Statically Equivalent Serial Chain Research Articles

The effect of model complexity on the human center of mass estimation using the statically equivalent serial chain technique

Estimating the human center of mass (CoM) has long been recognized as a highly complex process. A relatively recent and noteworthy technique for CoM estimation that has gained popularity is the statically equivalent serial chain (SESC). This technique employs a remodeling of the human skeleton as a serial chain where the end effector represents the CoM location. In this study, we aimed to evaluate the impact of model complexity on the estimation capability of the SESC technique. To achieve this, we designed and rigorously assessed four distinct models with varying complexities against the static center of pressure (CoP) as reference, by quantifying both the root-mean-square (RMS) and correlation metrics. In addition, the Bland–Altman analysis was utilized to quantify the agreement between the estimations and reference values. The findings revealed that increasing the model complexity significantly improved CoM estimation quality up to a specific threshold. The maximum observed RMS difference among the models reached 9.85 mm. However, the application and task context should be considered, as less complex models still provided satisfactory estimation performance. In conclusion, the evaluation of model complexity demonstrated its impact on CoM estimation using the SESC technique, providing insights into the trade-off between accuracy and complexity in practical applications.

Evaluation of center of mass estimation for obese using statically equivalent serial chain

The complex structure of the human body makes its center of mass (CoM) estimation very challenging. The typically used estimation methods usually suffer from large estimation errors when applied to bodies with structural differences. Thus, a reliable estimation method is of utmost importance. In this paper, we present a detailed evaluation of a subject-specific CoM estimation technique named Statically Equivalent Serial Chain (SESC) by investigating its estimation ability over two different groups of subjects (Fit and Obese) in comparison to the segmental analysis method. For this study, we used an IMU-based motion capture system and a force platform to record the joint angles and corresponding center of pressure (CoP) values of twenty-five participants while performing a series of static postures. The root-mean-square errors (RMSE) of SESC’s estimation for both groups showed close and lower mean values, whereas the segmental analysis method showed significantly larger RMSE values in comparison to SESC (p < 0.05). In addition, we used the Bland–Altman analysis to evaluate the agreement between the two techniques and the ground truth CoP, which showed the accuracy, precision, and reliability of SESC over both groups. In contrast, the segmental analysis method did not present neither accurate nor precise estimations, as our analysis revealed considerable fixed and proportional biases.

An extended statically equivalent serial chain—Identification of whole body center of mass with dynamic motion

Background:Tracking the whole body center of mass (CoM) trajectory of balance-impaired individuals with a personalized model is useful in the development of customized fall prevention strategies. A personalized CoM estimate can be obtained using the statically equivalent serial chain (SESC) method, but the subject has to perform an identification procedure to determine the set of subject-specific SESC parameters. During this identification, the subject must hold a series of static poses, some of which are unsuitable for balanced-impaired individuals. Research question:Can non-static poses be used to replace the static poses during SESC parameter identification? Methods:A new method that extends the range of postures used to determine SESC parameters is presented. It takes advantage of CoM dynamics and can be executed by predominantly using dynamic motions with a few static frames. Furthermore, it is implemented using a Kalman filter to allow automatic switching between the dynamic and static models. The proposed method was tested with motion data obtained from seven healthy adults using a Vicon motion capture system and an AMTI force platform. Results:We found that dynamic motions could be used to estimate the SESC parameter and even reproduce ground reaction forces; however a small number of static poses are still required to determine the subject’s CoM position. The SESC-based CoM estimate obtained with this new approach was similar to that obtained using conventional full-static identification, except that the subject did not have to assume and maintain static poses. Significance:Our proposed extension of the conventional SESC method would facilitate its application in the field of neuro-rehabilitation, especially in patients who need balance training. This personalized CoM method could be applicable for patients who are not able to maintain a static posture. In addition, this method helps minimize the total identification time by increasing the number of usable recorded frames.

A Synergistic Approach to the Real-Time Estimation of the Feet Ground Reaction Forces and Centers of Pressure in Humans With Application to Human–Robot Collaboration

This letter proposes a novel technique for the real-time estimation of the human feet ground reaction forces (GRFs) and centers of pressure (CoP) from the whole-body CoP and body configuration. The estimated variables are used for the estimation of the overloading torques in human joints during double support, with the aim to provide an evaluation of the human ergonomics while performing heavy manipulation tasks with a robot, or when exposed to an external force. The estimation of the feet GRFs and CoP is achieved using a synergistic approach that combines a simplified geometrical model of the whole-body CoP and a learning technique to address the underdetermined force distribution problem. First, a statically equivalent serial chain (SESC) model which enables the whole-body CoP estimation is identified. Then, the estimated whole-body CoP and the simplified body pose information are used for the training and validation of the learning technique. The displacements between the feet CoP estimated using the synergistic model and the values measured using insole sensors, along with the GRFs vectors are finally used for the estimation of the body overloading joint torques. The proposed synergistic model is first validated experimentally in five subjects. Next, its real-time efficacy is assessed in a human–robot load sharing task, in which the robot trajectories are optimized to minimize the effect of the external load on the human joints.

A real-time and reduced-complexity approach to the detection and monitoring of static joint overloading in humans.

This paper proposes a novel technique for the real-time estimation of the joint torques variations in humans while performing heavy manipulation tasks. To achieve this, the method is based on the deviations of the Centre of Pressure (CoP) and Ground Reaction Force (GRF) in the presence of interaction forces. The CoP and GRF variations are calculated from the difference between the estimated values (assuming no interaction forces) using a pre-identified statically equivalent serial chain (SESC) and the measured ones (with the effect of interaction forces) using an external device. The calculated variation vectors and the measured joint angles of the human body are then used for the estimation of the overloading joint torques in real-time. We evaluated the efficacy of the proposed method both in simulations and experiments, in various poses of the human and interaction force profiles.

Improving Techniques in Statically Equivalent Serial Chain Modeling for Center of Mass Estimation

Any articulated system of rigid bodies defines a statically equivalent serial chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. An SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed, followed by the experimental validation of SESC modeling. Second, the problem of generating an SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.

Adaptive Interface for Personalized Center of Mass Self-Identification in Home Rehabilitation

As the center of mass (CoM) position can be used to determine stability, current rehabilitation standards may be improved by tracking it. A personalized CoM estimate can be obtained using the statically equivalent serial chain (SESC) once the model parameters are identified. The identification phase can be completed using low-cost sensors (Kinect and WBB) outside the laboratory making CoM estimation feasible in a patient’s home. This work focuses on: (1) improving the SESC identification quality and speed, and (2) using the estimated CoM to determine stability. Identification time is reduced by creating a visual adaptive interface where the subject’s limbs are colored based on the convergence of the SESC parameters. A study was conducted on eight subjects and showed a faster convergence and lower root mean square error (rmse) when the adaptive interface was used. We found that a model capable of estimating the CoM position with an rmse of 27 mm could be obtained after only 90 s of identification when the interface was used, whereas twice as much time was needed when the interface was not used. The interface that was developed can be used by a subject to track his/her CoM position in a self-directed way. Stability was determined for a squat task using a dynamic index obtained from the estimated CoM trajectory and using only Kinect measurements. This shows one potential application for home rehabilitation and monitoring.