Mathematical Modeling in Robotics and Artificial Intelligenc (AI & New Age Math)

Introduction: The Rise of Intelligent Machines
In the last few decades, humanity has entered a technological era that has completely transformed the boundaries of science, engineering, and imagination. Robotics, once confined to industrial assembly lines and controlled environments, has now become a symbol of human progress — merging mechanics, electronics, and intelligence into one cohesive entity. Artificial Intelligence (AI), on the other hand, has provided machines the ability to think, learn, and adapt.
But the real transformation lies not in the existence of these two domains separately — rather, it lies in their fusion. When mathematics becomes the language of robotic motion, and artificial intelligence becomes its brain, we witness the birth of mathematical modeling in robotics and AI — a discipline that combines precision, prediction, and perception to create truly intelligent machines.
This book, “Mathematical Modeling in Robotics and Artificial Intelligence,” explores that fusion in depth. Written for students, researchers, engineers, and academic professionals, this text serves as both a foundation and a future guide for designing, analyzing, and implementing robotic systems enhanced with AI-driven control and decision-making mechanisms.

Why This Book?
While many books discuss robotics, and others focus on AI, very few integrate the mathematical backbone of robotics with the intelligent adaptability of AI in a unified framework. This book bridges that critical gap. It systematically explores how mathematical models — equations, matrices, and control algorithms — can be extended and optimized using modern AI techniques such as neural networks, fuzzy logic, and reinforcement learning.
The book is designed for:

• Undergraduate and postgraduate students of B.Tech, MCA, M.Tech, and Robotics Engineering.
• Researchers in Control Systems, Artificial Intelligence, and Mechatronics.
• Engineers working in robotics design, automation, and AI integration.
• Educators and academicians seeking a comprehensive and application-oriented resource.

Each chapter provides a blend of theoretical depth, practical modeling, and AI-based implementation, reinforced with illustrative examples, equations, and conceptual diagrams.

Core Philosophy of the Book
The central idea of this book is to understand robotics as a living system driven by mathematics and empowered by AI.
Just as biological organisms rely on internal models to perceive and act, robots rely on mathematical models to predict, plan, and execute movements. However, as environments become uncertain and complex, purely mathematical precision falls short — this is where artificial intelligence complements modeling with adaptability.
This synergy between determinism (mathematics) and learning (AI) is the focus of the book.

Structure and Approach
The book is divided into six major parts, each progressing from basic mathematical concepts to advanced AI-driven applications.
Part I: Foundations of Mathematical Modeling in RoboticsThe book begins with an introduction to the world of robotics and the importance of mathematical modeling in understanding robotic motion, structure, and control.
Readers are guided through coordinate systems, transformations, vectors, and matrix algebra, which form the foundation of every robotic operation.
It also introduces essential tools like MATLAB, Python, and ROS (Robot Operating System) to establish a computational foundation.