A Unified Motion–Stability Architecture for Robotics

Abstract

A Unified Motion–Stability Architecture for Robotics introduces a composite operator framework that stabilizes robotic motion under noise, drift, and nonlinear actuator behavior. The architecture combines Subtracted Chaos (SC)—a contractive–expansive operator pair that suppresses jitter and enforces manifold confinement—with Adaptive Convergence for Chaotic Randomness (ACCR), a supervisory layer that monitors instability and prevents basin exit. The paper provides a formal stability theorem for SC, defines the tension index Δ=λ+γ, and identifies the contractive regime Δ<0 as the condition for bounded variance and finite attractor collapse. Numerical experiments validate these guarantees across parameter sweeps, noise injections, and attractor geometries. Results show: bounded variance for all Δ<0, deterministic collapse to a finite attractor set, robustness to moderate noise (σ≤0.2), zero attractor switching in the stable region, and a sharp transition curve as Δ→0+. Together, these findings demonstrate that SC behaves predictably under realistic noise and drift conditions, and that ACCR provides reliable supervision near instability thresholds. The work serves as a foundational operator‑level blueprint for future hardware validation and integration into robotic control pipelines.