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

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Seyed Fakoorian ◽  
Vahid Azimi ◽  
Mahmoud Moosavi ◽  
Hanz Richter ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Reaction Force ◽  
Force Estimation ◽  
Joint Angles ◽  
Estimation Errors ◽  
Reaction Forces

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-mean-square (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.

scholarly journals End-Effector Pose Estimation in Complex Environments Using Complementary Enhancement and Adaptive Fusion of Multisensor

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Mingrui Luo ◽  
En Li ◽  
Rui Guo ◽  
Jiaxin Liu ◽  
Zize Liang
Keyword(s):  
Kalman Filter ◽  
Pose Estimation ◽  
Unscented Kalman Filter ◽  
Rbf Neural Network ◽  
Estimation Error ◽  
Estimation Method ◽  
Original Data ◽  
Measurement Unit ◽  
Complex Environments ◽  
End Effector

Redundant manipulators are suitable for working in narrow and complex environments due to their flexibility. However, a large number of joints and long slender links make it hard to obtain the accurate end-effector pose of the redundant manipulator directly through the encoders. In this paper, a pose estimation method is proposed with the fusion of vision sensors, inertial sensors, and encoders. Firstly, according to the complementary characteristics of each measurement unit in the sensors, the original data is corrected and enhanced. Furthermore, an improved Kalman filter (KF) algorithm is adopted for data fusion by establishing the nonlinear motion prediction of the end-effector and the synchronization update model of the multirate sensors. Finally, the radial basis function (RBF) neural network is used to adaptively adjust the fusion parameters. It is verified in experiments that the proposed method achieves better performances on estimation error and update frequency than the original extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithm, especially in complex environments.

Stereovision-based relative states and inertia parameter estimation of noncooperative spacecraft

2018 ◽  
Vol 233 (7) ◽  
pp. 2489-2502 ◽  
Author(s):  
Xun Wang ◽  
Zhaokui Wang ◽  
Yulin Zhang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Target Surface ◽  
State Equation ◽  
Moment Of Inertia ◽  
Transition Rule ◽  
Estimation Errors ◽  
Fixed Frame ◽  
Adaptive Unscented Kalman Filter ◽  
Relative States

Autonomous proximity operations have recently become appealing as space missions. In particular, the estimation of the relative states and inertia properties of a noncooperative spacecraft is an important but challenging problem, because there might be poor priori information about the target. Using only stereovision measurements, this study developed an adaptive unscented Kalman filter to estimate the relative states and moment-of-inertia ratios of a noncooperative spacecraft. Because the accuracy of the initial relative states has an effect on the estimation convergence performance, attention was also given to their determination. The target’s body-fixed frame was defined in parallel to the chaser’s initial body-fixed frame, and then the initial relative attitude was known. After formulating kinematic constraint equations between the relative states and multiple points on the target surface, particle swarm optimization was utilized to determine the initial relative angular velocity. The initial relative position was also determined under the assumption that the initial relative translational velocity was known. To estimate the relative states and moment-of-inertia ratios using the adaptive unscented Kalman filter, the relative attitude dynamic model was reformulated by designing a novel transition rule with five moment-of-inertia ratios, described in the defined target’s body-fixed frame. The moment-of-inertia ratios were added to the state space, and a new state equation with variant process noise covariance matrix Q was formulated. The measurement updating errors of the relative states were utilized to adaptively modify Q so that the filter could estimate the relative states and moment-of-inertia ratios in two stages. Numerical simulations of the adaptive unscented Kalman filter with unknown moment-of-inertia ratios and the standard unscented Kalman filter with known moment-of-inertia ratios were conducted to illustrate the performance of the adaptive unscented Kalman filter. The obtained results showed the satisfactory convergence of the estimation errors of both the relative states and moment-of-inertia ratios with high accuracy.

Dynamic-joint-strength-based two-dimensional symmetric maximum weight-lifting simulation: Model development and validation

2020 ◽  
Vol 234 (7) ◽  
pp. 660-673
Author(s):  
Ritwik Rakshit ◽  
Yujiang Xiang ◽  
James Yang
Keyword(s):  
Joint Strength ◽  
Reaction Force ◽  
Weight Lifting ◽  
Ground Reaction Forces ◽  
Two Dimensional ◽  
Joint Angles ◽  
Maximum Weight ◽  
Strength Based ◽  
Optimization Formulation ◽  
Reaction Forces

This article presents an optimization formulation and experimental validation of a dynamic-joint-strength-based two-dimensional symmetric maximum weight-lifting simulation. Dynamic joint strength (the net moment capacity as a function of joint angle and angular velocity), as presented in the literature, is adopted in the optimization formulation to predict the symmetric maximum lifting weight and corresponding motion. Nineteen participants were recruited to perform a maximum-weight-box-lifting task in the laboratory, and kinetic and kinematic data including motion and ground reaction forces were collected using a motion capture system and force plates, respectively. For each individual, the predicted spine, shoulder, elbow, hip, knee, and ankle joint angles, as well as vertical and horizontal ground reaction force and box weight, were compared with the experimental data. Both root-mean-square error and Pearson’s correlation coefficient ( r) were used for the validation. The results show that the proposed two-dimensional optimization-based motion prediction formulation is able to accurately predict all joint angles, box weights, and vertical ground reaction forces, but not horizontal ground reaction forces.

Comparison of Estimation Techniques for the Crankshaft Dynamics of an Opposed Piston Engine

2019 ◽  
Author(s):  
Joseph A. Drallmeier ◽  
Jason B. Siegel ◽  
Anna G. Stefanopoulou
Keyword(s):  
Kalman Filter ◽  
Internal Combustion Engines ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Weight Ratio ◽  
Expansion Ratio ◽  
Piston Engine ◽  
Lower Estimation ◽  
Crank Angle ◽  
Scavenging Efficiency

Abstract This study provides a comparison of a linear and unscented Kalman filter to estimate the dynamics of a two-stroke opposed piston engine. These engines maintain several advantages over conventional internal combustion engines including reduced heat transfer, higher power to weight ratio, and a larger expansion ratio. Additionally, a crank angle phasing is introduced between the two cranks to improve scavenging efficiency. However, the coupling of the two crankshafts through a large geartrain can cause high amounts of noise and vibration harshness (NVH) and mechanical efficiency losses. By removing the geartrain and controlling the decoupled crankshafts with motor-generators, the NVH can be minimized while maintaining the benefits of crank angle phasing. To control the input torque of the motors to the engine, accurate estimations of the crankshaft position and dynamics are necessary. While the unscented Kalman filter exhibits lower estimation error, the filter is sensitive to model uncertainty relating to cylinder pressure, demanding further investigation of the robustness of the nonlinear filter.

H∞-Property of the Continuous-Time Extended Kalman Filter

2016 ◽  
Author(s):  
Jennifer L. Bonniwell ◽  
Susan C. Schneider ◽  
Edwin E. Yaz
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Continuous Time ◽  
Estimation Error ◽  
Finite Energy ◽  
Minimum Variance ◽  
Nonlinear Observer ◽  
Minimum Variance Estimator ◽  
Error Energy ◽  
Special Case

This work elucidates another theoretical property of the ubiquitous extended Kalman filter by analyzing the energy gain of the continuous-time extended Kalman filter used as a nonlinear observer in the presence of finite-energy disturbances. The analysis provides a bound on the ratio of estimation error energy to disturbance energy, which shows that the extended Kalman filter inherently has the H∞-property along with being the locally optimal minimum variance estimator. A special case of this result is also shown to be the H2-property of the extended Kalman filter.

scholarly journals An Adaptive UKF Based SLAM Method for Unmanned Underwater Vehicle

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hongjian Wang ◽  
Guixia Fu ◽  
Juan Li ◽  
Zheping Yan ◽  
Xinqian Bian
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Underwater Vehicle ◽  
Statistical Parameters ◽  
Sea Trial ◽  
Unmanned Underwater Vehicle ◽  
Noise Statistic ◽  
Localization And Mapping ◽  
Slam Algorithm

This work proposes an improved unscented Kalman filter (UKF)-based simultaneous localization and mapping (SLAM) algorithm based on an adaptive unscented Kalman filter (AUKF) with a noise statistic estimator. The algorithm solves the issue that conventional UKF-SLAM algorithms have declining accuracy, with divergence occurring when the prior noise statistic is unknown and time-varying. The new SLAM algorithm performs an online estimation of the statistical parameters of unknown system noise by introducing a modified Sage-Husa noise statistic estimator. The algorithm also judges whether the filter is divergent and restrains potential filtering divergence using a covariance matching method. This approach reduces state estimation error, effectively improving navigation accuracy of the SLAM system. A line feature extraction is implemented through a Hough transform based on the ranging sonar model. Test results based on unmanned underwater vehicle (UUV) sea trial data indicate that the proposed AUKF-SLAM algorithm is valid and feasible and provides better accuracy than the standard UKF-SLAM system.

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