A Virtual Force Guidance Law for Trajectory Tracking and Path Following

This paper presents a virtual force guidance law for trajectory tracking of autonomous vehicles. Normally, three virtual forces are designed to govern the vehicles. The virtual centripetal force counteracts the influence of the reference heading rate. The virtual spring force pulls the vehicle to the reference trajectory and the virtual drag force prevents oscillations. When local obstacles are detected, an extra virtual repulsive force is designed to push the vehicle away from its way to get around the obstacles. Using the guidance law, the reference trajectory can be straight line, circle and general curve with time-varying curvature. The guidance law is directly applicable to path-following problem by redefining the reference point. The use of artificial physics makes the guidance law be founded on solid physical theory and computationally simple. Besides, the physical meanings of the parameters are definite, which makes it easy to tune in application. Simulation results demonstrate the effectiveness of the proposed guidance law for problems of trajectory tracking, path following, and obstacle avoidance.