Some illuminating ideas of the existing first order pedestrian models such as the Gradient navigation model with additive neighbor repulsions , Synthetic vision-based model based on time-to-interaction and bearing angle  and Velocity obstacle
approach borrowed from robotic  are added to optimize the velocity-based models.
Oh, "Velocity obstacle
based local collision avoidance for a holonomic elliptic robot," Autonomous Robots, pp.
The common local planners in literature include nearness diagram, dynamic window, velocity obstacle
, and potential field methods.
For each moving obstacle, the programming calculates a velocity obstacle
, which is the set of robot velocities that will lead to a collision with the robot.
The equation can be used to predict maximum water velocity capable of being traversed by fish moving through channels, fishways, culverts or other high velocity obstacles
. We used this relationship to predict maximum water velocities traversable by Topeka shiners over a range of distances from 1-15 m.
Shiller, "Motion planning in dynamic environments using velocity obstacles
," International Journal of Robotics Research, vol.