Unit-Dual-Quaternion-Based PID Control Scheme for Rigid-Body Transformation

Abstract

This paper proposes a unit-dual-quaternion-based PID control scheme for rigid-body transformation in 6 degree-of-freedom, taking advantage of the unit dual quaternion for its compactness, computational effectiveness and non-singularity in describing arbitrary rigid-body transformation globally. Both the discrete form and the incremental form of the generalized PID control scheme are obtained after a new kinematic control model for rigid-body transformation based on unit dual quaternion in body-frame is derived. The proposed control scheme can deal with rotation and translation simultaneously and preserve the interconnection between rotation and translation with compact form. Simulation results based on USARSim platform and quadrotor are provided to demonstrate the effectiveness of the proposed control scheme.