A drift-diffusion model for robotic obstacle avoidance

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 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. 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 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.

A drift diffusion model of biological source seeking for mobile robots

“…While on the one hand existing theoretical models assumed noise free sensors, on the other hand, many experimental research results have shown this bio-inspired source seeking mechanism works with noisy sensors. While it is well known that adding a random vector field to the gradient of a potential field contributes to avoid local minima, in a recent work [17] a drift diffusion approach with a similar spirit is presented, adding random noise to the navigation function itself. The resulting model for the robot motion is a drift-diffusion equation which allows obtaining some theoretical results on the probability of avoiding local minima.…”

“…To test the validity of the heading deviation variance, equation (17), in a constant gradient stimulus we performed simulations and compared the results of additive and nonadditive noise. Figures 4(a) and 4(b) show simulations of 500 different realisations of the noise for a vehicle 3a immersed in a stimulus with a constant gradient with its initial orientation aligned in the opposite direction to the gradient.…”

“…Second, under certain assumptions, the model can provide analytical results like the deterministic equations driving the average and dispersion evolution of the vehicles over time, and a bound for the angular dispersion. Finally, it has been shown recently that adding noise to navigation functions can improve the obstacle avoidance behaviour in the presence of potential minima [17]. However, little is known about the effect that this would have on the accuracy to reach the target position.…”

Human Decision-Making in Multi-agent Systems

“…Researchers from systems and control have looked into the convergence properties of this model (Cao et al 2010;Woodruff et al 2012) and used it to predict group decision-making dynamics (Stewart et al 2012). New applications to robotic systems have also been reported (Reverdy et al 2015).…”

Autonomous legged hill ascent

“…To better interact with obstacles that are not detectable by the current sensory implementation, the robot could rely on its legs to feel such disturbances (Johnson et al, 2010) and temporarily modify its control policies (Revzen et al, 2012) if they persist. Similar deformations could be utilized to circumvent detectable obstacles violating our simple world model, an elementary version of which is presented in (Reverdy et al, 2015).…”