• to study sensing of various signals in the drive train, in particular, those not utilized in conventional practice such as acceleration signals, force signals in the drive train and end effector’s position,
• to develop signal processing and decision making algorithms including their auto-tuning methodologies that take advantage of the sensed signals for the betterment of performance and other mechatonic advantages, and
• to demonstrate these benefits experimentally.

where x is the position, u is the force input. When the position is measured, the velocity may be estimated by a model based Kalman Filter (MBKF) or state observer. Defining two state variables by x1 = x and x2 = dx/dt, the system and the Kalman filter are obtained in the following form:

where w(t) and v(t) are input noise and measurement noise, respectively. w(t) and v(t) are independent Gaussian white noise processes.

Model Based Kalman Filter (MBKF)

where f 1 and f 2 are the filter gains.

The MBKF depends on the plant parameters. Thus, if the plant parameters are poorly known or subject to change, its performance deteriorates.

If the position and acceleration are both measured, the system equation and the KKF are obtained in the following form:

System Model for KKF

where w(t) and v(t) are accelerometer measurement noise and position measurement noise, respectively.

Kinematic Kalman Filter (KKF)

where f k1 and f k2 are the filter gains.

KKF does not depend on model parameters at all. Thus, if the acceleration and the position are both measured, the velocity may be reliably estimated by KKF.

The figure below show that the KKF provides an accurate estimate of the velocity even when the resolution of an encoder is low.

Estimation of Speed by MBKF and KKF
Encoder resolution = 256 pulse per revolution

• Two link robot

• Two Inertia System with Harmonic Gear