On Kalman Active Observers

Abstract

The paper introduces the Active Observer (AOB) algorithm in the framework of Kalman filters. The AOB reformulates the Kalman filter to accomplish model-reference adaptive control based on: (1) A desired closed loop system. (2) An extra equation to estimate an equivalent disturbance referred to the system input. An active state is introduced to compensate unmodeled terms, providing a feedforward compensation action. (3) Stochastic design of the Kalman matrices. Stability analysis with model errors is discussed. An example of robot force control with an external and unknown nonlinear disturbance is presented (SISO system). Another example of model-matching control for steer-by-wire (SBW) vehicles with underactuated structure is discussed (MIMO system).

Hunt–Crossley model based force control for minimally invasive robotic surgery

“…Different from traditional Kalman filters, the goal of the active observer, as shown in Fig. 9, is to estimate and compensate this error by using a feedforward term based on an extra state, also called as active state p(k), given by [34,35]:…”

“…With the Kalman filter based AOB, the stochastically driven active state p(k) aims to compensate the effect of neglected nonlinear terms in real time [34,35]. Simulation studies are carried out to test the range of validity of the controller based on linearized Hunt-Crossley model (around 5 N as an example) with AOB.…”

Nonlinear bilateral teleoperation using extended active observer for force estimation and disturbance suppression

“…An Active Observer (AOB) 11,12 is a variation of a Kalman filter (KF), one of the first estimators to include disturbance in the optimization process. The AOB concept relies on adopting an extra relationship (auxiliary input) to estimate an equivalent disturbance referred to as the system input.…”

“…[11,12], can be used to estimate the disturbance in a dynamic system, as well as where * is the output of the system, * is a unit matrix, and the state observation matrix * 0 0 0 , and * , * and * represent the process noises and measurement noises, respectively, / and * represent the rates at which the vectors of external forces and inertial robot parameters are estimated to vary.…”

Exact External Torque Sensing System for Flexible-Joint Robot: Kalman Filter Estimation with Random-Walk Model

“…예를 들어, 시스템에 작용하는 미 지의 외란(unknown equivalent disturbance)을 알아내기 위해, 그것이 시스템에 랜덤하게 들어온다고 가정하여 능동상태 (active state)에 포함시킴으로써 능동관측기(active observer (AOB)) 제어구조를 통해 외란을 추정할 수 있다 [8] . 제안한 알고리즘에서는 다음과 같은 입력동역학 모델을 가정한다 [9] : 을 이산화(discretization)한 후에 다음과 같은 선형칼만필터 를 적용한다 [7,10] .…”