Consensus control and CBF experiments

Requirements

Basic behaviour requirements described in requirements.txt. To use the main script of cbf.py and formation.py, you will need to install Protobuf and the grSim simulator. Once installed, please follow this setup

Usage

Python files should be run from the root folder (where ibuki_lab and src reside) and launched in one of the following manners

# Method 1: Running as module
python3 -m src.discrete

# Method 2: Declaring root folder in `PYTHONPATH`
## a) Temporarily
PYTHONPATH=$PYTHONPATH:$PWD python3 src/discrete.py

## b) During this bash session
export PYTHONPATH=$PYTHONPATH:$PWD
python3 src/discrete.py

for the src/discrete.py file. This was necessary to be able to use the src folder as a module.

Available scripts

continuous.py | Continuous consensus

Single function achieving consensus algorithm applied in 1D. An array of relative offsets can be specified between agents.

discrete.py | Discrete-time consensus

Two ways to achieve discrete-time consensus We always consider the dynamics x(k+1) = x(k) + u(k) in the following functions. The main script of the file will just plot a simulation of discrete-time consensus over given time steps.

• discrete_consensus_cfunc() This function returns the control values u(k) to apply to the system to drive it to a consensus value.

• discrete_consensus_step() Taking the same parameters as the previous function, this will return the vector of the state x(k+1) when provided with the current state x(k). This version uses the Perron matrix used for stability analysis to compute the next state.

• discrete_consensus_sim_complete() Simple wrapper to run discrete-time consensus for given steps. Returns the vector of all states x(k) for k in [0, num_steps]

cbf.py | CBF (Control Barrier Functions)

Implementation of the Zeroing CBF method as a Quadratic Program (QP) problem, used for collision avoidance. Before running this script, you need to install the grSim simulator, install Protobuf gencode version <= 29, and run the following scripts :

pip install -r ssl_traj/requirements.txt
./ssl_traj/generate_protobuf.sh 

Note: if this directory is empty, use this command to make it appear

git submodule update --init --recursive

The function zeroing_cbf() takes a nominal speed vector v, and returns the solution obtained by the QP solver, which is the adapted speed value v_safe to use for collision avoidance. The last parameter of this function must be a list of Obstacle objects, defined in the same module.

Function obstacles_except() is used to generate obstacles from data provided by the grSim simulator, so we can apply CBF in that simulator.

formation.py | 2D formation control in grSim

Runs the discrete-time consensus algorithm by applying it on the (x, y) positions of robots. To use it, install the grSim simulator as well as Protobuf installed, and follow this setup

The main script will make robot 0 in grSim move to the target location while avoiding all other robots using the CBF technique.

data/

After running the consensus algorithm with drones, using the configuration provided by the Ibuki laboratory at Meiji University, position data has been collected over time to measure the performance of the consensus algorithm. This data has been collected using the discrete-time version of consensus algorithm. Parameters used are listed inside the sub-folders.

Sub-folders contain NumPy array data collected. There are often two files :

• real_results.npy : Positions over time
• achievement.npy : L2 norm of each drone to its requested offset to achieve formations (current offset minus requested offset). In case of multiple neighbours, we sum all L2 norms of offsets to each neighbour.

The two scripts plot the achievement rate of the formation over time, and the positions over time of all drones. These scripts do not have any dependencies, so you can just run them with python3 without having to specify the PYTHONPATH environment variable.