Modeling and Analysis of Stochastic Dynamics and Emergent Phenomena in Swarm Robotic Systems Using the Fokker-Planck Formalism
Abstract
This research lays down a mathematical framework within which a system of interacting entities, such as a swarm robotic system, operating in a dynamic and uncertain environment can be analyzed for its properties such as stability, robustness, and emergent behavior. The framework, based upon stochastic differential equations and the Fokker-Planck formalism, allows the calculation of transient and steady state probability densities of the states of these systems. The framework has been applied to two scenarios related to swarm systems. The first scenario relates to a robotic swarm, the dynamics of which is inspired by ant foraging. The article develops a continuous time reaction-diffusion model based on Keller-Segel model of bactetrial chemotaxis and establishes a connection with the Fokker-Planck formalism. In addition, the authors also present a distributed control law in continuous time that combines gradient following for pheromone concentration as well as food scent with random motion seen in ants. The second scenario relates to a system of robots interacting via non-linear potentials and experiencing random excitations. The proposed framework allows calculation of probability density functions of states of the robots, such as positions and velocities, that helps analyze the stability of system and study its response to random excitations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 29, 2010
- Accession Number
- ADA547014
Entities
People
- Manish Kumar
- Subramanian Ramakrishnan
Organizations
- University of Cincinnati