Continuum Robot Kinematics Without Singularities in 3D Control

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Solution Overview

Problem

Conventional kinematic parameterization schemes for continuum robots are computationally expensive, prone to singularities, and limited to two-dimensional motion, which hinders their effectiveness in complex environments.

Innovation Solution

A singularity-free parameterization model for continuum robots, utilizing two degrees of freedom per joint (bending radius and rotation) to enable efficient kinematic operations in three-dimensional space, avoiding matrix inversion and allowing for computationally efficient forward and inverse kinematics.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional parameterization schemes are used for continuum robots, then the robot can be controlled, but the computational cost becomes very expensive and introduces substantial lag in real-time control

Engineering Contradiction:
Improvecontrol accuracyVSAvoidcomputational lag
Core Design Contradiction:
ReliabilityVSLoss of time

Solution Approach 1:

The patent transforms the kinematic parameterization from conventional approaches (which use complex matrix representations) to a simplified parameter set based on bending radius and rotation angle. This parameter transformation reduces the computational complexity of kinematic calculations while maintaining accuracy, directly resolving the contradiction between control reliability and computational speed

Inventive Principle:
Principle #35Parameter changes

Solution Approach 2:

The patent replaces the traditional matrix-based mechanical computation system with a simplified geometric computation system based on bending radius and rotation parameters. This substitution eliminates the need for complex matrix operations and their associated computational overhead, achieving real-time control performance

Inventive Principle:
Principle #28Mechanics substitution (Replace mechanical system)

2Ease of operation

If conventional inverse kinematic solutions based on matrix inversion are used, then solutions can be generated, but the system breaks down mathematically at singularities such as when a flexible joint is oriented as a straight line

Engineering Contradiction:
Improveinverse kinematics solutionVSAvoidmathematical stability
Core Design Contradiction:
Ease of operationVSReliability

Solution Approach 1:

The patent changes the parameterization from matrix-based representations to bending radius and rotation angle parameters. This transformation eliminates the singularity problem because the new parameters remain well-defined and computable even when the robot configuration reaches traditional singular positions (e.g., straight-line configurations), ensuring mathematical stability throughout the entire workspace

Inventive Principle:
Principle #35Parameter changes

Solution Approach 2:

The patent converts the harmful effect of singularities (where matrix inversion fails) into a beneficial situation by using parameters that are naturally well-behaved at these configurations. The bending radius and rotation angle parameters provide continuous, differentiable solutions even at configurations that would traditionally cause mathematical breakdowns

Inventive Principle:
Principle #22Blessing in disguise (Convert harm into benefit)

3Productivity

If known approaches for motion planning and inverse kinematics are used, then computational complexity is reduced, but the approaches are limited to continuum robot motion in two dimensions

Engineering Contradiction:
Improvecomputational efficiencyVSAvoidmotion dimensionality
Core Design Contradiction:
ProductivityVSAdaptability or versatility

Solution Approach 1:

The patent extends the simplified parameterization approach from two-dimensional to three-dimensional space by adding the rotation angle parameter around the beam axis. This dimensional extension maintains the computational efficiency of the simplified model while enabling full three-dimensional motion capability, resolving the contradiction between productivity and adaptability

Inventive Principle:
Principle #17Another dimension (Dimensionality change)

Data Source

PatentEP3978203B1Singularity-free kinematic parameterization of soft robot manipulators
Publication Date: 2026.04.22 AUTODESK INC
  • EP3978203B1 patent drawingFigure 1
  • EP3978203B1 patent drawingFigure 2
  • EP3978203B1 patent drawingFigure 3

AI summary

A computer-implemented method for controlling a robot, the method comprising: determining a first value for a first joint parameter associated with a first continuum joint included in the robot and a first value for a second joint parameter associated with the first continuum joint, wherein the first joint parameter indicates a bending radius of a flexible portion of the continuum joint, and the second joint parameter indicates a rotation of the flexible portion of the continuum joint with respect to a base portion of the first continuum joint; and positioning an end portion of the robot at a final target location based on the first value of the first joint parameter and the first value of the second joint parameter.