Robotics: Overview

This file is the index for the concepts/robotics/ folder. It lists planned and written subtopic notes, organizes them by theme, and collects the canonical references for the field. Use it to decide what to write next without needing to re-survey the landscape.

This cluster is the math backbone for the SO-101 Robotics Curriculum — each note here corresponds to one or two chapters of Modern Robotics (Lynch & Park), the curriculum’s anchor textbook for Modules 0, 1, and 3, written up with full derivations rather than paraphrased.

Notes in This Folder

File Status Topic
configuration-space.md ✅ Written Configuration space, degrees of freedom, Grubler’s formula, holonomic/nonholonomic constraints, task space vs. configuration space
rigid-body-motions.md 🔲 Planned Rotation matrices, angular velocity, exponential coordinates for rotation (SO(3))
forward-kinematics.md 🔲 Planned Product-of-exponentials formula, Denavit-Hartenberg convention, homogeneous transforms (SE(3))
velocity-kinematics.md 🔲 Planned Space/body Jacobians, manipulability, kinematic singularities
inverse-kinematics.md 🔲 Planned Newton-Raphson iterative IK, numerical and analytic approaches
dynamics.md 🔲 Planned Lagrangian formulation, mass matrix, Coriolis/centrifugal terms, equations of motion for open chains

Subtopic Map

Configuration and Motion Representation

Subtopic Key Idea Primary Source
Configuration space The manifold of all possible configurations of a mechanical system Modern Robotics Ch. 1–2
Degrees of freedom Dimension of the configuration space; counted via Grubler’s formula for linkages Modern Robotics Ch. 2
Rigid-body motion Rotation matrices (SO(3)) and rigid transforms (SE(3)), exponential coordinates Modern Robotics Ch. 3

Kinematics

Subtopic Key Idea Primary Source
Forward kinematics Mapping joint angles to end-effector pose via product-of-exponentials or DH parameters Modern Robotics Ch. 4
Velocity kinematics Jacobian relating joint velocities to end-effector twist; singularities Modern Robotics Ch. 5
Inverse kinematics Solving for joint angles given a target end-effector pose Modern Robotics Ch. 6

Dynamics

Subtopic Key Idea Primary Source
Lagrangian dynamics Equations of motion for open kinematic chains, mass matrix, Coriolis terms Modern Robotics Ch. 8

Dependency Graph

flowchart TD
    CS["Configuration Space
configuration-space.md"]
    RBM["Rigid-Body Motions
rigid-body-motions.md"]
    FK["Forward Kinematics
forward-kinematics.md"]
    VK["Velocity Kinematics
velocity-kinematics.md"]
    IK["Inverse Kinematics
inverse-kinematics.md"]
    DYN["Dynamics
dynamics.md"]
    CS --> RBM
    RBM --> FK
    FK --> VK
    FK --> IK
    VK --> DYN

Master References

Reference Authors Year What It Covers Link
Modern Robotics: Mechanics, Planning, and Control Kevin M. Lynch, Frank C. Park 2017 Full textbook — configuration space through dynamics and control; anchor for this entire cluster Free PDF, modernrobotics.org
16-811 Math Fundamentals for Robotics Matt Mason (CMU) — Grad-level supplementary rigor on linear algebra, differential geometry, and configuration-space topics used in the curriculum’s Module 1 cs.cmu.edu/~me/courses/811