Fig 1.
The illustration of the postural controller feedback loop is studied in this paper.
The body’s dynamical system is activated by control input u(t) and affected by disturbances w(t). The sensory system receives the motion dynamic x(t) and transfers it to neuromuscular contorted by noise v(t) and time delay td. The delayed sensory information and a buffer of the control input up to the current time u(t) are used in the neuromuscular by EKF method to estimate delayed states. The optimal controller block refers to all optimal methods explained in this work. The reference angular position xref(t) = 0 is considered zero degrees in an upright stance.
Fig 2.
Illustration of two joints dynamical model of the human body in standing position.
qa and qh represent the angular position of the ankle and hip joints respectively. COM is the location of the center of the system’s total mass, while m1 and m2 are the mass of the lower body and upper body respectively. Lf is the length of the foot.
Table 1.
Body characteristics.
Table 2.
Parameters bounds and limitations.
Fig 3.
Phase portraits comparison of the mentioned methods for the ankle joint.
The solid black line indicates the small perturbation and the dashed red line illustrates the higher perturbation.
Fig 4.
Phase portraits comparison of the mentioned methods for the hip joint.
The solid black line indicates the small perturbation and the dashed red line illustrates the higher perturbation.
Fig 5.
Energy consumption at each joint for different methods.
Fig 6.
Hip versus ankle joints torque for different methods.
The solid black line indicates the small perturbation and the red dashed line indicates the higher perturbation.
Table 3.
Controllers gains.
Fig 7.
One step ahead prediction of COP with different methods.
The subject body parameters are M = 67 kg, L = 1.68 m. The noise is estimated as white noise with a standard deviation of 0.005. The reaction time of the subject is 0.310 s.
Fig 8.
COP validation of measured experimental data of a random subject in the data set with the result of the generated COP of each method for the total time of the prediction.
The subject body parameters are M = 67 kg, L = 1.68 m. The noise is estimated as white noise with a standard deviation of 0.005. The reaction time of the subject is 0.310 s.
Table 4.
Mean± standard deviation of RMSE and VAF for the prediction of COP of ten subjects with different methods.
Fig 9.
PSD comparison of measured experimental data of a random subject in the data set and the mentioned methods.
Fig 10.
Evolution of changing controllers gain in IPD controller.
The upper plot shows the effect of gain change on the total energy consumption in the joints and the RMSE. The lower plot represents the effect on the joints’ torques and standing strategy.
Fig 11.
Evolution of changing weights in the optimization of the MPC controller.
The upper plot shows the effect of gain change on the total energy consumption in the joints and the RMSE. The lower plot represents the effect on the joints’ torques and standing strategy.
Fig 12.
Evolution of changing the COP distance error’s weight (α) inCOP-BC controller.
The upper plot shows the effect of gain change on the total energy consumption in the joints and the RMSE. The lower plot represents the effect on the joints’ torques and standing strategy.