Active and Reactive Mechanical Power – Part I: Foundations and Applications in Motion Control

This paper introduces active and reactive mechanical power as complementary physical quantities for analysing energy exchange and interaction dynamics in motion control and robotic systems. A model-based energy analysis distinguishes internal kinetic–potential energy redistribution from cyclic variations in total stored energy under specified operating conditions. Two measurement- based formulations are then developed: a signal-based method using Hilbert-transform quadrature at individual ports and a geometric method using instantaneous orthogonal force–motion decomposition across actuator ports. Together, these formulations provide distinct perspectives on net energy transfer, storage-related energy exchange, and port-to-port power transmission and distribution, with their physical interpretations established under specified motion and interaction conditions. The proposed power framework enables environmental impedance characterisation, interaction-performance analysis, energetic monitoring, and power-aware control using measured motion and force signals. In particular, the geometric formulation enables instantaneous power decomposition without explicit system models or non- causal filtering, and its use in real-time monitoring and control is demonstrated through cooperative manipulation and bilateral teleoperation. Experimental studies demonstrate the effectiveness and versatility of the proposed framework across a range of monitoring, analysis, and control tasks in motion control systems.