Robotics

When robot arms approach full extension, the inverse kinematics equations become ill-conditioned—the Jacobian matrix loses rank and traditional numerical methods struggle. Standard approaches like Damped Least Squares introduce tracking errors proportional to the damping factor, while ε-regularization creates position-dependent bias.

ZeroProofML handles these cases by extending arithmetic to include tagged infinity values (+∞, −∞, Φ), allowing computation to continue through mathematical singularities with well-defined semantics.

In simulation benchmarks: ZeroProofML reduced mean squared error by 30–47% in the most problematic near-singularity regions (|det(J)| < 10⁻⁴) compared to ε-regularization, while maintaining similar performance elsewhere. Training is 12× faster than ensemble methods.

Potential applications:

• Inverse kinematics near workspace boundaries
• Control systems operating near singular configurations
• Path planning that must traverse near-singular regions