Robot Grasp Configuration Ranking via GA-CSG Distance Modeling
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Solution Overview
Problem
Existing robotic grasping methods face challenges with non-regular computational performance, non-parallelizability, and lack of shape generalization due to the Eberly formulation, leading to inefficient and unreliable grasping computations in diverse environments.
Innovation Solution
The use of geometric algebra and constructive solid geometry (GA-CSG) for robot representation, which decomposes robot models into geometric primitives and employs directed distance computations to enhance grasping efficiency and stability, allowing for high-performance oriented-distance calculations and robust grasping configurations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Eberly formulation is used for directed distance computations in robotic grasping, then the grasping computations can be performed with a established mathematical framework, but the computational performance becomes non-regular and the method lacks parallelizability
Solution Approach 1:
The patent replaces the traditional Eberly formulation (which relies on iterative numerical optimization) with a closed-form mathematical solution based on geometric algebra. This substitution eliminates the need for iterative computation, providing both regular computational performance and parallelizability while maintaining accuracy in directed distance calculations for grasping synthesis.
Solution Approach 2:
The patent transforms the computational approach by changing the mathematical parameters and representation used in directed distance computations. By using geometric algebra with homogeneous coordinates and dual quaternions, the system achieves closed-form solutions that are computationally regular and can be parallelized across multiple processing units, unlike the iterative Eberly method.
2Adaptability or versatility
If traditional grasping methods are used, then the system can handle simple geometries, but it lacks shape generalization for diverse object forms
Solution Approach 1:
The patent implements a universal directed distance computation framework using geometric algebra that can handle diverse geometric primitives (spheres, ellipsoids, cylinders, cones, polyhedra) through a unified mathematical representation. This single framework generalizes across different object shapes and types, eliminating the need for shape-specific algorithms while maintaining computational efficiency.
Solution Approach 2:
The patent segments complex objects into basic geometric primitives and applies directed distance computations to each primitive independently. This segmentation approach allows the system to handle complex shapes by decomposing them into simpler components, each processed using the same generalizable mathematical framework, thereby achieving shape generalization without proportionally increasing system complexity.
3Reliability
If comprehensive grasping configuration analysis is performed, then the robustness of grasping is improved, but the time and energy consumption increases significantly
Solution Approach 1:
The patent performs preliminary computation of directed distances from grasp points to geometric primitives before evaluating grasping configurations. By pre-computing these fundamental geometric relationships using closed-form solutions, the system reduces the computational burden during actual grasping evaluation, enabling comprehensive robustness analysis without proportional increases in computation time or energy consumption.
Solution Approach 2:
The patent replaces computationally intensive iterative optimization methods with closed-form geometric algebra solutions for evaluating grasping configuration robustness. This substitution eliminates repeated numerical computations while maintaining comprehensive analysis of grasp stability, thereby reducing time and energy consumption without sacrificing grasping robustness evaluation quality.
Data Source
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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.