Seyed Abolfazl Fakoorian

Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise

State estimation in the presence of non-Gaussian noise is discussed. Since the Kalman filter uses only second-order signal information, it is not optimal in non-Gaussian noise environments. The maximum correntropy criterion (MCC) is a new approach to measure the similarity of two random variables using information from higher-order signal statistics. The correntropy filter (C-Filter) uses the MCC for state estimation. In this paper we first improve the performance of the C-Filter by modifying its derivation to obtain the modified correntropy filter (MC-Filter). Next we use the MCC and weighted least squares (WLS) to propose an MCC filter in Kalman filter form, which we call the MCC-KF. Simulation results show the superiority of the MCC-KF compared with the C-Filter, the MC-Filter, the unscented Kalman filter, the ensemble Kalman filter, and the Gaussian sum filter, in the presence of two different types of non-Gaussian disturbances (shot noise and Gaussian mixture noise).

Ground reaction force estimation in prosthetic legs with an extended Kalman filter

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) prosthetic leg for transfemoral amputees, and includes four degrees of freedom (DOF): vertical hip displacement, thigh angle, knee angle, and ankle angle. We design a continuous-time extended Kalman filter (EKF) to estimate not only the states of the robot/prosthesis system, but also the GRFs that act on the prosthetic foot. The simulation results show that the average RMS estimation errors of the thigh, knee, and ankle angles are 0.007, 0.015, and 0.465 rad with the use of four, two, and one measurements respectively. The average GRF estimation errors are 2.914, 7.595, and 20.359 N with the use of four, two, and one measurements respectively. It is shown via simulation that the state estimates remain bounded if the initial estimation errors and the disturbances are sufficiently small.

Ground Reaction Force Estimation in Prosthetic Legs With Nonlinear Kalman Filtering Methods

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-meansquare (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF. [DOI: 10.1115/1.4036546]

Robotics and Prosthetics at Cleveland State University: Modern Information, Communication, and Modeling Technologies

This chapter concentrates on the correlation between research-based education, government priorities and research funding. Special attention is paid to an analysis of the role of modern information and communication technology (ICT) in the education of engineering students. Successful cases with specific description of computer modeling methods for the implementation of prosthesis and robotics research projects are presented based on experiences in the Embedded Control Systems Research Laboratory of Cleveland State University.

Robust Adaptive Impedance Control With Application to a Transfemoral Prosthesis and Test Robot

This paper presents, compares, and tests two robust model reference adaptive impedance controllers for a three degrees-of-freedom (3DOF) powered prosthesis/test robot. We first present a model for a combined system that includes a test robot and a transfemoral prosthetic leg. We design these two controllers, so the error trajectories of the system converge to a boundary layer and the controllers show robustness to ground reaction forces (GRFs) as nonparametric uncertainties and also handle model parameter uncertainties. We prove the stability of the closed-loop systems for both controllers for the prosthesis/ test robot in the case of nonscalar boundary layer trajectories using Lyapunov stability theory and Barbalat’s lemma. We design the controllers to imitate the biomechanical properties of able-bodied walking and to provide smooth gait. We finally present simulation results to confirm the efficacy of the controllers for both nominal and off-nominal system model parameters. We achieve good tracking of joint displacements and velocities, and reasonable control and GRF magnitudes for both controllers. We also compare performance of the controllers in terms of tracking, control effort, and parameter estimation for both nominal and off-nominal model parameters. [DOI: 10.1115/1.4040463]

Derivative-free Kalman filtering-based control of prosthetic legs

A derivative-free method for state estimation-based control of a robot/prosthesis system is presented. The system is the combination of a test robot that emulates human hip and thigh motion, and a powered transfemoral prosthetic leg. The robot/prosthesis combination is modeled as a three degree-of-freedom (DOF) robot: vertical hip displacement, thigh angle, and knee angle. We develop a derivative-free Kalman filter (DKF) for state estimation-based control for an n-DOF robotic system. We then propose a method to make the DKF robust when the robot dynamics include disturbances. In the robust DKF, we use two different methods for disturbance rejection: PD and PI. These disturbance compensators are used for supervisory control to make the DKF robust in the presence of disturbances. The simulation results show the advantages of the DKF and the robust DKF for the three-DOF robot/prosthesis system for state estimation-based control.

Maximum Correntropy Criterion Constrained Kalman Filter

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.