A drift-diffusion model for robotic obstacle avoidance

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 Péclet number considered in the literature on mass transport in advection-diffusion 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.

Authors

• Paul Reverdy
• B. Deniz Ilhan
• Daniel E. Koditschek

Keywords

• Mathematical model
• Stochastic processes
• Navigation
• Robot kinematics
• Boundary conditions
• Collision avoidance
• Obstacle Avoidance
• Deterministic
• Dynamical
• Differential Equations
• Mobile Robot
• Stochastic Differential Equations
• Presence Of Obstacles
• Robot Navigation
• Peclet Number
• Normal Distribution
• Function Of Time
• Background Noise
• Control Parameters
• Partial Differential Equations
• Advection
• Dirac Delta
• Particle Interactions
• Specular Reflection
• Fokker Planck Equation
• Implications For Control
• Escape Probability
• Escape Time
• Navigation Function
• Stochastic Geometry
• Percolation Theory
• Subject Of Future Work
• Reflecting Boundary Conditions
• Closed Curve
• Advection Diffusion Equation
• Noise Intensity