# Using Wearable Sensors to Estimate Vertical Ground Reaction Force Based on a Transformer
## 1 Introduction  
Kinetic data on human movements, such as ground reaction forces (GRF) and joint movement have become indicators of injury risk and pain during exercise. GRF are often used to assess gait dynamics and balance measures, with the vertical ground reaction force (vGRF) being the most significant component of GRF during walking. The curve of vGRF consists of two peaks: a passive (weight acceptance) peak and an active (push-off) peak. The passive peak (PP) results from the foot colliding with the ground, while the active peak (AP) is generated by the foot's primary force applied to the ground as it pushes off. The magnitude and timing of these peaks can affect the joints and muscles of the lower limb. They can lead to the development or progression of musculoskeletal overuse injuries and conditions such as osteoarthritis [1, 2]. For healthy people, the vGRF at the bottom of the foot remains almost constant. However, for patients with an asymmetrical gait, the vGRF at the bottom of the foot changes as the right and left feet alternate. In previous work, motion analysis was often used and was achieved in the laboratory using a precision motion tracker and treadmill force plates that could be embedded in an instrumented treadmill or ground walkway. The disadvantages of this measurement method included the cost of equipment, space requirements, and the limitations of testing in a laboratory setting rather than a natural environment [3]. Recent work has used wearable sensors for gait analysis to address this limitation [4, 5, 6, 7]. Alternatively, inertial measurement units (IMUs; wireless wearable devices that measure magnetism, linear acceleration, and angular velocity) have been used to measure athletes' leg joint angles, stride kinematics, and segmental accelerations during competitive events. Although IMUs cannot directly measure GRFs, previous studies have used algorithms to estimate discrete biomechanical variables like peak vertical GRF, ground contact time, vertical impulse, and vertical loading rate from IMU data. With the wider adoption of machine learning approaches to the monitoring of human movement using wearable sensors, it is possible to estimate ground reaction forces from IMUs using several differentmachine learning algorithms. [PERSON] et al. [8] wore four IMUs on the foot, lower leg, distal thigh, and proximal thigh and moved at different speeds on a treadmill equipped with force plates. A random forest model was used to estimate vertical ground reaction forces from the data collected from each IMU. [PERSON] et al. [9] used two artificial neural networks to predict ground reaction forces. The first artificial neural network mapped data (rotation and acceleration) from three inertial sensors (located at the left and right calf and pelvis) to lower limb joint angles. The estimated joint angles were combined with the measured vertical accelerations and input to a second artificial neural network, which estimated the vertical ground reaction forces. [PERSON] et al. [10] used an IMU mounted on the pelvis to estimate the GRF during everyday gait, a calibration procedure, and an error-state extended Kalman filter (EEKF) for converting the acceleration at the center of mass (CoM) into a 3D GRF. When GRF are used in conjunction with the calculated kinematics, the GRF can calculate inverse dynamics and estimate the internal forces and interactions between different joints, muscles, and bones in the subject [11; 12]. In the field of biomechanics, LSTM networks have been used to make frame-by-frame predictions of GRF waveforms using motion capture data and predictions of the center of mass position relative to the center of pressure from IMU data during walking [13; 14; 15]. The method used in this paper differs from previous work in two main ways. Firstly, the model of the neural network is different. Previous works have used _RNN_, _LSTM_[16; 17], or other neural network models.