Extending Virtual Force Field for Obstacle Avoidance via Polynomial Extrapolation

This paper presents an extension of the Virtual Force Field (VFF) approach to solve the obstacle avoidance problem, which is fundamental for autonomous systems. In this approach, due to continuity, the future motions of the vehicle and dynamic obstacles are estimated based on polynomial extrapolation from their past movements and potential collisions are predicted. This method integrates and simulates the VFF theory that has been widely used in obstacle avoidance. First, a simplified dynamics of an autonomous vehicle with stationary and dynamic obstacles is considered. To ensure that the vehicle avoids collisions under combined attractive and repulsive forces, a polynomial extrapolation is proposed using past trajectories of the vehicle or dynamic obstacles to predict its future trajectory. As the extrapolated trajectory of the vehicle intersects with static obstacles or extrapolated trajectories of dynamic obstacles in the environment, these obstacles are included in the VFF calculations, considering both time and trajectories to guide the vehicle in avoiding obstacles.