CMU-16-715-Robot-Dynamics

Lecture notes for CMU 16715 Advanced Robot Dynamics.

Overview

• Describe a system: Newton-Euler, Lagrangian, and Hamiltonian
• Simulate a system: discretization, integration, SO(3)
• Contact: simulate contact and friction.
• Understand simulator: why it diverges, why it is not deterministic, why the contact not act the way we want, what could be the sim2real gap.

Outline

Basics: discretization, integration, SO(3)

• Lecture 1: A Brief History of Dynamics, Basics of Newtonian Mechanics
• Lecture 2: state space, euler integration, energy, Lyapunov stability (tell if simulation would diverge.)
• Lecture 3: Taylor integration, Runge-Kutta integration (achieve higher-order integration without calculating the higher-order gradient. ), Implicit midepoint.
• Lecture 4: Higher-order RK Method, Stiffness + Stability of RK methods.

Single Rigid Body Dynamics

• Lecture 5: Rigid Body, Reference Frames, Attitude Representation, Rotation Matrix.
• Lecture 6: Linear Systems, Group Theory, Rotation Matrix Kinematics, Quaternion Geometry.
• Lecture 7: Kinematic Energy, Intertia, Euler's Equation (F=ma in rotation form)
• Lecture 8: Stability of spinning rigid body, numerical simulation of 3d Rotations,
• Lecture 9: Newton-Euler dynamics, SE3, Quadrotor, Airplane

Optimization Recap Notebook

• Lecture 10: Root finding, Minimization.
• Lecture 11: Constrained Minimization, Equality Constraints, Inequality Constraints.

Lagrangian Dynamics Notebook

• Lecture 12: Calculus of Variations, Euler-Lagrange Equation.
• Lecture 13: Dynamics from Energy, Lagrangian Mechanics, Least-action principle.
• Lecture 14: Interpretation of Least Action, Manipulator Equation, Non-convervative, Contraints, Coordinates.
• Lecture 15: Simulation with Constraints, Differential Algebraic Equations, Variational Integrator.
• Lecture 16: Momentum, Legendre Transform, Hamiltonian Mechanics
• Lecture 17: Discrete Legendre Transform, Variational Integrator with Constraints.

Contact Dynamics Notebook

• Lecture 18: Contact Dynamics, Discrete Mechanics with Impacts.
• Lecture 19: Coulomb Friction, Maximum Dissipation Principle, LCP Methods.

Applications and Extensions

• Lecture 20: Fixed-based Manipulators, Forward Kinematics, Floating-based Systems
• Lecture 21: Kinematics in 3D, Least-action for rigid body, Floating-based robot dynamics.
• Lecture 22: Floating-based dynamics in maximal coordinates, variational integrators in maximal coordinates.
• Lecture 23: "Fast" Dynamics Algorithms

Resources

Course Syllabus

Lecture Notebooks

Video Lectures

Physics-Based Simulation

Mujoco Offical Documentation