Spring-loaded inverted pendulum modeling improves neural network estimation of ground reaction forces.

Inertial-measurement-unit (IMU)-based wearable gait-monitoring systems provide kinematic information but kinetic information, such as ground reaction force (GRF) are often needed to assess gait symmetry and joint loading. Recent studies have reported methods for predicting GRFs from IMU measurement data by using artificial neural networks (ANNs). To obtain reliable predictions, the ANN requires a large number of measurement inputs at the cost of wearable convenience. Recognizing that the dynamic relationship between the center of mass (CoM) and GRF can be well represented by using spring mechanics, in this study we propose two GRF prediction methods based on the implementation of walking dynamics in a neural network. Method 1 takes inputs to the network that were CoM kinematics data and Method 2 employs forces approximated from CoM kinematics by applying spring mechanics. The gait data of seven young healthy subjects were collected at various walking speeds. Leave-one-subject-out cross-validation was performed with normalized root mean square error and r as quantitative measures of prediction performance. The vertical and anteroposterior (AP) GRFs obtained using both methods agreed well with the experimental data, but Method 2 yielded improved predictions of AP GRF compared to Method 1 (p = 0.005). These results imply that knowledge of the dynamic characteristics of walking, combined with a neural network, could enhance the efficiency and accuracy of GRF prediction and help resolve the tradeoff between information richness and wearable convenience of wearable technologies.

Prediction of Lower Limb Kinetics and Kinematics during Walking by a Single IMU on the Lower Back Using Machine Learning.

Recent studies have reported the application of artificial neural network (ANN) techniques on data of inertial measurement units (IMUs) to predict ground reaction forces (GRFs), which could serve as quantitative indicators of sports performance or rehabilitation. The number of IMUs and their measurement locations are often determined heuristically, and the rationale underlying the selection of these parameter values is not discussed. Using the dynamic relationship between the center of mass (CoM), the GRFs and joint kinetics, we propose the CoM as a single measurement location with which to predict the dynamic data of the lower limbs, using an ANN. Data from seven subjects walking on a treadmill at various speeds were collected from a single IMU worn near the sacrum. The data was segmented by step and numerically processed for integration. Six segment angles of the stance and swing leg, three joint torques, and two GRFs were estimated from the kinematics of the CoM measured from a single IMU sensor, with fair accuracy. These results indicate the importance of the CoM as a dynamic determinant of multi-segment kinetics during walking. The tradeoff between data quantity and wearable convenience can be solved by utilizing a machine learning algorithm based on the dynamic characteristics of human walking.

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics.

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected, off-centered curvy foot.

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.