Robotic Arm Inverse Kinematics Seeding With Analytical-Numerical Solvers
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Solution Overview
Problem
Existing methods for calculating inverse kinematics for robotic arms are excessively time-consuming, especially when using as-manufactured length values, which hinders real-time motion planning.
Innovation Solution
A hybrid approach that uses an analytical solver based on design values to generate a seed value for a numerical solver, allowing for faster determination of joint parameters to achieve a desired tool center point location.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If numerical solver is used with as-manufactured values for accurate inverse kinematics calculation, then manufacturing precision is improved, but calculation time increases significantly
Solution Approach 1:
The patent applies preliminary action by pre-calculating an analytical solution using design values before performing numerical optimization. This pre-computed analytical solution serves as a starting point that significantly reduces the computational burden and time required for the subsequent numerical solver to achieve accurate results with as-manufactured values.
Solution Approach 2:
The patent segments the inverse kinematics calculation into two distinct phases: first, an analytical solution phase using design values to obtain a preliminary result, and second, a numerical optimization phase using as-manufactured values to refine the solution. This segmentation allows each phase to leverage its strengths while mitigating its weaknesses.
2Productivity
If analytical solver with design values is used, then calculation speed is improved, but accuracy deteriorates due to manufacturing tolerances
Solution Approach 1:
The patent uses the analytical solution with design values as an intermediary step. This intermediary provides a close approximation that serves as an excellent starting point for the numerical solver, which then refines the result using actual as-manufactured values. The intermediary analytical solution bridges the gap between speed and accuracy requirements.
Solution Approach 2:
The analytical calculation serves as a preliminary action that prepares a near-final solution before the accuracy-critical numerical optimization. This preliminary computation eliminates the need for the numerical solver to search from scratch, dramatically reducing computation time while maintaining final accuracy.
3Manufacturing precision
If full numerical optimization is performed for each robot configuration, then accuracy is improved, but real-time planning capability is lost
Solution Approach 1:
The analytical solution acts as a preliminary action that provides a close initial estimate of the joint parameters. This pre-computation is based on idealized design values and geometric relationships, establishing a starting point that is already near the optimal solution, thereby reducing the computational effort needed for real-time adjustments.
Solution Approach 2:
The computation is segmented into an offline analytical phase (using design values) and an online numerical refinement phase (using as-manufactured values). This segmentation enables real-time performance by eliminating the need for full numerical optimization at each control cycle, while still achieving high accuracy through the refinement step.
Data Source
AI summary
Methods of reducing calculation time for inverse kinematics for a robotic arm are presented. An analytical solver is used based on design values for a robot type to generate an analytical solution of joint parameters to achieve a desired location of a tool center point of the robot type, wherein the robotic arm has the robot type. The analytical solution of joint parameters is provided as a seed value to a numerical solver for the robotic arm of the robot type. A numerical solution is determined using the numerical solver and the seed value, the numerical solution comprising joint parameters for the robotic arm to achieve the desired location of a tool center point of the robotic arm.