jaskiratsingh2000

Heat Potential Vector-Field CBFs for Multi-Robot Navigation

Rohan Chandra

Abstract—This paper develops a comprehensive and selfcontained background on control barrier functions (CBFs), covering fundamental notions of forward invariance, Nagumo's viability theorem, Lie derivatives, zeroing and reciprocal CBFs, high relative degree and higher-order CBFs, robustness to disturbances, sampled-data and discrete-time variants, and CLF-CBF quadratic programs with feasibility guarantees. Building on this foundation, we introduce Vector-Field Control Barrier Functions (VFCBFs), where the barrier is a vector object rather than a scalar function. We present two complementary formulations. The first enforces directional safety by constraining the system velocity relative to a prescribed barrier vector field. The second enforces evolutionary safety via Lie-bracket constraints that regulate how the barrier field itself evolves under the closed-loop flow. We also give a third formulation for vector-valued barrier func

jaskiratsingh2000

import os
import time
import threading
import math
import numpy as np
import matplotlib.pyplot as plt
from numpy import e
from hyperparameters import (
    spread, noise, radius, delt, pert, b, sensor_range, number_of_uavs, maxv,
    attractive_gain, repulsive_gain, collision_distance, clipping_power, seed, priority_type

jaskiratsingh2000

import os
import time
import threading
import numpy as np
import matplotlib.pyplot as plt
from numpy import e
from hyperparameters import (
    spread, noise, radius, delt, pert, b, sensor_range, number_of_uavs, maxv,
    attractive_gain, repulsive_gain, collision_distance, clipping_power, seed, priority_type
)