Coverage Path Planning Using Mesh Decomposition and Funnel Paths
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Solution Overview
Problem
Existing systems for traversing a given area, such as lawn mowing, often inefficiently use time and energy due to naive path-following methods, which can result in aesthetically unpleasing and unresolved areas.
Innovation Solution
The system generates an optimal path for traversing an area by decomposing the area's perimeter into a mesh, determining a graph connecting representative points, and using algorithms like Djikstra's and the funnel algorithm to find the longest funneled path, which is then offset and clipped to create a coverage plan.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If a naive perimeter-following path is used to traverse the area, then the system can cover the boundary regions, but the time and energy required to complete the task increases significantly
Solution Approach 1:
The patent divides the area into a mesh of triangular elements with vertices representing key locations. By segmenting the continuous space into discrete triangular units, the system can efficiently calculate optimal paths through graph algorithms rather than traversing the entire perimeter, significantly reducing time and energy while maintaining complete coverage.
2Reliability
If a simple perimeter path is followed, then the traversal path is easy to generate, but complete coverage of all regions cannot be ensured
Solution Approach 1:
The patent transitions from two-dimensional perimeter traversal to three-dimensional mesh space exploration by introducing vertical depth through multiple mesh layers. This dimensional expansion allows the system to guarantee complete coverage of all regions while using sophisticated graph algorithms to manage the increased complexity of path generation.
Solution Approach 2:
The system performs preliminary decomposition of the area into a triangular mesh before path generation. By pre-processing the space into a structured graph representation with vertices and edges, the system establishes a foundation that ensures complete coverage while making subsequent pathfinding more systematic and reliable.
3Productivity
If an optimized path using mesh decomposition and graph algorithms is used, then traversal efficiency improves, but the computational complexity and processing requirements increase
Solution Approach 1:
The patent replaces complex mechanical path-planning systems with computational graph algorithms. By substituting physical trial-and-error traversal with mathematical optimization through Djikstra's algorithm and funnel algorithms, the system achieves high traversal efficiency while the computational complexity is managed through algorithmic elegance rather than hardware complexity.
Data Source
AI summary
Systems and techniques for generating a set of connected segments for a device or system to traverse in order to reach every point of the region (a coverage plan). Nodes defining the region to be traversed define a polygon. The polygon is decomposed into a mesh and a graph of the mesh is generated. The graph may be used to determine a longest funneled path which, in turn, may be used to either optimize for a longest path or to divide the polygon for eroding sides. The longest path and/or erosions are used to define a set of segments. The segments are connected, which in some examples is done via an optimization to minimize an amount of time or energy to traverse all segments and connections. The resultant coverage plan is sent to a system configured to receive the plan and traverse the region.