Robot Motion Control With Hyperbolic Geodesic Trajectories
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Solution Overview
Problem
Existing methods for robot hand control using Gaussian Process Hyperbolic Latent Variable Model (GPHLVM) generate physically impractical motions due to lack of training data in regions between clusters, leading to reliance on non-informative Gaussian Process mean.
Innovation Solution
Implement a Gaussian Process Hyperbolic Dynamical Model (GPHDM) that incorporates a hyperbolic dynamics prior and pullback metric to ensure physically consistent motion generation by embedding high-dimensional observations in a hyperbolic manifold, aligning with a robotics taxonomy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If GPHLVM is used to generate robot motions, then taxonomy structure is followed, but physically impractical motions occur due to lack of training data between clusters
Solution Approach 1:
The patent pre-computes and stores motion trajectories between all pairs of taxonomy clusters during an offline phase. This preliminary action ensures that when the robot needs to transition between poses, pre-validating physically practical paths are already available, eliminating the problem of generating impractical motions in real-time due to lack of training data coverage.
Solution Approach 2:
The patent introduces an intermediate trajectory database that acts as a mediator between the taxonomy structure and motion generation. Instead of directly generating motions from GPHLVM without sufficient training data, the system queries pre-computed trajectories from this intermediate storage, ensuring physically practical motions while maintaining taxonomy consistency.
2Reliability
If geodesics are used for motion generation in hyperbolic space, then taxonomy consistency is achieved, but physically impractical motions result from default Gaussian Process mean
Solution Approach 1:
The patent pre-computes valid motion trajectories between taxonomy clusters and stores them in advance. When generating motions, instead of relying on the default Gaussian Process mean which produces impractical motions, the system retrieves pre-validating trajectories that are guaranteed to be physically practical while maintaining taxonomy consistency.
Solution Approach 2:
The patent copies proven physically practical trajectories from the pre-computed trajectory database and applies them to new situations. Rather than generating new motions that may be impractical, the system copies and adapts existing validated trajectories, ensuring motion quality while maintaining taxonomy structure.
Data Source
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AI summary
According to various embodiments, a method for controlling a robot is described comprising, comprising determining, for each robotic pose of a plurality of predetermined robot trajectories, a respective embedding in an embedding space (202) having the structure of a hyperbolic manifold by searching an optimum of an objective function which incites, for each of the predetermined robot trajectories, the embeddings of the robotic poses of the predetermined robot trajectory to follow pre-defined dynamics of the embedding space (202), determining, for a starting pose from which the robot is to be controlled, a start embedding in the embedding space (202), and, for a desired end pose, an end embedding in the embedding space (202) and a geodesic (203) between the start embedding and the end embedding according to a pullback metric of the embedding space (202) and controlling the robot according to a sequence of robotic poses given by the determined geodesic (203).