PerKE

perKE is a term used to describe a dimensionless metric that measures how kinetic energy is distributed within a dynamic system. The acronym can be read as “perceived kinetic energy,” and it is typically applied in contexts such as multi-agent robotics, swarm dynamics, and kinetic theory to assess energy allocation and coordination.

Mathematically, perKE can be defined for a system of N agents with masses m_i and speeds v_i as perKE = (1/N) times the sum over all agents of (0.5 m_i v_i^2) divided by a reference kinetic energy E_ref. A common choice for the reference is E_ref = 0.5 M_total V_max^2, where M_total is the total mass and V_max is the maximum admissible speed. For continuous media, perKE can be expressed as perKE = (∫ 0.5 ρ v^2 dV) / E_ref, with ρ the density and v the velocity field. Under these normalizations, perKE is intended to fall between 0 and 1, depending on how energy is spread across components.

Applications of perKE include monitoring energy efficiency and coordination in swarm robotics, evaluating control strategies, and diagnosing imbalances in energy distribution. A high perKE value generally indicates a broad, even distribution of kinetic energy, while a low perKE can signal concentration of energy in a subset of agents or regions. The metric is also used to compare dynamic regimes, calibrate task allocation, and inform energy-aware decision making in distributed systems.

Limitations and considerations include sensitivity to the choice of E_ref, potential distortion by outliers, and dependence on accurate mass and velocity measurements. PerKE is typically one tool among several for understanding system dynamics, not a standalone measure of performance. See also: kinetic energy, energy efficiency, multi-agent systems.