$\newcommand{\deriv}[2][]{\dfrac{\partial #1}{\partial #2}} \newcommand{\tderiv}[2][]{\tfrac{\partial #1}{\partial #2}} \newcommand{\fderiv}[2][]{\dfrac{d #1}{d #2}} \newcommand{\derivII}[3][]{\dfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\tderivII}[3][]{\tfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\derivIII}[4][]{\dfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\tderivIII}[4][]{\tfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\derivIV}[5][]{\dfrac{\partial^4 #1}{\partial #2 \partial #3 \partial #4 \partial #5}} \newcommand{\half}{\tfrac{1}{2}} % Macro for 1/2 \newcommand{\ud}{\mathrm{d}} \newcommand{\op}{\circ} \newcommand{\dq}{\dot{q}} \newcommand{\ddq}{\ddot{q}} \newcommand{\dt}{\Delta t}$

Trep: Dynamic Simulation and Optimal Control

Release:vbea7a8 Date:September 02, 2023

Trep is a Python module for modeling rigid body mechanical systems in generalized coordinates. It provides tools for calculating continuous and discrete dynamics (based on a midpoint variational integrator), and the first and second derivatives of both. Tools for trajectory optimization and other basic optimal control methods are also available.

You can find detailed installation instructions on our website. Many examples are included with the source code (browse online).

The API Reference has detailed documentation for each part of trep. We have also put together a detailed Tutorials that gives an idea of the capabilities and organization of trep by stepping through several example problems.

If you have any questions or suggestions, please head over to our project page.

API Reference

• Core Components
  • System - A Mechanical System
  • Frame – Coordinate Frame
  • Config – Configuration Variables
  • Input – Input Variables
  • Force – Base Class for Forces
  • Potential – Base Class for Potential Energies
  • Constraint – Base Class for Holonomic Constraints
  • MidpointVI - Midpoint Variational Integrator
• Potential Energies
  • Gravity – Basic Gravity
  • LinearSpring – Linear spring between two points
  • ConfigSpring – Linear Spring acting on a configuration variable
  • NonlinearConfigSpring – Nonlinear spring acting on a configuration variable
• Forces
  • Damping – Damping on Configuration Variables
  • LinearDamper – Linear damper between two points
  • ConfigForce – Apply forces to a configuration variable.
  • BodyWrench – Apply a body wrench to a frame.
  • HybridWrench – Apply a hybrid wrench to a frame.
  • SpatialWrench – Apply a spatial wrench to a frame.
• Holonomic Constraints
  • Distance - Maintain a specific distance between points
  • PointToPoint - Constrain the origins of two frames together
  • PointOnPlane - Constraint a point to a plane
• Discrete Optimal Control
  • Discrete LQ Problems
  • DSystem - Discrete System wrapper for Midpoint Variational Integrators
  • DCost - Discrete Trajectory Cost
  • DOptimizer - Discrete Trajectory Optimization
• ROS Tools
  • URDF Import Tool
  • ROSMidpointVI - ROS Midpoint Variational Integrator
• Misc. Components
  • Spline – Spline Objects
  • TapeMeasure – Measuring distances between frames

Tutorials

• Trep “Hello World”
• Create a pendulum
• Design linear feedback controller
• Design energy shaping swing-up controller
• Calculate optimal switching time
• Discrete Dynamics and Variational Integrators

Indices and tables

• Index
• Module Index