Bachelor of Science · Self-Directed · Semester One

ROBOTICS
LEARNING
PATH

A university-grade first semester curriculum modeled after MIT 2.12 (Introduction to Robotics) and Stanford CS223A. Covering the mathematical foundations, mechanical reasoning, and software systems every roboticist must know.

16 Weeks
5 Modules
MIT OpenCourseWare Referenced
Stanford CS223A Referenced
Self-Paced
MIT 2.12Intro to Robotics
Stanford CS223AIntro to Robotics
MIT CSAILUnderactuated Robotics
Stanford AA274ARobot Autonomy I
MIT OCWOpen CourseWare
5
Core Modules
16
Weeks
12
Textbooks
∞
Free Resources
00
Prerequisites
∫
Calculus & Linear Algebra
Derivatives, integrals, matrices, eigenvalues. These appear in kinematics and dynamics constantly.
Linear Algebra Done Right
Sheldon Axler · Springer
Core
⚙
Physics & Mechanics
Newton's laws, rigid body statics, basic dynamics. Required before robot dynamics makes sense.
Engineering Mechanics: Dynamics
Hibbeler · Pearson
Ref
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Python Programming
Loops, functions, NumPy basics, and comfort with the command line. All course labs use Python.
Python Crash Course
Eric Matthes · No Starch Press
Core
01
Mathematical Foundations of Robotics
MODULE 01
WEEKS 1–3
Spatial Transformations & Rigid Body Geometry
The mathematical language that describes where a robot is and how it moves. MIT 2.12 and Stanford CS223A both begin here — rotation matrices, homogeneous transforms, and reference frames underpin everything that follows.
Rotation matrices: SO(2) and SO(3) groups
Euler angles, roll-pitch-yaw, gimbal lock
Quaternions for rotation representation
Homogeneous transformation matrices (4×4)
Reference frames and coordinate transforms
Screw theory: twist and wrench
TEXTBOOKS
Modern Robotics: Mechanics, Planning, and Control
Lynch & Park · Cambridge University Press, 2017
★ Primary text — free PDF available at modernrobotics.org. Used by Northwestern & CMU.
Core
Introduction to Robotics: Mechanics and Control
John J. Craig · Pearson, 3rd Ed.
Stanford CS223A's classic reference for kinematics and transforms.
Reference
02
Robot Kinematics
MODULE 02A
WEEKS 4–5
Forward Kinematics
Given joint angles, find where the end-effector is in space. This is the "position of a robot arm" problem at the heart of both MIT and Stanford's curricula.
Denavit-Hartenberg (DH) convention
Product of exponentials formulation
Manipulator workspace analysis
URDF robot descriptions (ROS)
MODULE 02B
WEEKS 6–7
Inverse Kinematics
Given a target position, what joint angles are required? IK is the hard direction — multiple solutions, singularities, and numerical methods are all covered here.
Closed-form IK for 6-DOF manipulators
Jacobian-based numerical IK
Singularities and workspace limits
Redundancy resolution strategies
TEXTBOOKS FOR MODULE 02
Modern Robotics: Mechanics, Planning, and Control
Lynch & Park · Chapters 4–6
Chapters on forward kinematics via screw theory and product of exponentials.
Core
Robotics: Modelling, Planning and Control
Siciliano, Sciavicco, Villani, Oriolo · Springer
Excellent detailed coverage of Jacobians and IK numerical methods.
Supplemental
03
Robot Dynamics & Control
MODULE 03A
WEEKS 8–9
Rigid Body Dynamics
How forces cause motion. The Euler-Lagrange and Newton-Euler equations describe how torques applied at joints translate to robot motion.
Lagrangian mechanics for manipulators
Newton-Euler recursive dynamics
Mass matrix, Coriolis terms, gravity
Actuator models: DC motors, gearboxes
MODULE 03B
WEEKS 10–11
Control Systems
Making a robot go where you want reliably. MIT's 2.12 course covers joint, Cartesian, and force control — Stanford CS223A adds operational space control.
PID control — tuning and stability
Joint space vs Cartesian space control
Computed torque / feedback linearization
Impedance control and force control
TEXTBOOKS FOR MODULE 03
Robot Modeling and Control
Spong, Hutchinson & Vidyasagar · Wiley, 2nd Ed.
★ The standard undergraduate textbook for dynamics and control. Used in university courses worldwide.
Core
Robot Analysis and Control
Asada & Slotine · Wiley
The original MIT 2.12 textbook by the course's professors.
MIT Official
Control Systems Engineering
Nise · Wiley, 7th Ed.
Control theory background reference. Great for PID and frequency-domain analysis.
Background
04
Motion Planning & Navigation
MODULE 04
WEEKS 12–13
Planning in Configuration Space
How does a robot decide what path to take from A to B while avoiding obstacles? Stanford's AA274A focuses heavily on these algorithms — they power everything from autonomous cars to surgical robots.
Configuration space (C-space) concept
Potential field methods
Probabilistic Roadmaps (PRM)
Rapidly-Exploring Random Trees (RRT, RRT*)
A* and Dijkstra's graph search
Trajectory generation and smoothing
TEXTBOOKS
Planning Algorithms
Steven LaValle · Cambridge, 2006
Free at planning.cs.uiuc.edu — the definitive motion planning textbook.
Core
Probabilistic Robotics
Thrun, Burgard & Fox · MIT Press
Stanford AA274A required text. Covers SLAM, localization, and Bayesian filtering.
Stanford AA274A
05
Sensing, Perception & ROS
MODULE 05A
WEEKS 14–15
Sensors & Perception
Robots must sense their world. MIT 2.12's labs cover vision and navigation hardware. Stanford AA274A covers the full perception-to-planning pipeline.
Camera models & projection geometry
LiDAR, IMU, encoders, force sensors
Kalman Filter & Extended Kalman Filter
Point cloud processing (basic)
Intro to SLAM (Localization & Mapping)
MODULE 05B
WEEK 16
ROS & Integration Lab
The Robot Operating System is the industry standard middleware. MIT 2.12 labs and Stanford AA274A both rely heavily on ROS. Final week integrates everything.
ROS 2 nodes, topics, and services
URDF model loading in RViz/Gazebo
MoveIt! for arm motion planning
Final integration project: pick & place
TEXTBOOKS FOR MODULE 05
Probabilistic Robotics
Sebastian Thrun, Wolfram Burgard, Dieter Fox · MIT Press
★ The definitive reference on sensor models, Kalman filters, particle filters and SLAM.
Core
A Gentle Introduction to ROS
Jason O'Kane · Free PDF at cse.sc.edu/~jokane/agitr/
Stanford AA274A recommended reading. Concise and free.
Free
Computer Vision: Algorithms and Applications
Richard Szeliski · Springer (free PDF available)
Best reference for camera geometry and visual perception fundamentals.
Supplemental
—
16-Week Schedule
Semester Timeline
~10–15 HRS / WEEK RECOMMENDED
WK 1
Rotation matrices, SO(3), reference frames MOD 01
WK 2
Homogeneous transforms, Euler angles, quaternions MOD 01
WK 3
Screw theory, twists, wrenches, exponential coordinates MOD 01
WK 4
Forward kinematics: DH parameters, product of exponentials MOD 02A
WK 5
Workspace analysis, velocity kinematics, Jacobian matrix MOD 02A
WK 6
Inverse kinematics: closed-form solutions, singularities MOD 02B
WK 7
Numerical IK, Jacobian pseudo-inverse, redundancy MOD 02B
WK 8
Lagrangian dynamics, equations of motion for robot arms MOD 03A
WK 9
Newton-Euler dynamics, actuator models, DC motors MOD 03A
WK 10
PID control, joint-space control, stability analysis MOD 03B
WK 11
Computed torque control, Cartesian & force control MOD 03B
WK 12
Configuration space, potential fields, graph search (A*) MOD 04
WK 13
Sampling-based planning: PRM, RRT, trajectory smoothing MOD 04
WK 14
Camera models, LiDAR, Kalman Filter, basic SLAM MOD 05A
WK 15
Extended Kalman Filter, particle filter, sensor fusion MOD 05A
WK 16
ROS 2 integration, final project: pick-and-place in simulation MOD 05B
—
Free Online Resources
MIT OpenCourseWare
2.12 Introduction to Robotics
Full course materials, lecture notes, and lab descriptions from Prof. Harry Asada. Free at ocw.mit.edu
Stanford Engineering Everywhere
CS223A Introduction to Robotics
Full video lecture series, slides, and problem sets. Free at see.stanford.edu/course/cs223a
MIT CSAIL · Free Textbook
Underactuated Robotics (Tedrake)
Free online book and course videos from Prof. Russ Tedrake covering nonlinear control and optimization.
Free Textbook
Modern Robotics (Lynch & Park)
Full PDF + Coursera course available free at modernrobotics.org. Excellent for modules 1–3.
Free Textbook
Planning Algorithms (LaValle)
The complete motion planning textbook, freely available at planning.cs.uiuc.edu for module 4.
ROS 2 Official Docs
ROS 2 Humble / Iron Docs
Free tutorials, installation guides, and API references at docs.ros.org. Start with the Beginner tutorials.
Curriculum modeled after MIT 2.12 (Prof. Harry Asada) & Stanford CS223A
Sources: MIT OpenCourseWare · Stanford Engineering Everywhere · Stanford AA274A Syllabus
All free resources verified available as of 2025.
ROBOTICS BS · S1