Discrete Unilateral Constrained Extended Kalman Filter in an Embedded System

Area of Science:

• Control Systems Engineering
• Robotics
• Mechanical Engineering

Background:

• The Kalman Filter (KF) is a cornerstone of optimal state estimation for smooth systems.
• Existing KF variants often struggle with non-smooth systems, particularly those with unilateral constraints.

Purpose of the Study:

• To introduce the Discrete Unilateral Constrained Extended Kalman Filter (DUCEKF) algorithm.
• To extend the Extended Kalman Filter (EKF) capabilities to hybrid mechanical systems exhibiting unilateral constraints, which are characterized by non-smooth positions and discontinuous velocities.

Main Methods:

• Development of the Discrete Unilateral Constrained Extended Kalman Filter (DUCEKF) algorithm.
• Application of Lyapunov stability theory to prove estimation error stability.
• Comparative analysis against the Extended Kalman Filter (EKF) using simulations and experimental validation.

Main Results:

• The DUCEKF algorithm demonstrates superior performance in state estimation for systems with unilateral constraints compared to the EKF.
• Simulations confirmed the DUCEKF's effectiveness in handling non-smooth and discontinuous system dynamics.
• Experimental validation using an embedded system and DAC hardware corroborated the simulation findings.

Conclusions:

• The DUCEKF algorithm successfully extends optimal state estimation to hybrid mechanical systems with unilateral constraints.
• The proposed method offers a robust solution for state estimation challenges in non-smooth dynamic systems.
• The study validates the DUCEKF's practical applicability through both simulation and real-world experimentation.