Performance analysis of flexible intelligent hand prosthesis

3.1. Feasibility analysis

In order to control the grasping force at fingertips, a control method based on linear tension feedback [8] is proposed. Its core idea is to calculate fingertip grasping force by measuring the line tension at the entrance side of the lasso. Firstly, the non-linear friction loss in the cable drive is compensated, and the line tension at the exit side of the lasso is obtained. Then the fingertip grasping force is further calculated by the static mechanical model of the finger. Finally, the grasping force is effectively controlled by the control method proposed in this paper. The specific control block diagram is shown in Fig. 1.

In this paper, incremental PID control is adopted for tension control. In Fig. 1, $F_d$ is the desired contact force between fingertips and objects. $F_c$ is the estimated contact force between fingertips and objects. $F_r$ is the actual contact force between fingertips and objects. $e_f$ is force deviation. $T_{in}$ is the tension of the side line at the entrance of the lasso. $F_{erro}$ is the actual contact force deviation between fingertips and objects. $u$ is motor drive input. The line tension $F_{out}$ measured at the entrance side of the sling is used to calculate the fingertip contact force $F_c$ by friction compensation and static mechanical model of the finger. Make it track the desired contact force $F_d$ between fingertips and objects. The contact force of the fingertip measured by the thin film pressure sensor in the control block diagram does not act as feedback on the closed-loop control of the system. It verifies the feasibility of the finger static mechanical model and the friction compensation scheme by calculating the error between the finger static mechanical model and the expected contact force.

Fig. 1The specific control block diagram

3.2. Structure and force analysis

In order to obtain the relationship between the tension of the side line at the exit of the lasso and the contact force between the fingertips, a static mechanical model of a single finger was established as shown in Fig. 2. The following assumptions are used in modeling: (1) Every joint is a pure rotating joint. (2) The friction between the tension line and the conductor groove is neglected. (3) The position of the conductor groove relative to the finger does not move under the action of force. Based on the above assumptions, a single finger can be considered as a three-bar structure. Because the effect of placing wire grooves on both sides of phalanges on phalanges is the same as that of placing wire grooves on the central axis of phalanges. Therefore, it is considered to be placed in the phalanx axis position for modeling.

Fig. 2The static mechanical model of a single finger

In order to facilitate the representation and analysis of static mechanical models, the base coordinate system {$X_0$, $Y_0$, $Z_0$} is established at the axis of MCP joint of finger. The coordinate systems $X_1$, $Y_1$, $Z_1$}, {$X_2$, $Y_2$, $Z_2$} and {$X_3$, $Y_3$, $Z_3$} were established at the axes of MCP, PIP (proximal interphalangeal joint) and DIP (distal interphalangeal joint), respectively. The origins are located at the axes of MCP, PIP and DIP joints respectively. The coordinate axes of $Z_0$, $Z_1$, $Z_2$ and Z₃ coincide with the axes of each joint axis, and all $Z$-axis directions are perpendicular to the paper facing out. The coordinate axes of $X_0$, $X_1$, $X_2$ and $X_3$ point from the current axis to the next axis along the common vertical direction. The coordinate axes of $Y_0$, $Y_1$, $Y_2$ and $Y_3$ are determined by the right-hand rule. The bending angle of each joint of the finger is described by ${\theta }_i$ ($i=$ 1, 2, 3). The angle of the tension line passing through the conductor groove $P_i$ ($i=$ 1, 2, 3) at the conductor groove $P_i$ is described by ${\alpha }_i$. The homogeneous transformation matrix from coordinate system $i$ to coordinate system $j$ is obtained by Eq. (1) and Eq. (2):

In order to obtain the static mechanical model of the finger, the position usage formula of all conductor grooves in flexible intelligent hand prosthesis can be transformed base on Eq. (3) with coordinate system 0. $P_{tgi}^i$ is the position vector in the coordinate system $i$ of the conductor slot. In the base coordinate system 0, the unit vector ${\widehat{\nu }}_{tgj}^{tgi}$ from conductor groove $P_i$ to conductor groove $P_j$ is calculated by Eq. (4):

Because the pull line indirectly acts on the finger, the resultant force $F_i$ ($i=$ 1, 2, 3) of each phalanx is located at the corresponding position of $D_i^0$ which is on the back of the finger. Therefore, in order to obtain the torque produced by resultant force $F_i$ to the $P_i$ joint, $D_i^0$ is regarded as the force action point. The interaction torque ${\tau }_i$ is shown in Eq. (5):

where ${\tau }_{rmi}$ represents the blocking torque at the $P_i$ joint.

3.3. Friction compensation

In order to reduce the influence of the change of bowden-cable shape on grasping force control, a physical method is adopted to limit the range of the cumulative bending angle of the cable and to compensate the friction by means of median value. Considering that wheelchairs are necessary for the movement of most patients who have lost the motor function of their hands. Therefore, the driving mechanism of the flexible hand prosthesis can be installed on the back of the wheelchair, fixed part of the lasso on the wheelchair. The change range of in the final patient is between 0°-90° when grasping the target object. For the friction compensation part, the cumulative bending angle of the cable cannot be measured in real time. Therefore, the paper chooses half of the maximum friction loss between 0°-90° to compensate the cumulative bending angle of the lasso. In order to reduce the influence of the shape change of the lasso on the grasping force control, the friction compensation controller is designed to add the friction compensation value to the tension of the side line at the entrance of the cable, to ensure that the tension at the exit of the lasso can follow the expected value well.

3.4. Experimental test and analysis

In order to verify the effectiveness of friction compensation through experiments, on the basis of the experimental system, a linear guide with a tension sensor is used to replace the main part of the flexible hand prosthesis for measuring the linear tension at the exit side of the lasso. Aiming at the friction compensation method proposed in this paper, when the cumulative bending angle of the cable is 90°, the friction characteristic curve of the cable is obtained, then the actual friction model is established. During the experiment, the cumulative bending angle of the lasso was fixed at 90°, the relative sliding velocity between rope and casing is set to 0.0042 m/s. The experimental verification results are shown in Fig. 3. As can be seen from the Fig. 3, the experimental results are consistent with the fitting results.

The friction factor of the lasso remains unchanged during the experiment. Change the cumulative bending angle of the lasso. Six groups of angles were selected in the range of the cumulative bending angle of the lasso (as shown in Fig. 4), and the interval between the angles was 15°. For each group of experiments, the experiments were carried out under the condition of friction-free compensation and friction-free compensation respectively. The linear tension at the outlet side of the expected Lasso is set to 10 N. From Fig. 4, it can be seen that the absolute error values of six groups of frictionless compensation and frictional no-compensation during the experiment could be superposed and summed respectively. The sum of the absolute value of force tracking error without friction compensation is 10.21 N. The sum of absolute force tracking error with friction compensation is 5.77 N. The experimental results basically coincide with the integral of the absolute value of the force estimation error. Therefore, the friction compensation experiment proves that the proposed friction compensation method can effectively reduce the force estimation error at the exit side of the bowden-cable.

Fig. 3Verification of friction torque

Fig. 4Error comparison at different bending angle