Targeted Marching Path Finding in Multi-Dimensional Space
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Solution Overview
Problem
Existing path finding methods in continuous spaces often require significant computational resources and may not guarantee optimal solutions, especially when dealing with multi-dimensional spaces and varying constraints.
Innovation Solution
The method employs a targeted marching approach that approximates a path by calculating accumulated path costs and estimated costs to a target, using a cost function that balances computational efficiency with path optimality, allowing for a smooth and efficient path determination in both discrete and continuous spaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Fast-Marching methods are used to solve continuous path problems with grid based numerical approximations, then computational speed is improved, but manufacturing precision (path optimality) deteriorates due to approximation errors
Solution Approach 1:
The patent changes the numerical approximation parameters by using higher-order finite difference schemes and adaptive grid refinement. This allows the method to maintain fast computational performance while significantly improving the accuracy of the calculated minimal paths through parameter optimization rather than fundamental algorithmic changes
Solution Approach 2:
The patent implements dynamic adaptation of the computational grid and numerical parameters during the path finding process. The grid resolution and approximation order are adjusted dynamically based on local path complexity and cost function variations, enabling the system to maintain speed in simple regions while achieving high precision in complex regions
2Ease of operation
If A* algorithm converts continuous path problems to discrete graph problems, then ease of operation is improved through simplified computation, but measurement precision (path accuracy) worsens due to discretization errors
Solution Approach 1:
The patent segments the search space into multiple hierarchical levels with different discretization resolutions. Coarse-grained segments provide computational simplicity for initial path planning, while fine-grained segments refine the path accuracy in critical regions, combining the benefits of both discrete and continuous approaches
Solution Approach 2:
The patent introduces an intermediary continuous cost field that bridges the discrete graph structure and the desired continuous path accuracy. This cost field is computed on the discrete graph but used to guide continuous path optimization, serving as a mediator that preserves computational simplicity while improving measurement precision
3Manufacturing precision
If more neighbors are considered in cost function computations, then manufacturing precision (path optimality) is improved, but device complexity (computational requirements) increases
Solution Approach 1:
The patent applies partial action by considering only the necessary number of neighbors based on local path characteristics. In regions where the cost function varies smoothly, fewer neighbors are sufficient, while in regions with sharp cost variations, more neighbors are engaged. This selective approach achieves high path optimality without the full computational burden of considering all possible neighbors everywhere
Solution Approach 2:
The patent implements local quality by adapting the neighborhood size and consideration criteria based on local path complexity and cost function gradients. Different regions of the search space use different levels of neighbor consideration, with computationally intensive neighbor analysis applied only where it significantly improves path optimality, rather than uniformly across the entire space
4Reliability
If the path finding method guarantees optimal solutions, then reliability is improved, but productivity (processing time) deteriorates due to exhaustive search requirements
Solution Approach 1:
The patent implements feedback mechanisms where the cost function evaluations and path explorations provide information that guides subsequent search directions. This feedback allows the algorithm to prune clearly suboptimal paths early in the search process, maintaining reliability by systematically evaluating promising paths while avoiding exhaustive exploration of unlikely candidates, thus improving productivity
Data Source
AI summary
A method of finding a path from a start point to a target point, in multi-dimensional space, including: (a) determining a plurality of points in a physical space, including a start point and an target point; (b) computing, using a cost function, for said points an accumulated path cost from the start point to a point; representing a minimal cost path from the start point to the point with respect to an optimization criteria; (c) computing for at least some of said points an estimated-cost-to-target from a point to the target point; and (d) after computing said costs, determining at least one of a minimal path or a minimal path cost of a path from the start point to the target point in the physical space, wherein the determination is based on said accumulated path costs, and is minimal with respect to the optimization criteria.