This work introduces the four parameter logistic (4PL) curve as a new smooth path planning tool for mobile robots with nonholonomic constraints such as car-like robots and fixed-wing UAVs. The key contribution is a local path planning methodology that generates multiple smooth upper curvature bounded paths with obstacle avoidance. The 4PL tool is used in

1. Generation of flyable UAV paths satisfying airspace restrictions such as waypoint constraints, arbitrary shaped obstacle avoidance, and airspace confinement

2. Collision-free maneuver generation for parallel parking a realistic-size car from any given starting position on a ray with a novel point-to-ray framework 

3. Smooth path planning inside passages (prescribed boundaries) with guaranteed existence

The proposed tool is capable of generating solutions with less computations as compared to existing smooth path planning curves (such as Bézier curve, B-spline, and clothoid) based solutions which is demonstrated with comparative studies.

• S. Upadhyay, and A. Ratnoo, “Continuous-Curvature Path Planning With Obstacle Avoidance Using Four Parameter Logistic Curves,” IEEE Robotics and Automation Letters (RA-L), vol. 1, no. 2, 2016, pp. 609-616.   (Link to the paper)

• S. Upadhyay, and A. Ratnoo, “Smooth Path Planning for Unmanned Aerial Vehicles with Airspace Restrictions,” AIAA Journal of Guidance, Control, and Dynamics vol. 40, no. 7, 2017, pp. 1596-1612. (Link to the paper)

• S. Upadhyay and A. Ratnoo, "A Point-to-Ray Framework for Generating Smooth Parallel Parking Maneuvers," in IEEE Robotics and Automation Letters, vol. 3, no. 2, April 2018, pp. 1268-1275. (Link to the paper)

• S. Upadhyay, and A. Ratnoo, “On Existence and Synthesis of Smooth Four Parameter Logistic Paths Inside Annular Passages,” IEEE Robotics and Automation Letters, vol. 3, no. 4, 2018, pp. 4375-4382. (Link to the paper)

In this work, a novel 4PL curve-based path planning methodology is utilized to generate feasible lane-change maneuvers for the autonomous vehicle. The motivation is to consider all collision possibilities and, at the same time, present an analytic solution that is computationally light. Being an explicit relation, 4PL presents an alternate framework for analyzing collision possibilities in a deterministic manner. Moreover, satisfying the collision avoidance and final point reachability constraints, the proposed curve offers multiple solutions to the lane-change problem as expressed in a 2-D design parameter space. Case studies highlight that the proposed method is able to generate smooth lane-change trajectories while maintaining a safety distance with respect to neighboring vehicles on the destination and origin lane 

• Sharma, Yash Raj, and Ashwini Ratnoo. "Designing Safe Lane-Change Maneuvers Using an Explicit Path Planner." 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE). IEEE, 2021. 

(Link to the paper)