ComplexBRAT: Complex Backward Reach Avoid Tubes

Code for the Hamilton-Jacobi-Isaacs Analysis of the murmurations paper: ComplexBRAT: Complex Backward Reach Avoid Tubes.

For the technical details on the theory behind this work, please see this paper:

@article{ComplexBRAT,
title   = {ComplexBRAT: Complex Backward Reach-Avoid Tubes. An Emergent Collective Behavior Framework.},
author  = {Ogunmolu, Olalekan.},
journal = {Algorithm Foundations of Robotics, XV (WAFR).},
year    = {2022},
}

A preprint can be downloaded here: ComplexBRAT: Complex Backward Reach-Avoid Tubes. An Emergent Collective Behavior Framework.

Evolution of BRAT for Different Flocks

Here, we initialized various flocks on a state space to constitute a simple murmuration's trajectory verification. Within each flock are 6 or 7 individual agents, whose trajectories must respect certain safety constraints. We evolve the trajectories over a time horizon -100 <= t <= 0 so that at the end of each integration run, we obtain the robustly controllable backward reach-avoid tube or (RCBRAT) for each flock within the system.

RCBRAT because each agent within each flock must avoid other agents that fall within a circle constructed from a pre-specified radius defined on its body frame; while as a group/murmuration, all agents must evade capture by a (multiple) pursuing attacker (s).

Fast Stitching of 𝜖-BRATs via Voronoi Implicit Interface Methods

The stiching together of the respective BRATs are then carried out using a variation of the Voronoi Implicit Interface Method and the so-called "redistancing" or "reinitialization" method in level set methods.

Under Development

Setup

It's best to create a virtual or conda environment in python 3.6+ (I used Python 3.8/3.9) to reproduce the results in this paper.

Dependencies

• All the dependencies listed below are installable via: pip install -r requirements.txt

Dependency	Dependency	Dependency
H5py	Numpy	Cupy
LevelSetPy	Scipy	Scikit-image

Running

    python Examples/murmurations.py <options>

Options:

• --flock_num: Label of a flock within a murmuration to run. This is useful for single agent optimization Defaults to an int type.
• --save: Save the BRAT at the end of each integration step? Defaults to a bool type.
• --out_dir: Directory in which to dump the BRATs. Defaults to './data'.
• --visualize: Visualize the flock's zero-level set? Defaults to a bool type.
• --flock_payoff: Should we compute the payoff of (a/every) flock? Defaults to a bool type.
• --resume: Should we resume the optimization from a previously computed BRAT iteration? Defaults to a str type.
• --mode: What mode are we running the computation in? For individual flocks or stitching together the BRATs of computed flocks? Defaults to a str type.
• --verify: Whether we want to verify a murmuration's trajectory after the optimization? Defaults to a bool type.
• --elevation: What elevation angle should we display the BRAT if visualize is set to True? Defaults to float type.
• --azimuth: What azimuth angle should we display the BRAT if visualize is set to True? Defaults to float type.
• --pause_time: How many seconds to wait between displaying a zero-level set on pyplot? Defaults to float type.

Further Examples

Note that these do not have anything to do with murmurations or emergent collective behavior.

• Basic Double Integrator: Time to reach the origin for the double integrator with switching curve dynamics.
• Robustly Controlled Backward Reachable Tube -- Two Dubins Vehicles in Relative Coordinates: Evaluate the backward reachable tube for two Dubins vehicles in relative coordinates. The pursuer is at the origin.