A driftdiffusion model for robotic obstacle avoidance
2015 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sep, 2015. (to appear)
Paul Reverdy, B. Deniz Ilhan and D. E. Koditschek
Electrical and Systems Engineering, University of Pennsylvania
Full PDF (preprint)  Penn Scholarly Commons

Fig. 1. Typical geometry of robot interaction with a concave obstacle. 
Abstract 
We develop a stochastic framework for modeling and analysis of robot navigation in the presence of obstacles. We show that, with appropriate assumptions, the probability of a robot avoiding a given obstacle can be reduced to a function of a single dimensionless parameter which captures all relevant quantities of the problem. This parameter is analogous to the Peclet number considered in the literature on mass transport in advectiondiffusion fluid flows. Using the framework we also compute statistics of the time required to escape an obstacle in an informative case. The results of the computation show that adding noise to the navigation strategy can improve performance. Finally, we present experimental results that illustrate these performance improvements on a robotic platform. 
Acknowledgements This work was funded in part by the Air Force Office of Scientific Research under the MURI FA9550–10–1−0567. The authors thank D. Guralnik for discussions on the generalized definition of obstacle convexity developed in Section IIB. 