Simultaneous Floating-Base Estimation of Human Kinematics and Joint Torques

Abstract

The paper presents a stochastic methodology for the simultaneous floating-base estimation of the human whole-body kinematics and dynamics (i.e., joint torques, internal and external forces). The paper builds upon our former work where a fixed-base formulation had been developed for the human estimation problem. The presented approach is validated by presenting experimental results of a health subject equipped with a wearable motion tracking system and a pair of shoes sensorized with force/torque sensors while performing different motion tasks, e.g., walking on a treadmill. The results show that joint torque estimates obtained by using floating-base and fixed-base approaches match satisfactorily, thus validating the present approach.

Keywords: floating-base dynamics estimation; human joint torque analysis; human wearable dynamics.

Figure 1

Graphical representation of the system topological order for links and joints.

Figure 2

Human model with distributed inertial measurement units. Joint reference frames are shown by using RGB (Red–Green–Blue) convention for x–y–z-axes. (left) Detail of the sensor position on the link.

Figure 3

Subject equipped with the Xsens wearable motion tracking system and six-axis force/torque shoes.

Figure 4

Task T4, Sequence 2: walking on a treadmill.

Figure 5

Classification of feet contacts: (left) single support on the right foot; (middle) double support; and (right) single support on the left foot.

Figure 6

Tasks representation from initial time $t_i$ to final time $t_f$ (left); and feet contact pattern classification obtained via Algorithm 1 (right).

Figure 7

The base linear proper sensor acceleration ${\mathit{\alpha }}_{lin}^g$ [$\mathrm{m}/{\mathrm{s}}^2$] comparison between measurement (mean and standard deviation, in red) and floating-base MAP estimation (mean, in blue), for tasks T1, T2, T3 and T4.

Figure 8

The external force ${\mathit{f}}^x$ [N] and moment ${\mathit{m}}^x$ [Nm] comparison between measurement (mean and standard deviation, in red) and estimation via floating-base MAP algorithm (mean, in blue) for (a) the left foot and (b) the right foot, respectively, for tasks T1, T2, T3 and T4.

Figure 9

Norm of the overall error of the entire set of joint accelerations $\epsilon \left(\ddot{\mathit{s}}\right)$ [$\mathrm{rad}/{\mathrm{s}}^2$] between measurement and estimation via floating-base MAP algorithm, for tasks T1, T2, T3 and T4.

Figure 10

Floating-base MAP estimation in task T4 of the joint torques $\mathit{\tau }$ [$\mathrm{N}$$\mathrm{m}$] (in blue) for the (b) left leg and (a) right leg, respectively, along with the related joint angles $\mathit{s}$ [deg] (in black). Gait estimations were performed by following the procedure for the feet contact classification in Algorithm 1.

Figure 11

Norm of the error of the base proper body linear acceleration $\epsilon \left({\mathit{a}}_{lin}^g\right)$ [$\mathrm{m}/{\mathrm{s}}^2$] and angular acceleration $\epsilon \left({\mathit{a}}_{ang}^g\right)$ [$\mathrm{rad}/{\mathrm{s}}^2$] between the estimation with the fixed-base and the floating-base MAP, for tasks T1, T2 and T3. The proper body acceleration for the floating-base estimation is obtained via Equation (13).

Figure 12

Norm of the error of the overall set of the overall external forces $\epsilon \left({\mathit{f}}^x\right)$ [N] and the moments $\epsilon \left({\mathit{m}}^x\right)$ [Nm] between the estimation with the fixed-base and the floating-base MAP, for tasks T1, T2 and T3.

Figure 13

Norm of the error of the overall set of joint accelerations $\epsilon \left(\ddot{\mathit{s}}\right)$ [$\mathrm{rad}/{\mathrm{s}}^2$] and torques $\epsilon \left(\mathit{\tau }\right)$ [Nm] between the estimation with the fixed-base and the floating-base MAP, for tasks T1, T2 and T3.