Γ and S Shaped Logistic Curves for Path Planning With Obstacle Avoidance

Path planning for urban environment with obstacle is considered. Candidate Γ and S shaped curves are derived using Four Parameter Logistic curves. Two basic obstacle shapes are chosen and closed form analytic conditions are derived to avoid them. Simple analytic conditions for the heading and the curvature at the start and end points are derived for generating Γ and S shaped curves, respectively. Further, using the analytic curvature continuity condition Γ and S shaped curves can be joined (as Γ – S or S – S) to generate feasible paths with intermediate waypoints. Simulation studies are carried out to generate multiple feasible paths in dense obstacle environment.