Estimation of the Flexural States of a Macro–Micro Manipulator Using Point-Acceleration Data

The work reported here was motivated by the development of manipulator systems comprising one long-reach, flexible-link subsystem, termed the macromanipulator, and a short-reach, rigid-link subsystem, called the micromanipulator. The flexural states of the macromanipulator, needed for controlling such systems effectively, are not usually measurable directly. For this reason, a state-estimation algorithm is proposed which uses the velocity and angular-velocity data of the micromanipulator base to estimate the flexural states of the macromanipulator. The velocity data are inferred from the acceleration signals delivered by a kinematically redundant set of triaxial accelerometers. The accelerometer signals are also utilized to calculate the translational and angular accelerations of the micromanipulator base, which are, in turn, used along with the dynamics equations of the micromanipulator to obtain the reaction force and moment acting between the two subsystems. Treating the force and the moment as inputs, the dynamics equations of the macromanipulator alone are used in the observer, thus reducing the order of the dynamics model. The state–output relations, on the other hand, are linearized in closed form to lower the computational cost. The relations thus obtained are then used in an extended Kalman filter to estimate the flexural states of the system.