ABSTRACT
Sigma-Point Kalman Filters
(SPKFs) are popular estimation techniques for high nonlinear system
applications. The benefits of using SPKFs include (but not limited to) the
following: the easiness of linearizing the nonlinear matrices statistically
without the need to use the Jacobian matrices, the ability to handle more
uncertainties than the Extended Kalman Filter (EKF), the ability to handle
different types of noise, having less computational time than the Particle Filter
(PF) and most of the adaptive techniques which makes it suitable for online
applications, and having acceptable performance compared to other nonlinear
estimation techniques. Therefore, SPKFs are a strong candidate for nonlinear
industrial applications, i.e. robotic
arm. Controlling a robotic arm is hard and challenging due to the system
nature, which includes sinusoidal functions, and the dependency on the sensors’
number, quality, accuracy and functionality. SPKFs provide with a mechanism
that reduces the latter issue in terms of numbers of required sensors and their
sensitivity. Moreover, they could handle the nonlinearity for a certain degree.
This could be used to improve the controller quality while reducing the cost.
In this paper, some SPKF algorithms are applied to 4-DOF robotic arm that
consists of one prismatic joint and three revolute joints (PRRR). Those include
the Unscented Kalman Filter (UKF), the Cubature Kalman Filter (CKF), and the
Central Differences Kalman Filter (CDKF). This study gives a study of those
filters and their responses, stability, robustness, computational time,
complexity and convergences in order to obtain the suitable filter for an
experimental setup.