Axon Curriculum

Axon is an educational curriculum designed from first principles to bridge high-school mathematics and physics into university-level applied mathematics, physical dynamics, autonomous robotics (FIRST Robotics Competition / FRC), machine learning, large language models, and agentic decision systems.

Pedagogical Philosophy

• FRC & Everyday Intuition First: We start with real robot scenarios (scoring targets, joystick steering, sensor jitter, elevator chains, shooter ballistics, obstacle avoidance) before presenting formal equations.
• Code-First Explanations (Java & WPILib): Every concept is solved in clean, boilerplate-free Java with descriptive variable names, paired with the official production WPILib class equivalent.
• “Math!” Translation Sidebars: Formal mathematical symbols, equations, and pronunciation guides are introduced as friendly translations of the code.
• Bridge to Machine Learning & Modern Robotics: Every concept explicitly connects to its role in modern deep learning (embeddings, transformer position encoding, dense layers, diffusion models, backpropagation) and physical robotic autonomy.
• Clean Interactive Visualizers: Concepts include companion interactive HTML5/Canvas demos with dark/light theming.

The 7 Axon Tracks

                        ┌───────────────────────────────┐
                        │   1. Mathematical Foundations │
                        └───────────────┬───────────────┘
                                        │
             ┌──────────────────────────┴──────────────────────────┐
             ▼                                                     ▼
┌───────────────────────────────┐               ┌─────────────────────────────────────┐
│ 2. Machine Learning & Vision  │               │   4. Physics, Dynamics & Actuation  │
└────────────┬──────────────────┘               └──────────────────┬──────────────────┘
             │                                                     │
             ▼                                                     ▼
┌───────────────────────────────┐               ┌─────────────────────────────────────┐
│ 3. Large Language Models      │               │   5. Kinematics & Motion Planning   │
└────────────┬──────────────────┘               └──────────────────┬──────────────────┘
             │                                                     │
             └──────────────────────────┬──────────────────────────┘
                                        ▼
                        ┌───────────────────────────────┐
                        │ 6. Localization & Estimation  │
                        └───────────────┬───────────────┘
                                        │
                                        ▼
                        ┌───────────────────────────────┐
                        │ 7. Reinforcement Learning     │
                        └───────────────────────────────┘

Axon 01: Mathematical Foundations

• Geometry for Robotics: Coordinates, Poses, Distance, Lines & Intersections, Bounding Boxes & Collision, Polygon Field Zones.
• Trigonometry & Angles: Unit Circle, atan2, Angle Wrapping, 180° Swerve Speed Flips, 3D Quaternions.
• Linear Algebra & Matrix Transformations: Vectors, Dot Products, Matrices, Determinants, Matrix Inverses.
• Calculus, Motion & Optimization: Rates of Change, S-Curves & Jerk, Numerical Integrals, Multivariable Gradients.
• Probability & Uncertainty: Sensor Noise & Bell Curves, Bayes’ Rule 1D Fusion, Softmax, Expected Value & Monte Carlo.

Axon 02: Machine Learning & Vision

• Loss Functions & Optimization: MSE, MAE, Cross-Entropy, Gradient Descent, Learning Rates.
• Neural Layers & Activation Functions: Dense weights y = W @ x + b, non-linear activations (ReLU, GELU, Sigmoid).
• Vector Backpropagation Engine: Computational DAG graphs, multivariate Chain Rule, micro-autograd engine.
• Computer Vision & Object Detection: 2D Spatial Convolutions, Sobel edge filters, YOLO bounding boxes, IoU, Non-Maximum Suppression (NMS).

Axon 03: Large Language Models & Transformers

• Tokenization & Vector Embeddings: BPE subword tokenization, vocabulary lookup spaces, high-dimensional semantic vectors, cosine similarity.
• Scaled Dot-Product & Self-Attention: Query, Key, Value (Q, K, V) projections, attention heatmaps, Multi-Head Attention feature subspaces.
• The Transformer Architecture: Pre-RMSNorm normalization, residual skip connections (gradient highway), SwiGLU Feed-Forward Blocks.
• Generation, RoPE & Sampling: Rotary Position Embeddings (RoPE), 2D coordinate rotations, Temperature scaling, Top-k, Top-p (Nucleus) sampling, KV-Caching.

Axon 04: Physics, Dynamics & Actuation

• DC Motors & Electromechanics: Brushless motor curves, Back-EMF, K_t and K_v constants, planetary reductions, reflected load inertia (J / G²).
• Projectile Ballistics & Trajectories: 2D parabolic kinematic arcs, air drag deceleration, Magnus backspin lift, shooting on the move vector compensation.
• Dynamics, Friction & Energy: Coulomb friction circles (F_max = μ_s · N), static vs kinetic slip cliffs, kinetic energy (½ m v²), elevator constant-force spring counterbalancing.
• Control Physics & Voltage Models: Physics feedforward (kS, kV, kA, kG), SimpleMotorFeedforward, ElevatorFeedforward, ArmFeedforward, closed-loop PID tuning and stability.

Axon 05: Kinematics & Motion Planning

• Chassis Speeds & Kinematics: Forward/Inverse kinematics, wheel velocity desaturation.
• Swerve Kinematics & 2nd-Order Twist: 4-wheel decomposition, azimuth optimization, Lie group twist discretization.
• Motion Profiling: Trapezoidal and 7-segment S-Curve velocity profiles.
• Holonomic Trajectory Tracking: Hermite splines, HolonomicDriveController, dynamic obstacle potential fields.

Axon 06: Localization & State Estimation

• Wheel Odometry & Gyro Integration: Twist dead reckoning, encoder tick accumulation, IMU heading integration.
• AprilTag Computer Vision & PnP Pose: Pinhole camera matrix K, Perspective-n-Point solvers, camera latency compensation.
• Extended Kalman Filter (EKF): Multi-state sensor fusion combining high-frequency odometry with low-frequency vision.

Axon 07: Reinforcement Learning & Agentic Decision Systems

• Markov Decision Processes: States, actions, reward shaping, discount factors.
• Value Functions & Deep Q-Learning: Bellman optimality, Deep Q-Networks (DQN), experience replay.
• Policy Gradients & Actor-Critic: Continuous action spaces, REINFORCE, PPO.
• Monte Carlo Tree Search: UCT tree search, AlphaZero search, real-time match strategists.