Summary of Machine Learning Optimized Orthogonal Basis Piecewise Polynomial Approximation, by Hannes Waclawek et al.
Machine Learning Optimized Orthogonal Basis Piecewise Polynomial Approximation
by Hannes Waclawek, Stefan Huber
First submitted to arxiv on: 13 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents a novel approach to 1D trajectory planning in electronic cam design, leveraging Piecewise Polynomials (PPs) and modern Machine Learning (ML) optimizers. PPs are commonly used to approximate position profiles given a set of points, but traditional methods offer limited flexibility. To overcome this limitation, the authors combine PP models with ML optimizers from TensorFlow, outside of their typical application in Artificial Neural Networks (ANNs). The resulting approach utilizes an orthogonal polynomial basis, specifically Chebyshev polynomials of the first kind, to improve approximation and continuity optimization performance. A novel regularization approach is developed, demonstrating improved convergence behavior and outperforming power basis for all relevant optimizers. The presented method has practical applications in electronic cam design and showcases the versatility of PP models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine you want to plan a path for an object to move along, like a robot arm or a camera lens. This can be done using special mathematical formulas called Piecewise Polynomials (PPs). But these formulas have limitations when it comes to changing the shape of the curve or adding extra requirements. To overcome this limitation, researchers combined PP models with powerful optimization tools from Machine Learning (ML). They used a special type of polynomial called Chebyshev polynomials to create a new way of optimizing the curves. This approach worked better than previous methods and has potential applications in electronic cam design. |
Keywords
* Artificial intelligence * Machine learning * Optimization * Regularization
