Mathematical Modeling in Robotics and Artificial Intelligence

A Unified Approach to Kinematics, Path Planning, and AI-Based Control Systems (Vol. 1)

The rapid advancement of Artificial Intelligence, Robotics, Autonomous Systems, Industrial Automation, and Intelligent Machines has transformed the way modern engineering systems are designed and controlled. Behind every intelligent robot lies a sophisticated mathematical framework that enables perception, motion, planning, optimization, and decision-making.

Mathematical Modeling in Robotics and Artificial Intelligence: A Unified Approach to Kinematics, Path Planning, and AI-Based Control Systems (Vol. 1) provides a comprehensive introduction to the mathematical foundations of modern robotics integrated with Artificial Intelligence. The book combines classical robotics principles with contemporary AI techniques to help readers understand how intelligent robots model, analyze, and interact with complex environments.

Beginning with mathematical modeling fundamentals, the book introduces coordinate systems, linear algebra, transformation matrices, quaternions, Jacobians, forward and inverse kinematics, robotic dynamics, intelligent control systems, optimization methods, and AI-powered path planning. Practical examples, algorithmic explanations, and simulation concepts using MATLAB, Python, and ROS make the content highly relevant for both academic and industrial applications.

Whether you are an undergraduate student, postgraduate researcher, robotics engineer, AI developer, or faculty member, this book offers a structured learning path from mathematical foundations to advanced intelligent robotic systems.

What You’ll Learn

✔ Mathematical Modeling Fundamentals

✔ Robotics Mathematics

✔ Artificial Intelligence in Robotics

✔ Coordinate Systems and Transformations

✔ Linear Algebra for Robotics

✔ Vector and Matrix Operations

✔ Homogeneous Transformation Matrix

✔ Rotation Matrices

✔ Euler Angles

✔ Quaternion Representation

✔ Jacobian Matrix

✔ Differential Motion Analysis

✔ Forward Kinematics

✔ Inverse Kinematics

✔ Denavit-Hartenberg (DH) Convention

✔ Serial Robot Manipulators

✔ Parallel Robots

✔ MATLAB Robotics Simulation

✔ Python Robotics Programming

✔ Differential Kinematics

✔ Velocity Analysis

✔ Robot Singularities

✔ Acceleration Modeling

✔ Newton-Euler Formulation

✔ Lagrangian Dynamics

✔ Recursive Newton-Euler Algorithm

✔ Multi-Link Robot Dynamics

✔ Inertia and Coriolis Forces

✔ PID Controller Design

✔ Adaptive Control Systems

✔ Robust Control Techniques

✔ Fuzzy Logic Controllers

✔ Neural Network Controllers

✔ Lyapunov Stability

✔ Model Predictive Control (MPC)

✔ Genetic Algorithm Optimization

✔ Swarm Intelligence

✔ Deep Reinforcement Learning

✔ Robot Path Planning

✔ Configuration Space

✔ Obstacle Avoidance

✔ Dijkstra Algorithm

✔ A* Search Algorithm

✔ D* Algorithm

✔ Probabilistic Roadmap (PRM)

✔ Rapidly Exploring Random Tree (RRT)

✔ Potential Field Method

✔ AI-Based Path Planning

✔ Autonomous Robot Navigation

Part I – Foundations of Mathematical Modeling in Robotics

Chapter 1
Introduction to Mathematical Modeling and Robotics

Chapter 2
Mathematical Preliminaries for Robotics

Part II – Kinematics Modeling of Robots

Chapter 3
Forward Kinematics

Chapter 4
Inverse Kinematics

Chapter 5
Differential Kinematics and Velocity Analysis

Part III – Dynamics and Control System Modeling

Chapter 6
Dynamics of Robotic Systems

Chapter 7
Control System Design for Robots

Chapter 8
Stability and Optimization

Part IV – Path and Trajectory Planning

Chapter 9
Path Planning Algorithms

Who Should Read This Book?

This book is ideal for:

B.Tech Students
B.E. Students
M.Tech Students
MCA Students
BCA Students
Computer Science Students
Robotics Engineering Students
Mechanical Engineering Students
Mechatronics Students
Electrical Engineering Students
Artificial Intelligence Students
Machine Learning Engineers
Robotics Engineers
Automation Engineers
Embedded Systems Engineers
Research Scholars
University Faculty
AI Researchers
Industrial Professionals
Competitive Examination Aspirants

Key Features

✅ Comprehensive Robotics Mathematics

✅ AI-Integrated Robotic Modeling

✅ Step-by-Step Mathematical Derivations

✅ Robotics Kinematics and Dynamics

✅ Intelligent Control System Design

✅ Advanced Path Planning Algorithms

✅ MATLAB, Python, and ROS Integration

✅ AI-Based Robot Navigation

✅ Modern Optimization Techniques

✅ Deep Reinforcement Learning Applications

✅ Industry-Oriented Case Studies

✅ University Curriculum Aligned

✅ Suitable for Self-Learning and Research

Why This Book?

Unlike conventional robotics textbooks that focus only on mechanical systems or isolated mathematical concepts, this book presents a unified framework connecting Mathematical Modeling, Robotics, Artificial Intelligence, Machine Learning, Control Engineering, Optimization, and Autonomous Navigation.

Readers gain practical knowledge of how intelligent robots compute movement, estimate positions, optimize trajectories, avoid obstacles, and make autonomous decisions using modern AI algorithms. The inclusion of MATLAB, Python, and ROS-based simulation concepts further enhances practical understanding and prepares readers for research and industrial applications in robotics and intelligent automation.

This book serves as an excellent academic textbook, research reference, and professional guide for anyone interested in the mathematical foundations of intelligent robotic systems.

Book Details

Title: Mathematical Modeling in Robotics and Artificial Intelligence

Subtitle: A Unified Approach to Kinematics, Path Planning, and AI-Based Control Systems

Volume: Vol. 1

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Language: English

Homogeneous Transformation Matrix

Mathematical Modeling in Robotics and Artificial Intelligence VOL-1