Discrete Mechanics

We have developed an open source software package called trep that is suitable for simulating a variety of dynamic systems.  Trep uses a tree-based structure to represent mechanical systems comprised of interconnected rigid bodies.  The tree description isused to create a generic variational integrator applicable to arbitrary systems.  The tree structure allows the performance of the simulation to scale favorably with problem size. We are also interested in modeling impulsive systems, such as mechanical systems undergoing impacts.

Variational Integrators

One important aspect of this project is the creation of a dynamic simulation software package that is capable of simulating complex mechanical systems.  We have developed an open source software package called trep that is suitable for simulating a variety of dynamic systems.  Trep uses a tree-based structure to represent mechanical systems comprised of interconnected rigid bodies.  The tree description isused to create a generic variational integrator applicable to arbitrary systems.  The tree structure allows the performance of the simulation to scale favorably with problem size; i.e. a full 25-DOF model of a marionette can be integrated better than real-time. Variational integrators are particularly well-suited to marionettes because they preserve constraints and energetic quantities for all time.  This dynamic model is used for creating control strategies as well as for providing real-time animations of a virtual marionette.

High degree-of-freedom systems can experience instability as errors accumulate in the numerical method. Both of these simulations seem fine--initially. But after a few seconds, the simulation on the right becomes infeasible. This would be a major problem for a simulation-based planning algorithm.

Optimal Control and Estimation

This movie shows several trajectories during a trep optimization The figure on the left shows the desired motion. The figures on the right show the current optimal trajectory after each iteration of gradient descent algorithm. 

Credits: Elliot Johnson, Todd Murphey

 

 

 

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