The paper by J. A. Reeds and L. A. Shepp addresses the problem of finding the shortest path for a car that can move forward and backward, with a minimum turning radius. The authors show that the shortest path between two points, given initial and final directions, can be described by a sequence of arcs and line segments, with at most 2 cusps or reversals. They provide a set of 48 such paths, which they prove is both sufficient and small, containing at most 68 paths for any pair of endpoints and directions. These paths are explicitly given in terms of the form $C|S$, where $C$ represents an arc of a circle and $S$ represents a line segment. The authors also outline an algorithm to find the shortest path by calculating the length of each path and selecting the shortest one. The paper includes detailed proofs and examples to support their findings, and discusses the extension of their results to all admissible curves.The paper by J. A. Reeds and L. A. Shepp addresses the problem of finding the shortest path for a car that can move forward and backward, with a minimum turning radius. The authors show that the shortest path between two points, given initial and final directions, can be described by a sequence of arcs and line segments, with at most 2 cusps or reversals. They provide a set of 48 such paths, which they prove is both sufficient and small, containing at most 68 paths for any pair of endpoints and directions. These paths are explicitly given in terms of the form $C|S$, where $C$ represents an arc of a circle and $S$ represents a line segment. The authors also outline an algorithm to find the shortest path by calculating the length of each path and selecting the shortest one. The paper includes detailed proofs and examples to support their findings, and discusses the extension of their results to all admissible curves.