Month 5 of 6
The maths that makes robots actually work
The maths that makes robots actually work
Up to now you have used libraries that did the hard parts for you
This month is where you learn what they were doing, because the difference between someone who can configure Nav2 and someone who can fix Nav2 when it misbehaves is exactly this material
You do not need all of it at research depth. You need working fluency in control, enough kinematics to reason about an arm, and enough vision to get 3D information out of a camera
What to learn
1Control theory, starting with PID
You already tuned a PID controller by feel in month two. Now learn why it worked
Resources
Understanding PID Control, MATLAB Tech Talks with Brian Douglas (free)
Seven parts covering what PID is, integrator windup, derivative filtering, tuning, and manual versus automatic tuning. The fastest route from zero to a controller that works this week
Brian Douglas, Control System Lectures (free)
Intuition-first explanations across PID, state space, robust control and drone control, and the best fit for someone with no formal controls course behind them
The Fundamentals of Control Theory, Brian Douglas (free, Creative Commons)
The written companion to the videos, and a coherent narrative rather than scattered lessons
Control Bootcamp, Steve Brunton (free)
Thirty-nine videos and the right entry point to state space, controllability, observability, LQR and the Kalman filter
Feedback Systems, Åström and Murray (free PDF)
The rigorous textbook, released free by Princeton University Press, for when you want the proper version without paying
What to focus on
Practice task
take the balancing robot from month two and implement three controllers on the same hardware: P only, PD, then PID with feedforward. Log the step response of each to a CSV, plot all three, and write up which one you would ship and why. That plot is worth more in an interview than any certificate
2State space, LQR and MPC
Resources
Understanding Model Predictive Control, MATLAB Tech Talks (free)
Seven parts from why to use MPC through adaptive and nonlinear variants, and how to make it run fast enough to be real
Underactuated Robotics, Russ Tedrake, MIT (free)
This is where control theory becomes robotics: pendulums, cart-poles, walking, running and humanoids, with dynamic programming, LQR, Lyapunov analysis and trajectory optimisation. Free notes, free PDF and lecture videos
What to focus on
Practice task
implement LQR for a simulated cart-pole in Python, then implement the same thing with a hand-tuned PID and compare how each handles a disturbance. Tedrake's notes give you the model, so you are implementing rather than deriving
3Kinematics and dynamics
Resources
Modern Robotics, Kevin Lynch, Northwestern (free book, code and videos)
The free preprint of the standard textbook, plus companion libraries in Python, MATLAB and Mathematica and full video lectures. It uses screw theory and product-of-exponentials rather than DH parameters, which is cleaner and now the industry norm
Modern Robotics Specialization (Coursera, free audit available)
The same material as a structured six-course sequence with assessment, if you need deadlines to finish things
Robotics Toolbox for Python, Peter Corke (free, MIT)
Forward kinematics, Jacobians, numerical IK, trajectory generation and fifty-plus real robot models including Franka and UR, so you learn by running code against real arms
QUT Robot Academy, Peter Corke (free)
Over 200 video lessons of under ten minutes each, labelled by prerequisite level, and the best source of short atomic explanations of DH parameters, Jacobians and pose representation
What to focus on
Practice task
compute the forward kinematics of your SO-101 arm by hand from its link lengths, then verify against the Robotics Toolbox. Then write a numerical IK solver that moves the end effector to a commanded XYZ, and watch what it does near a singularity. Feeling the arm lose a degree of freedom is what makes the concept stick
4Perception and computer vision
Resources
FREE OpenCV Bootcamp (OpenCV.org official, free)
The official two-to-three hour course from OpenCV themselves, covering image manipulation, filtering, edge detection, tracking and the DNN module. Start here rather than a paid course
OpenCV Camera Calibration tutorial (official docs, free)
The canonical walkthrough with full Python code, from chessboard corners to undistortion to re-projection error. Every robotics engineer must be able to do this from memory
Cyrill Stachniss lectures, University of Bonn (free)
Full university lecture recordings on mobile sensing, photogrammetry and SLAM, and the best free source on the geometric side: projective geometry, bundle adjustment, EKF and graph SLAM
Open3D point cloud tutorials (free)
Voxel downsampling, normal estimation, ICP registration, plane segmentation and clustering, with far less friction than PCL for anyone already in Python
What to focus on
Practice task
calibrate an actual camera with a printed chessboard, save the intrinsics, then write a script that detects a coloured object and estimates its position in 3D relative to the camera. Then move the lighting and watch it fail, and fix it. That failure-and-fix write-up is portfolio material
5Manipulation and MoveIt 2
Resources
MoveIt 2 Getting Started (free, open source)
The official entry point, and the docs recommend Jazzy on Ubuntu 24.04 for the smoothest experience
Pick and Place with MoveIt Task Constructor (free)
The most useful manipulation tutorial in ROS 2, teaching how to decompose a task into stages and implement grasp generation, IK and collision management
Robotic Manipulation, Russ Tedrake, MIT (free)
Twelve chapters connecting hardware, kinematics, perception, grasping, planning and control into one coherent stack, and it now teaches model-based and learned approaches together, which is exactly how the industry now works
Contact-GraspNet, NVIDIA (free code)
Six-DOF grasp generation in cluttered scenes from a depth map, and the standard baseline for learned grasping
Practice task
get MoveIt 2 planning motions for a simulated arm, add collision objects to the planning scene, and execute a pick and place. Then make it fail by placing an obstacle in the only viable path and observe how the planner behaves. Understanding planner failure is more valuable than watching it succeed
Month 5 Milestone
By the end of this month you should be able to:
Check yourself
2–3 hours a day is the design load.