A G3-Continuous Extend Procedure for Path Planning of Mobile Robots with Limited Motion Curvature and State Constraints

Abstract

Provably correct and computationally efficient path planning in the presence of various constraints is essential for autonomous driving and agile maneuvering of mobile robots. In this paper, we consider the planning of G 3-continuous planar paths with continuous and limited curvature in a motion environment that is bounded and contains obstacles modeled by a set of (non-convex) polygons. In practice, the curvature constraints often arise from mechanical limitations for the robot, such as limited steering and articulation angles in wheeled robots, or aerodynamic constraints in unmanned aerial vehicles. To solve the planning problem under those stringent constraints, we improve upon known path primitives, such as Reeds–Shepp (RS) and CC-steer (curvature-continuous) paths. Given the initial and final robot configuration, we developed extend-procedure computing paths that can approximate RS paths with arbitrary precision, but guaranteeing G 3-continuity. We show that satisfaction of all stated path constraints is guaranteed and, contrary to many other methods known from the literature, the method of checking for collisions between the planned path and obstacles is given by a closed-form analytic expression. Furthermore, we demonstrate that our approach is not conservative, i.e., it allows for precise maneuvers in tight environments under the assumption of a rectangular robot footprint. The presented extend procedure can be integrated into various motion-planning algorithms available in the literature. In particular, we utilized the Rapidly exploring Random Trees (RRT*) algorithm in conjunction with our extend procedure to demonstrate its feasibility in motion environments of nontrivial complexity and low computational cost in comparison to a G 3-continuous extend procedure based on η 3-splines.

Special Feature on Advanced Mobile Robotics

“…Xue [32] presented a multi-objective evolutionary algorithm for the path planning problem. Another approach, authored by Gawron and Michałek [33], is available for the path planning problem of mobile robots. They showed that their path planning, which is collision-free, satisfies curvature constraints, and preserves continuity of the curvature arc-length derivative.…”

A Dynamic Fusion Pathfinding Algorithm Using Delaunay Triangulation and Improved A-Star for Mobile Robots

“…According to the principle of geometry, the operating system regards the mobile robot as a point and realizes the path planning of the mobile robot from the start point to the target point [9]. The most direct method is visibility-based graphs, connect the vertices of obstacles to construct different polygons [10][11][12], and then use path planning algorithms to plan the path. The Dijkstra algorithm is a typical method and realizes the shortest path search by accumulating the path length.…”

An Inverse Vehicle Model for a Neural-Network-Based Integrated Lateral and Longitudinal Automatic Parking Controller

“…The mathematical optimization approaches, firstly formulating a cost function of the automatic parking problem and then minimizing the objective cost function [9][10][11][12][13]. Besides car-like vehicles, reference trajectory is feasible in the case of parking N-trailer vehicles when complicated kinematic constraints are taken into account in planning the trajectory [14][15][16].…”

“…in the case of parking N-trailer vehicles when complicated kinematic constraints are taken into account in planning the trajectory [14][15][16].…”