Modern Robotics: Mechanics, Planning, and Control

Course 1: Foundations of Robot Motion (Chapters 2 & 3)

Mathematical descriptions of spatial configuration and velocity:

• Configuration Space (C-space): Topology, holonomic and nonholonomic constraints, Grubler’s formula for degrees of freedom (DoF = m(N-1-J) + sum(f_i)).
• Spatial Rigid-Body Motions: Rotation matrices SO(3), exponential coordinates of rotation, and Rodrigues' formula.
• Twists & Screws: Homogeneous transformation matrices SE(3), spatial and body twists, screw axes, and spatial wrenches.

Course 2: Robot Kinematics (Chapters 4, 5, 6, 7)

Modern screw-theoretic formulation of kinematics bypassing traditional DH parameters:

• Product of Exponentials (PoE) Formula: Forward kinematics using exponential screw matrix products.
• Velocity Kinematics & Manipulator Jacobian: Body Jacobian and space Jacobian. Kinematic singularities and manipulability ellipsoids.
• Numerical Inverse Kinematics: Newton-Raphson method and damped least-squares (Levenberg-Marquardt) using the pseudoinverse.

Course 3: Robot Dynamics (Chapters 8 & 9)

Equations of motion for open-chain robot arms:

• Newton-Euler Inverse Dynamics: Forward-backward recursive algorithm calculating motor torques in O(n) time.
• Euler-Lagrange Forward Dynamics: Simulating joint accelerations using mass matrix inverse.
• Trajectory Generation: Quintic polynomials, trapezoidal velocity profiles, and time-optimal path parameterization.

Course 4: Robot Motion Planning and Control (Chapters 10 & 11)

• Motion Planning: Sampling-based planners: Rapidly-exploring Random Trees (RRT, RRT*), Probabilistic Roadmaps (PRM), and Artificial Potential Fields.
• Motion Control: Computed torque control, task-space error dynamics, feedforward control, and Passivity-based PID.

Course 5: Manipulation & Mobile Robots (Chapters 12 & 13)

• Contact Kinematics & Grasping: Friction cones, form closure, force closure, and rolling contact equations.
• Wheeled Mobile Robots: Kinematics of differential drive robots, unicycle models, car-like robots, and omnidirectional Mecanum bases.

Course 6: Capstone Project (Mobile Manipulation)

Program a simulated KUKA youBot (mobile base + 5-DOF arm) inside CoppeliaSim to autonomously drive to a standoff position, grasp a block, transport it across obstacles, and place it at a goal orientation using feedforward plus PI feedback control.