Stochastic Artificial Potentials for Online Safe Navigation

@article{Paternain2016StochasticAP,
  title={Stochastic Artificial Potentials for Online Safe Navigation},
  author={Santiago Paternain and Alejandro Ribeiro},
  journal={IEEE Transactions on Automatic Control},
  year={2016},
  volume={65},
  pages={1985-2000}
}
Consider a convex set of which we remove an arbitrary number of disjoints convex sets—the obstacles—and a convex function whose minimum is the agent's goal. We consider a local and stochastic approximation of the gradient of a Rimon–Koditschek navigation function where the attractive potential is the convex function that the agent is minimizing. In particular, we show that if the estimate available to the agent is unbiased, convergence to the desired location while avoiding the obstacles is… 

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