Robot Control Parameter Optimization on Non-Euclidean Manifolds
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Solution Overview
Problem
Bayesian optimization for robot control parameters faces challenges in high-dimensional non-Euclidean parameter spaces, leading to compromised performance and increased computational costs.
Innovation Solution
The method involves transforming the original high-dimensional control parameter space into a reduced space using geometry-aware dimensionality reduction techniques, such as principal nested sphere or orthonormal projection algorithms, and employing geometry-aware kernels and optimization methods like conjugate gradient to optimize the acquisition function on Riemannian manifolds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Bayesian optimization is applied to high-dimensional non-Euclidean parameter spaces for robot control, then robot skill learning and adaptation capability is improved, but computational cost and solution variance increase significantly
Solution Approach 1:
The patent transforms the high-dimensional non-Euclidean parameter space into a lower-dimensional Euclidean space through dimensionality reduction techniques. This allows Bayesian optimization to operate in a reduced dimensionality setting while still capturing the essential characteristics of the original parameter space, thereby reducing computational cost while maintaining adaptability.
Solution Approach 2:
The patent introduces a dimensionality reduction model as an intermediary between the high-dimensional non-Euclidean parameter space and the Bayesian optimization process. This intermediary transforms complex parameters (such as stiffness matrices and orientation vectors) into simplified representations that preserve the geometric structure while enabling more efficient optimization.
2Manufacturing precision
If standard Bayesian optimization is used in high-dimensional parameter spaces, then comprehensive parameter optimization is achieved, but convergence speed decreases and solution variance increases
Solution Approach 1:
By reducing the dimensionality of the parameter space, the patent enables faster convergence of Bayesian optimization while maintaining optimization accuracy. The reduced dimensionality decreases the computational burden of evaluating acquisition functions and updating Gaussian process models, leading to faster convergence without sacrificing the ability to find optimal parameters.
3Device complexity
If geometry-unaware dimensionality reduction is applied to non-Euclidean parameter spaces, then computational complexity is reduced, but optimization performance and accuracy deteriorate
Solution Approach 1:
The patent applies local quality by preserving the geometric structure of the parameter space in the reduced-dimensional representation. Instead of treating all parameters uniformly, the method maintains the specific geometric properties (such as the manifold structure of stiffness matrices and the spherical geometry of orientation vectors) that are critical for accurate optimization in robot control.
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AI summary
According to various embodiments, a method for controlling a robot using control parameter values from a non-Euclidean original control parameter space is described comprising performing a Bayesian optimization of an objective function representing a desired control objective of the robot over the original control parameter space; and controlling the robot in accordance with a control parameter value from the original control parameter space found in the Bayesian optimization; wherein the Bayesian optimization includes: Transforming the original control parameter space to a reduced control parameter space using the observed control parameter values, wherein the original control parameter space comprises a first number of dimensions, wherein the reduced control parameter space comprises a second number of dimensions, and wherein the first number of dimensions is higher than the second number of dimensions; Determining an evaluation point of the objective function in the reduced control parameter space by searching an optimum of an acquisition function in an iterative search, comprising, in each iteration, updating a candidate evaluation point using a search direction in the tangent space of the reduced control parameter space at the candidate evaluation point; mapping the updated candidate evaluation point from the tangent space to the reduced control parameter space; and using the mapped updated candidate evaluation point as evaluation point for a next iteration until a stop criterion is fulfilled; and Mapping the determined evaluation point from the reduced control parameter space to the original control parameter space.