An optimized bipedal model for estimating the vertical and anteroposterior ground reaction forces during slope walking while carrying a suspended load

Ground reaction force (GRF) is a key indicator for evaluating load-suspended backpacks, which have demonstrated biomechanical and energetic advantages during level walking but have not yet been studied for slope walking. Existing bipedal walking models are limited to level walking and cannot be extended to slope scenarios, which hinders the mechanical evaluation of load-carrying devices. To address this gap, this study presents an optimized bipedal model for estimating vertical (vGRF) and anteroposterior (apGRF) GRF curves during slope walking with and without suspended loads. The model modulates the asymmetric double-peak pattern of vGRF using two gait parameters (the ratios of the first single-support stance rds and double-support stance rds to the gait cycle) and captures the asymmetric braking-propulsive peaks of apGRF across different slopes by optimizing the anteroposterior force. Validation using literature datasets (N=10, 5 females, 5 males) covering 5 slopes and 3 walking speeds showed high Pearson correlation coefficients (PCC, 0.924-0.987) and high intraclass correlation coefficients (ICC, >0.889) between the estimated and measured GRF curves. The normalized root mean square error (NRMSE) of the vGRF and apGRF curves were less than 0.109 body weight (BW) and 0.055 BW, respectively. The estimation errors for all peaks and valleys of the GRFs were below 0.1101 BW. Further validation using a powered load-suspended backpack under load-locked (LL) and load-suspended (LS) conditions (N=6, male), covering 3 slopes and 3 walking speeds, showed high PCC (0.870 - 0.990) and high ICC (>0.763). The NRMSE of the GRF curves was less than 0.129 BW. The estimation errors of the peaks and valleys were below 0.124 BW for vGRF and 0.185 BW for apGRF. This model can simultaneously estimate vGRF and apGRF during slope walking with suspended loads, demonstrating its potential applicability to wearable robot evaluation.