Constrained Control in Three Dimensions via Explicit Reference Governor

Abstract

This paper investigates a constrained control problem of a rigid body in three dimensions via Explicit Reference Governor (ERG), which suitably modifies the exogenous reference to satisfy the constraints based on invariant sets. In this paper, force/torque input constraints and pose (position and attitude) constraints are considered. The objective of this paper is to propose a control scheme to regulate the rigid body pose to the desired pose while enforcing constraints at all times. To achieve the goal, a pre-stabilizing pose regulation controller is first introduced while ignoring the constraints. The pre-stabilized system is then augmented with the ERG to handle the constraints. All the proposed methods are based only on the special Euclidean group SE(3) elements without any parameterizations. Numerical simulations are finally carried out to show the effectiveness of the proposed methods.