Robot locomotion

Robotics is interdisciplinarity: whether you're into mechanics, electronics, machine learning, control theory, numerical optimization, raptor hunting, etc., you can contribute! The following notes connect the dots between bits of knowledge I found useful for locomotion in particular. I hope they help. Shoot me an e-mail if you find anything inaccurate or imprecise (yes, accuracy and precision are not the same thing).

Wondering where to start? The notes below are sorted from locomotion-specific to general. They assume you already know what a controller is. I imagine you've reached this page by searching for a particular topic, but if you're browsing out of curiosity that's also great :-) In that case, I'd advise you check out the How do biped robots walk? overview.

Walking ¶

• Capture point
• Floating base estimation
• How do biped robots walk?
• Linear inverted pendulum model
• Open loop and closed loop model predictive control
• Prototyping a walking pattern generator
• Tuning the LIPM walking controller

Models ¶

• Contact flexibility and force control
• Linear inverted pendulum model
• Point mass model

Contact dynamics ¶

• Contact flexibility and force control
• Contact modes
• Contact stability
• Friction cones
• Wrench friction cones
• ZMP support area

Dynamics ¶

• Computing torques to compensate gravity in humanoid robots
• Constrained equations of motion
• Equations of motion
• Forward dynamics
• Knee torque of a lumped mass model
• Newton-Euler equations
• Point de non-basculement
• Principle of virtual work
• Recursive Newton-Euler algorithm
• Revolute joints
• Screw theory
• Zero-tilting moment point

Kinematics ¶

• Inverse kinematics
• Kinematics jargon
• Kinematics of a symmetric leg
• Position and coordinate systems
• Revolute joints
• Screw axes
• Screw theory
• Spatial vector algebra cheat sheet

Software ¶

OpenRAVE

OpenRAVE is a C++/Python robotics software for forward kinematics and inverse dynamics of robot models. It provides other features not listed here such as symbolic inverse kinematics for serial manipulators. I used it in my PhD and developed the pymanoid library to add whole-body inverse kinematics and model predictive control to it for prototyping humanoid walking controllers.

• Computing the inertia matrix
• Converting robot models to OpenRAVE
• Getting started with OpenRAVE
• Installing OpenRAVE on Ubuntu 14.04
• Installing OpenRAVE on Ubuntu 16.04
• Troubleshooting OpenRAVE installation

See also ¶

Optimization

• An Introduction to Lagrange Multipliers
  How Lagrange multipliers arise from optimization constraints.
• Conversion from least squares to quadratic programming
  How to go from least squares to QP, which is slightly more general.
• Quadratic programming in Python
  The most common class of convex problems used in optimal control.

Physics

• Gyroscopic precession
  Experiments on angular momentum and torque.
• Integration Basics
  How to integrate the equations of motion.
• Some comments on the structure of the dynamics of articulated motion
  My go-to writeup on the equations of motion.
• The Principle of Least Action
  A special lecture by Richard Feynman.