Comparison of integrated and nonintegrated wide-field optic flow for vehicle navigation

Recent studies of vision-based navigation and guidance for robotic vehicles have been inspired by the biological systems found in flying insects. The wide-field integration of optic flow is one pre-existing method, in which the sensed optic flow is integrated along with sensitivity functions to mimic the action of directionally sensitive cells observed in some insects' visual systems. This study re-examines the wide-field integration method and reformulates the problem from a summation rather than an integral. This reformulation allows the wide-field integration measurement outputs to be directly compared with nonintegrated optic flow measurements. The method using nonintegrated optic flow measurements is shown to have some practical advantages, such as eliminating the need to define input sensitivity functions and having a measurement Jacobian that is easier to derive analytically. Also, the state estimates obtained with the nonintegrated method are proven to have minimum variance compared with those from the wide-field integration method. Numerical simulations of each method are shown for a vehicle maintaining level flight at constant altitude over a flat terrain.