Dubins Path Planning Within Constrained Turning Areas
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Solution Overview
Problem
Existing Dubins path generation methods fail to generate appropriate point-to-point paths within specific areas when the area is smaller than the turning radius of the turning circle or when the start and end points are close to the area's periphery, leading to paths being generated outside the specific area.
Innovation Solution
A path generating method that sets a first turning circle at the start or end point and a second turning circle within the specific area, using Dubins paths to ensure the path remains within the area, allowing for more combinations of start and end points, including tangent or non-tangent circles to optimize the path.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a conventional Dubins path is used to generate a point-to-point path, then the path can connect any start and end points regardless of position and orientation, but a part of the path may be generated outside the specific area when the area is small or points are near the periphery
Solution Approach 1:
The path generation is divided into two independent stages: first generating a Dubins path without area constraints, then generating a constraint satisfaction path that connects the same points while staying within the area. This segmentation allows each stage to optimize for its specific purpose without compromising the other.
Solution Approach 2:
A constraint satisfaction module acts as an intermediary between the Dubins path generator and the final path output. This intermediary takes the Dubins path as input, identifies portions that violate area constraints, and generates corrective path segments to replace those portions, ensuring the final path remains within the specific area.
2Area of stationary object
If the specific area is small (six times or less the turning radius) or points are close to the periphery, then the area available for path generation is limited, but a valid point-to-point path must still be generated within the area
Solution Approach 1:
The system first generates a Dubins path that establishes the optimal connection between start and end points in terms of distance and orientation, before considering area constraints. This preliminary path serves as a reference that guides the subsequent constraint satisfaction process, ensuring that the final path maintains good travel efficiency even in limited spaces.
Solution Approach 2:
The path generation problem is solved by introducing a temporal dimension through two-stage processing. Instead of attempting to satisfy all constraints simultaneously in space, the system first solves the path connection problem in one stage, then addresses the area constraint in a second stage, effectively adding a time dimension to the solution process.
3Productivity
If the Dubins path is generated without considering area constraints, then the path generation is simple and fast, but the path may go outside the specific area causing interference with obstacles
Solution Approach 1:
The path generation process is segmented into a fast Dubins path generation stage and a separate constraint checking and correction stage. This allows the system to benefit from the computational efficiency of Dubins paths while adding constraint satisfaction only where necessary, rather than using a slow comprehensive optimization method for the entire path.
Solution Approach 2:
The Dubins path generation rapidly skips through the path planning process by using closed-form mathematical solutions, generating a preliminary path without detailed constraint checking. This rapid generation provides a good initial solution that can then be refined, maintaining high speed while ultimately ensuring constraint satisfaction.
Data Source
AI summary
A path generating method includes setting a moving direction at each of two positions, setting a first turning circle with one of the positions as a contact point and the moving direction as a turning direction, setting a second turning circle that is within a specific area, setting a Dubins path that starts from a predetermined point of the second turning circle or ends at the predetermined point, and selecting, as a movement path, a path that is within the specific area among paths each including the first turning circle and the Dubins path.