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.
Highlights
In this paper, we focus on the development of a path primitive and the so-called extend procedure, which is crucial for many path-planning algorithms utilized in the navigation of mobile robots
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 G3 -continuous extend procedure based on η 3 -splines
We focus on the development of a path primitive and the so-called extend procedure, which is crucial for many path-planning algorithms utilized in the navigation of mobile robots
Summary
We focus on the development of a path primitive and the so-called extend procedure (i.e., a local planning algorithm generating a path connecting two robot configurations), which is crucial for many path-planning algorithms utilized in the navigation of mobile robots. Despite a large body of work concerning path planning for mobile robots and autonomous vehicles (e.g., References [1,2]), this problem remains a challenge, especially in the presence of various constraints arising in practical scenarios. To account for all these constraints, we built upon our approach introduced in Reference [3], where we proposed the extend procedure generating G3 -continuous planar paths (that is, paths with continuous curvature derivative with respect to curve arc length) taking into account a limited curvature of motion in cluttered environments. In contrast to Reference [3], we present the new extend procedure for the carlike kinematics taking into account vehicle-body dimensions in planning collision-free paths, admitting the nonconvex polygonal obstacles present in the operational space. The motion-planning strategy presented in the current paper inherits beneficial properties of the original approach presented in Reference [3], but extends its potential applications to more practical path-planning scenarios
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