Sensory prediction on a whiskered robot: a tactile analogy to "optical flow"

When an animal moves an array of sensors (e.g., the hand, the eye) through the environment, spatial and temporal gradients of sensory data are related by the velocity of the moving sensory array. In vision, the relationship between spatial and temporal brightness gradients is quantified in the "optical flow" equation. In the present work, we suggest an analog to optical flow for the rodent vibrissal (whisker) array, in which the perceptual intensity that "flows" over the array is bending moment. Changes in bending moment are directly related to radial object distance, defined as the distance between the base of a whisker and the point of contact with the object. Using both simulations and a 1×5 array (row) of artificial whiskers, we demonstrate that local object curvature can be estimated based on differences in radial distance across the array. We then develop two algorithms, both based on tactile flow, to predict the future contact points that will be obtained as the whisker array translates along the object. The translation of the robotic whisker array represents the rat's head velocity. The first algorithm uses a calculation of the local object slope, while the second uses a calculation of the local object curvature. Both algorithms successfully predict future contact points for simple surfaces. The algorithm based on curvature was found to more accurately predict future contact points as surfaces became more irregular. We quantify the inter-related effects of whisker spacing and the object's spatial frequencies, and examine the issues that arise in the presence of real-world noise, friction, and slip.