Robot Motion Control With Hyperbolic Geodesic Interpolation
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Solution Overview
Problem
Existing methods for controlling robot hands, such as GPHLVM, generate physically impractical motions due to a lack of training data in regions between clusters, leading to reliance on non-informative Gaussian Process means.
Innovation Solution
A Gaussian Process Hyperbolic Dynamical Model (GPHDM) is employed, incorporating a hyperbolic manifold and first-order Riemannian linear dynamics to ensure physically consistent motion by using geodesic interpolation and a pullback metric, ensuring smooth transitions and adherence to a taxonomy structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If GPHLVM is used to generate robot motions, then the motion can follow taxonomy structure, but the motion becomes physically impractical due to lack of training data in regions between clusters
Solution Approach 1:
The patent introduces a pullback metric as an intermediary mechanism that bridges the taxonomy structure and physical motion constraints. This metric acts as a mediator that translates abstract taxonomy relationships into physically valid motion trajectories, resolving the contradiction between following taxonomy structure and ensuring physical practicality.
Solution Approach 2:
The patent changes the metric parameter from a standard Euclidean distance to a pullback metric that incorporates physical constraints. By modifying the metric definition to account for robot-specific physical limitations, the system can generate motions that both follow taxonomy structure and remain physically practical.
2Device complexity
If high-dimensional robot poses are embedded in low-dimensional space, then the representation becomes more compact, but the physical consistency of motion is lost
Solution Approach 1:
The pullback metric serves as an intermediary that preserves physical consistency information during the dimensionality reduction process. It enables the low-dimensional embedding to maintain awareness of physical constraints that would otherwise be lost in the compression from high-dimensional pose space to low-dimensional latent space.
3Productivity
If training data is collected only within latent clusters, then the data collection is efficient, but motion prediction in regions between clusters reverts to non-informative Gaussian Process mean
Solution Approach 1:
The pullback metric acts as an intermediary that provides motion information in transition regions without requiring additional training data. It enables the system to infer physically valid motions in regions between clusters by leveraging the metric's ability to translate taxonomy relationships into physical motion constraints.
Solution Approach 2:
The patent performs preliminary action by pre-defining the pullback metric with embedded physical constraints before motion prediction is needed. This preliminary setup allows the system to handle transition regions effectively without requiring additional data collection or computation at prediction time.
Data Source
AI summary
A method for controlling a robot. The method includes determining, for each robotic pose of a plurality of predetermined robot trajectories, a respective embedding in an embedding space 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, determining, for a starting pose from which the robot is to be controlled, a start embedding in the embedding space (, and, for a desired end pose, an end embedding in the embedding space and a geodesic between the start embedding and the end embedding according to a pullback metric of the embedding space and controlling the robot according to a sequence of robotic poses given by the determined geodesic.