Space-Time Methods for Trajectory Optimization
Seminar given by Ton van den Bogert on Jan 23, 2014.
The Matlab code will work best if you have the IPOPT solver installed. IPOPT for Matlab can be found here. Find the MEX binary for your operating system and iInstall it either in the same folder, or somewhere in your Matlab search path.
If IPOPT is not installed, the optimization is done with a simple Newton method on the KKT conditions. This is less robust and more sensitive to initial guess. When it does not converge, solve a simpler problem first (smaller motion) and use this as an intial guess for a more difficult problem. And so on.
Here is a good example to try, and it works with or without IPOPT. Swing the pendulum up to vertical in 10 seconds, using 200 time points in the optimization.
>> pend(10, 180, 200)