MOTION: A Bounded Nonlinear Phase Controller Formulated as a Port-Hamiltonian System on Compact Manifolds

This paper introduces MOTION, a nonlinear phase-based control architecture that unifies bounded actuation, port-Hamiltonian energy shaping, and discrete-time computation within a single primitive. By mapping system configurations to compact manifolds (S1 and TN) and utilizing a sinusoidal control law, the architecture circumvents the energy inefficiencies associated with the artificial saturation of Cartesian linear controllers. We formally express the closed-loop dynamics as a dissipative port-Hamiltonian system, providing rigorous proofs of almost-global asymptotic stability (AGAS), input-to-state practical stability (ISpS), strict output passivity, and incremental stability via contraction analysis. The upload includes the technical white paper (PDF), a C++ implementation for embedded systems, and Python scripts for performance benchmarking. Results demonstrate a 30.8% reduction in control effort compared to classically clamped proportional controllers.