student and faculty conducting research

PhD Students and Post-Doctoral Researchers

Saptarshi Bandyopadhyay

  • Advisor:
      • Prof. Soon-Jo Chung
  • Departments:
    • Aerospace Engineering
  • Areas of Expertise:
      • Control Theory
      • Probability
      • Network Analysis

  • Thesis Title:
      • Distributed Estimation and Probabilistic Swarm Guidance
  • Thesis abstract:
      • The central theme of this thesis is to use consensus algorithms for distributed estimation by networked sensors and for probabilistic guidance of swarms. In this thesis, we first present the Bayesian consensus filter (BCF) for tracking a moving target using a networked group of agents and achieving consensus on the best estimate of the probability distributions of the states of the targets. Our BCF framework can incorporate nonlinear target dynamic models, heterogeneous nonlinear measurement models, non-Gaussian uncertainties, and higher￿order moments of the locally estimated probability distribution of the target￿s states obtained using Bayesian filters. If the agents combine their estimated probability distributions using a logarithmic opinion pool, then the sum of Kullback￿Leibler divergences between the consensual probability distribution and each of the individual estimates is minimized. Rigorous stability and convergence results for the proposed BCF algorithm with single or multiple consensus loops are presented. Transmission of probability distributions and computational methods for implementing the BCF algorithm have been discussed. In this thesis, we next present the probabilistic swarm guidance algorithm using inhomogeneous Markov chains (PSG￿IMC). Probabilistic swarm guidance involves designing a Markov chain so that each autonomous agent or robot determines its own trajectory in a statistically independent manner. The swarm converges to the desired formation and the agents repair the formation even if it is externally damaged. We present an inhomogeneous Markov chain approach to probabilistic swarm guidance algorithms for minimizing the number of transitions required for achieving the desired formation and then maintaining it. With the help of communication with neighboring agents, each agent estimates the current swarm distribution and computes the tuning parameter which is the Hellinger distance between the current swarm distribution and the desired formation. We design a family of Markov transition matrices for a desired stationary distribution, where the tuning parameter dictates the number of transitions. We discuss methods for handling motion constraints and prove the convergence and the stability guarantees of the proposed algorithms. Finally, we apply these proposed algorithms for guidance and motion planning of swarms of spacecraft in Earth orbit. In the future, we will develop a one-step distributed probabilistic swarm guidance algorithm using optimal transport. Using the consensus algorithm on probability distributions, each agent can estimate the current swarm distribution while the desired swarm distribution is already known. The cost function can incorporate motion constraints, dynamics of the spacecraft and other constraints on the swarm. We will solve the Monge￿Kantorovich minimization problem to determine the optimal transference plan, which will give the optimal open-loop desired trajectory for each agent.
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