Robot Controller Bayesian Optimization on Non-Euclidean Parameters
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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 inefficiency.
Innovation Solution
A method that incorporates geometry-awareness into Bayesian optimization by using search directions in tangent spaces and mapping points back to the parameter space, employing conjugate gradient methods and geometry-aware kernel functions to optimize acquisition functions on Riemannian manifolds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If standard Bayesian optimization is used for robot control parameters, then the method is simple to implement, but performance is seriously compromised in high-dimensional non-Euclidean parameter spaces
Solution Approach 1:
The patent transforms the optimization problem from the original non-Euclidean parameter space to a tangent space where standard Bayesian optimization can be applied. By changing the coordinate system and using the exponential map to map back to the manifold, the method maintains implementation simplicity while achieving reliable optimization performance in high-dimensional spaces.
Solution Approach 2:
The patent introduces the tangent space as an intermediary between the non-Euclidean parameter space and the optimization algorithm. The tangent space serves as a bridge that allows standard optimization techniques to work effectively while still respecting the geometric constraints of the original parameter space through the exponential map.
2Productivity
If geometry-aware Bayesian optimization is used with tangent spaces and manifold mapping, then convergence speed and accuracy are improved, but computational complexity increases
Solution Approach 1:
The patent segments the optimization process into distinct steps: computing the tangent space at the current point, performing optimization in the tangent space, and mapping the result back to the manifold using the exponential map. This segmentation makes the complex geometry-aware optimization more manageable and computationally efficient by breaking it into reusable sub-routines.
3Loss of time
If conjugate gradient method is used for optimizing acquisition function on manifold, then faster convergence is achieved, but implementation complexity increases
Solution Approach 1:
The patent replaces the need for complex constrained optimization mechanisms on the manifold with a simpler unconstrained optimization in the tangent space. The conjugate gradient method operates in this linearized space, avoiding the need for complex manifold-specific optimization routines while still achieving fast convergence through the geometrically-aware framework.
Data Source
AI summary
A method for controlling a robot using control parameter values from a non-Euclidean control parameter space. The method includes performing a Bayesian optimization of an objective function representing a desired control objective of the robot over the control parameter space, wherein evaluation points of the objective function are determined by searching an optimum of an acquisition function in an iterative search. In each iteration, the following are performed: updating a candidate evaluation point using a search direction in the tangent space of the parameter space at the candidate evaluation point, mapping the updated candidate evaluation point from the tangent space to the parameter space, and using the mapped updated candidate evaluation point as evaluation point for a next iteration until a stop criterion is fulfilled, and controlling the robot in accordance with a control parameter value found in the Bayesian optimization.