nakamura, Hideo Hanafusa
Citations: 1064 • 1986
Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles
Zhihua Qu, Jing Wang, R Hull
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Finite Time Controllers
V. T. Haimo
Citations: 907 • 1986
Solving Systems of Polynomial Equations
Bernd Sturmfels
Citations: 851 • 2002
Movement imitation with nonlinear dynamical systems in humanoid robots
Auke Jan Ijspeert, Jun Nakanishi, Stefan Schaal
Citations: 842 • 2003
A Stewart Platform- Based Manipulator: General Theory and Practical Construction
E. F. Fichter
Citations: 794 • 1986
Movement Smoothness Changes during Stroke Recovery
Brandon Rohrer, Susan E. Fasoli, Hermano Igo Krebs, Richard L. Hughes, Bruce T. Volpe, Walter R. Frontera, Joel Stein, Neville Hogan
Citations: 777 • 2002
Separable nonlinear least squares: the variable projection method and its applications
Gene H. Golub, Víctor Pereyra
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Applied Interval Analysis With Examples in Parameter and State Estimation, Robust Control and Robotics
Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
Citations: 754 • 1993
Nonsingular fast terminal sliding‐mode control for nonlinear dynamical systems
Liang Yang, Jianying Yang
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Dynamics of a cantilever beam attached to a moving base
T. R. Kane, R. R. Ryan, A. K. Banerjeer
Citations: 745 • 1987