Anytime Computation of Time-Optimal Off-Road Vehicle Maneuvers using the RRT*. Jeon, Karaman, Frazzoli. Decision and Control.
An empirical application of RRT*, this paper finds trail-breaking as something that naturally emerges from RRT*
I was excited because I thought this application would use stochasticity, but looks like it is a deterministic simulation.
They give the dynamics equations
There have been methods that applied numerical optimization from optimal control theory to this domain, but it requires “careful transcription to numerical optimization formulations. Most algorithms of this class must be started with a feasible initial solution, which is usually hard to generate in the first place.”
Also some suffer from local optimality (may be same as requiring initial solution)
Cites applications of optimal control to the domain, as well as a paper that compares other methods
In this application, they plan in the “task space”, which is some lower dimensional representation of the original problem that doesn’t throw out information
Plan in state space, and then require a method which will near-optimally nearly-steer between the two states
The one they use is based on shooting, the one they use requires another function that subdivides the input and increments or decrements it as needed
That is a pretty difficult problem in itself
Reminds me of binary action search
Uses branch and bound/admissible heuristics
Approach requires distance metric, as all RRT methods do