Comprehensive Roadmap for Humanoid Robotics

Phase 1: Foundations (3-6 months)

A. Mathematics & Physics

Linear Algebra

• Vectors, matrices, transformations, eigenvalues
• Calculus: Multivariable calculus, optimization, differential equations
• Probability & Statistics: Bayesian inference, probability distributions, estimation theory
• Classical Mechanics: Kinematics, dynamics, Newton-Euler equations, Lagrangian mechanics
• Control Theory: PID control, state-space representation, stability analysis

B. Programming Fundamentals

Core Languages

• Python: NumPy, SciPy, Matplotlib, object-oriented programming
• C++: Memory management, real-time systems, performance optimization
• Data Structures & Algorithms: Graph theory, optimization algorithms, search algorithms

C. Basic Robotics Concepts

Robot Anatomy

• Degrees of freedom, joints, links, end-effectors
• Coordinate systems: World frame, body frame, joint space vs. task space
• Sensors: IMUs, encoders, force/torque sensors, cameras, LiDAR
• Actuators: Motors (DC, servo, brushless), hydraulics, pneumatics

Phase 2: Core Robotics (6-9 months)

A. Kinematics

Forward Kinematics

• DH parameters, transformation matrices, homogeneous coordinates
• Inverse kinematics: Analytical solutions, numerical methods (Jacobian-based), optimization approaches
• Differential kinematics: Jacobian matrix, velocity propagation, singularities
• Workspace analysis: Reachability, dexterity measures

B. Dynamics

• Rigid body dynamics: Newton-Euler formulation, recursive algorithms
• Lagrangian mechanics: Generalized coordinates, equations of motion
• Forward dynamics: Computing accelerations from torques
• Inverse dynamics: Computing required torques for desired motion
• Dynamic simulation: Integration methods, collision detection

C. Control Systems

• Joint-space control: PID, computed torque control, feedback linearization
• Task-space control: Operational space formulation, impedance control
• Adaptive control: Parameter estimation, model reference adaptive control
• Robust control: H-infinity, sliding mode control
• Optimal control: LQR, MPC (Model Predictive Control)

Phase 3: Humanoid-Specific Topics (6-12 months)

A. Bipedal Locomotion

Gait Theory

• Walking patterns, step cycles, phase transitions
• Zero Moment Point (ZMP): Stability criteria, ZMP trajectory planning
• Center of Mass (CoM) control: Linear inverted pendulum model (LIPM)
• Footstep planning: Discrete search, optimization-based approaches
• Balance control: Ankle strategy, hip strategy, stepping strategy
• Dynamic walking: Passive dynamic walking, limit cycles, hybrid systems

B. Whole-Body Control

• Hierarchical control: Task prioritization, null-space projection
• Inverse dynamics: QP-based whole-body controllers, contact constraints
• Optimization frameworks: Quadratic programming, convex optimization
• Contact modeling: Point contacts, surface contacts, friction cones
• Multi-contact scenarios: Manipulation while walking, climbing, pushing

C. Motion Planning

• Sampling-based methods: RRT, RRT*, PRM
• Optimization-based planning: Trajectory optimization, CHOMP, TrajOpt
• Reactive planning: Dynamic window approach, potential fields
• Humanoid-specific: Whole-body motion planning, contact-implicit planning
• Learning-based planning: Neural motion planning, diffusion models

Phase 4: Perception & Cognition (4-8 months)

A. Computer Vision

• Image processing: Filtering, feature extraction, edge detection
• 3D vision: Stereo vision, structure from motion, SLAM
• Object detection: YOLO, R-CNN variants, transformer-based detectors
• Pose estimation: Human pose estimation, 6D object pose
• Scene understanding: Semantic segmentation, instance segmentation, panoptic segmentation

B. State Estimation & Localization

• Sensor fusion: Kalman filters, Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF)
• Particle filters: Monte Carlo localization, AMCL
• SLAM: Visual SLAM, RGB-D SLAM, LiDAR SLAM
• Inertial navigation: IMU integration, drift correction

C. Machine Learning & AI

• Supervised learning: Regression, classification for perception tasks
• Deep learning: CNNs, RNNs, Transformers, attention mechanisms
• Reinforcement learning: Q-learning, policy gradients, actor-critic methods
• Imitation learning: Behavioral cloning, inverse RL, learning from demonstration
• Sim-to-real transfer: Domain randomization, domain adaptation

Phase 5: Advanced Topics (Ongoing)

A. Manipulation

• Grasp planning: Force closure, grasp quality metrics
• Dexterous manipulation: Multi-fingered hands, in-hand manipulation
• Dual-arm coordination: Bimanual manipulation, cooperative control
• Contact-rich manipulation: Pushing, sliding, pivoting

B. Human-Robot Interaction

• Natural language processing: Intent recognition, dialogue systems
• Social robotics: Gesture recognition, emotion recognition, proxemics
• Physical HRI: Compliant control, safety, collaborative manipulation
• Teleoperation: Bilateral control, haptic feedback, retargeting

C. Learning & Adaptation

• Online learning: Real-time adaptation, meta-learning
• Transfer learning: Skill transfer, few-shot learning
• Sim-to-real: Reality gap bridging, system identification
• Multi-task learning: Shared representations, curriculum learning