AI Robotics Math
Welcome to AI Robotics Math. This page helps you explore what this area is about with tools, activities, and guided next steps.
Linear Algebra for Robotics & AI
Vectors, matrices, transformations, and decompositions powering perception and motion.
Units
- Vectors, norms, dot/cross products
- Matrix algebra, transformations, rotations
- Rank, invertibility, determinants
- Eigenvalues/eigenvectors, diagonalization
- LU/QR/SVD decompositions
- Projections & least squares (regression)
- Jacobians for kinematics (intro)
Applied Labs
- 2D/3D transforms for a robotic arm
- Image rotation/scaling with matrices
- Least‑squares line fitting from sensor data
Calculus for Robotics & AI
Differential, integral, and multivariable calculus with gradients and vector fields.
Units
- Limits, derivatives, chain rule
- Integrals and applications
- Multivariable: partials, gradients, Hessians
- Jacobians and change of variables
- Line/flux integrals (intro to vector calculus)
- Optimization with calculus
Applied Labs
- Trajectory smoothing with derivatives
- Gradient field visualization
- Energy minimization toy problems
Optimization for AI & Robotics
From gradient descent to constrained optimization for planning and learning.
Units
- Unconstrained optimization (GD, Momentum, Adam)
- Convexity, strong convexity, duality
- Constrained optimization, Lagrange/KKT
- Quadratic programming, regularization
- Numerical considerations and convergence
Applied Labs
- Path optimization on a grid
- Hyperparameter tuning with GD variants
- QP for actuator effort minimization
Control Theory (State‑Space)
Modeling, stability, feedback, and observers for reliable robot behavior.
Units
- Modeling dynamical systems (state‑space)
- Stability via eigenvalues
- PID control and tuning
- LQR basics
- Observers & Kalman filter (intro)
- Discrete‑time control
Applied Labs
- Line follower PID tuning
- Balancing robot (simulated)
- LQR on a simplified plant
Probability & Stochastic Processes
Uncertainty modeling for perception, filtering, and decision‑making.
Units
- Random variables & common distributions
- Bayes rule and inference
- Markov chains & transitions
- Gaussian models & noise
- Monte Carlo methods (intro)
Applied Labs
- Sensor noise characterization
- Simple Bayesian sensor fusion
- Random walk simulation
Kinematics & Dynamics
Geometry of motion, Jacobians, and dynamics for manipulators and mobile robots.
Units
- Coordinate frames & homogeneous transforms
- Forward kinematics
- Inverse kinematics
- Jacobians and singularities
- Dynamics (Newton‑Euler overview)
- Trajectory generation
Applied Labs
- 2‑link arm forward/inverse kinematics
- Jacobian‑based velocity control
- Trajectory timing and smoothing