Gravity compensation and optimal control of actuated multibody system dynamics

Abstract

This work investigates the gravity compensation topic, from a control perspective. Thegravity could be levelled by a compensating mechanical system or in the control law, suchas proportional derivative (PD) plus gravity, sliding mode control, or computed torquemethod. The gravity compensation term is missing in linear and nonlinear optimal con-trol, in both continuous- and discrete-time domains. The equilibrium point of the controlsystem is usually zero and this makes it impossible to perform regulation when the desiredcondition is not set at origin or in other cases, where the gravity vector is not zero at theequilibrium point. The system needs a steady-state input signal to compensate for the grav-ity in those conditions. The stability proof of the gravity compensated control law basedon nonlinear optimal control and the corresponding deviation from optimality, with proof,are introduced in this work. The same concept exists in discrete-time control since it usesanalog to digital conversion of the system and that includes the gravity vector of the sys-tem. The simulation results highlight two important cases, a robotic manipulator and atilted-rotor hexacopter, as an application to the claimed theoretical statements.