Lattice Tool Paths Using Admissible Coordinates and Dynamic Programming
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Solution Overview
Problem
Current tool path generation systems for numerically controlled machines are inefficient, leading to suboptimal and slow processing due to the need for high-precision calculations, resulting in tool path errors and surface artifacts, as they often prioritize smooth motion over fidelity to the target surface.
Innovation Solution
A data conversion system that uses Diophantine approximations to identify a subset of admissible lattice coordinates, allowing for a dynamic programming approach that reduces computational load and tool path error by generating an optimal tool path that conforms closely to the target surface without gouging, using a combination of lattice full and dynamic programming algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If brute force dynamic programming is used to compute the optimal path over all possible coordinates, then manufacturing precision is improved, but computing time and computational resources become impractically large
Solution Approach 1:
The patent extracts only the necessary admissible lattice coordinates that lie on or above the target polyline, rather than considering all possible coordinates in the workspace. This is achieved by identifying coordinates that satisfy the non-gouging constraint, thereby reducing the computational domain from the entire workspace to a minimal sufficient subset that still guarantees optimal path generation.
Solution Approach 2:
The patent segments the target polyline into line segments and processes each segment independently to identify admissible coordinates. By dividing the continuous target surface into discrete segments and handling each segment's coordinate constraints separately, the method reduces the overall computational complexity while maintaining global optimality through dynamic programming.
2Manufacturing precision
If candidate tool positions are represented in high-precision floating point coordinates, then manufacturing precision is improved, but device complexity and computational load increase
Solution Approach 1:
The patent uses approximate rational slope vectors as temporary computational objects to identify admissible coordinates, rather than directly using high-precision floating-point coordinates throughout the entire computation. These rational approximations serve as disposable intermediaries that simplify the identification process, with final high-precision coordinates only needed for the output tool path, not for the computational search process.
3Ease of operation
If smooth tool motion is prioritized by resampling and smoothing the path, then ease of operation is improved, but manufacturing precision deteriorates due to rejection of high-curvature parts
Solution Approach 1:
Instead of smoothing the tool path and accepting the resulting deviations from the target surface, the patent inverts the approach by directly computing the optimal path that maximizes surface fidelity. The dynamic programming algorithm inherently produces smooth motion by selecting the shortest path through admissible coordinates, eliminating the need for separate smoothing operations that would compromise precision.
Data Source
Figure 1A~1B
Figure 1C~1D
Figure 2
AI summary
A data conversion system includes an interface to receive path data, a memory to store a computer-executable program including a lattice full algorithm and a dynamic programing algorithm, a processor, in connection with the memory, configured to execute the computer-executable program. The processor is configured to perform steps including providing a coordinate system including admissible points, forming, from the path data, a target polyline on the coordinate system, wherein the target polyline represents an approximated surface line of an object, dividing the target polyline into line segments, generating a set of rational vectors by approximating slopes of the line segments based on the lattice full algorithm, arranging the rational vectors to form lower convex hull lines arranged on or above corresponding line segments, wherein the lower convex hull lines are arranged onto the admissible points, wherein the admissible points are on or above the corresponding line segments, selecting a set of endpoints of the lower convex hull lines, and forming a final polyline by merging the endpoints based on the dynamic programing algorithm, wherein the final polyline is arranged to lay on or above the target polyline.