Kinematic Control of Free Rigid Bodies Using Dual Quaternions

This paper proposes a new type of control laws for free rigid bodies.The start point is the dual quaternion and its characteristics.The logarithm of a dual quaternion is defined,based on which kinematic control laws can be developed.Global exponential convergence is achieved using logarithmic feedback via a generalized proportional control law,and an appropriate Lyapunov function is constructed to prove the stability.Both the regulation and tracking problems are tackled.Omnidirectional control is discussed as a case study.As the control laws can handle the interconnection between the rotation and translation of a rigid body,they are shown to be more applicable than the conventional method.