Robot Grasp Point Estimation Using Geometric Algebra

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Solution Overview

Problem

Existing robotic grasping methods face challenges in efficiently calculating oriented distances between points and geometric primitives, leading to non-regular computational performance, lack of parallelizability, and limited shape generalization, which affects the reliability and speed of grasp synthesis and stability assessment.

Innovation Solution

The use of geometric algebra and constructive solid geometry (GA-CSG) for robot representation, enabling efficient computation of directed distances between points and geometric primitives, allowing for high-performance grasping computations and robust grasping configurations in diverse environments.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of time

If traditional methods are used to calculate oriented distances between points and geometric primitives, then computational accuracy is maintained, but computational time and energy consumption increase significantly

Engineering Contradiction:

Improvecomputational timeVSAvoidcomputational performance regularity

Core Design Contradiction:

Loss of timeVSReliability

Solution Approach 1:

The patent transforms the computational parameters by representing geometric primitives (spheres, ellipsoids, cylinders, cones) using unified algebraic equations in a transformed coordinate system. This parameter transformation enables the use of simplified distance calculation formulas that reduce computational complexity while maintaining accuracy, directly addressing the contradiction between computational speed and reliability

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces traditional iterative numerical methods and complex geometric algorithms with direct algebraic computation based on transformed coordinate systems. This substitution eliminates the need for repeated calculations and iterative convergence checks, providing regular computational performance with reduced time loss

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If complex geometric algorithms are used to ensure accurate grasping configuration, then grasping stability is improved, but device complexity and computational load increase

Engineering Contradiction:

Improvegrasping stabilityVSAvoidcomputational system complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

By changing the parameter representation of geometric primitives to a unified algebraic form in transformed coordinates, the patent simplifies the computational system while preserving the accuracy needed for stable grasping. The transformed parameters enable direct calculation of oriented distances without complex iterative algorithms

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent segments the grasping computation into distinct phases: coordinate transformation, primitive classification, and distance calculation. Each phase uses simplified algorithms appropriate to its specific task, reducing overall system complexity while maintaining grasping stability through systematic processing

Inventive Principle:

Principle #1Segmentation

3Productivity

If traditional point-to-surface distance computation is used, then comprehensive shape analysis is achieved, but productivity and processing speed decrease

Engineering Contradiction:

Improvegrasping computation speedVSAvoidoriented distance accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent substitutes traditional point-to-surface distance computation with direct algebraic evaluation in transformed coordinate systems. This substitution provides closed-form solutions that compute oriented distances in constant time while maintaining measurement precision through exact algebraic relationships

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

By transforming the coordinate system and representing geometric primitives with unified algebraic parameters, the patent enables direct computation of oriented distances without iterative approximation. This parameter transformation maintains measurement precision while dramatically improving productivity through faster computation

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS20240416510A1Object-agnostic fast grasping-points estimation via geometric-algebra

Publication Date: 2024.12.19 INTEL CORP

AI summary

Various aspects of techniques, systems, and use cases for selecting grasping configurations for a robot are disclosed. Geometric primitives are generated to model the robot for grasping and manipulation by the robot. The geometric primitives are combined using various functions to determine which configuration to use. The instantaneous configuration is determined, as well as the forward kinematics and links to determine active geometric primitives of the gripper. The active geometric primitives are used to approximate an x, y, and z coordinate of each point of the primitives, a distance between the point and a grasping target, and an associated surface link. The configurations are ranked based on grasping metrics and one of the configurations selected to use accordingly.