ABSTRACT
Spatial rigid motion with both translational and rotational evolutions has been found in a variety of dynamical systems, such as robotics, spacecraft, biomechanics, and physics engines. Precise real-time motion estimation is critical for autonomous motion control when disturbances that require frequent tracking of the motion states are considered. The commonly used motion tracking instrument is the inertial navigation system (INS) equipped with a computer, motion sensors, and
9.1 Introduction .......................................................................................................................... 145 9.2 Dual Quaternion and Kinematics ......................................................................................... 147
9.2.1 Quaternion ................................................................................................................ 147 9.2.2 Dual Quaternion ....................................................................................................... 147 9.2.3 Dual Kinematics ....................................................................................................... 147
9.3 Development of Single Sensor EKF Algorithm Based on Dual Kinematics ....................... 148 9.3.1 Introduction to Extended Kalman Filter................................................................... 148 9.3.2 State Transition Model Based on Dual Kinematics .................................................. 149 9.3.3 Observation Model ................................................................................................... 150
9.4 Dual Subgradient-Based Distributed Estimation Algorithm ................................................ 151 9.4.1 Multisensor Networks and Problem Formulation ..................................................... 151 9.4.2 Distributed Dual Subgradient Method ..................................................................... 153 9.4.3 Convergence Analysis ............................................................................................... 155
9.5 A General Motion Estimation Example ............................................................................... 157 9.6 Conclusion ............................................................................................................................ 160 References ...................................................................................................................................... 161
rotation sensors to continuously provide position, orientation, and velocity of a moving object [1,2]. However, when such an INS instrument is not available or the concerned object is not accessible for INS installation, real-time estimation of both translational and rotational motion of a dynamical system becomes a challenging task.
