A compact summary of the full Modern Robotics series, connecting rigid-body motion, screw theory, Jacobians, inverse kinematics, dynamics, and motion planning into one coherent picture.
A mathematically grounded introduction to Modern Robotics, covering rigid-body motion, twists, screw axes, and the Product of Exponentials formulation behind robot kinematics.
A detailed mathematical walkthrough of screw axes, twists, and the exponential map in Modern Robotics, forming the basis for robot kinematics and Jacobian computation.
A continuation of the screw-theory introduction, focusing on spatial vs. body frames, Lie group/Lie algebra intuition, and the connection to Jacobian construction.
A detailed derivation of the Jacobian from screw axes and twists, showing how end-effector velocity is computed from joint rates and why singularities arise.
A deeper look at Jacobian-based velocity control, manipulability measures, and pseudoinverse methods for achieving task-space motion under constraints.
A detailed explanation of inverse kinematics using Jacobian-based methods, analytic solutions, and iterative numerical strategies for robot pose solving.
A deep-dive connecting kinematics, twist-based motion generation, and dynamics to task-space control and robot motion generation.
A continuation of the kinematics-to-planning story, focused on trajectory generation, time scaling, constraints, and the geometry behind motion planning.