## 3 Method
### Control Schemes
#### 3.4.2 Adaptive Semi-Autonomous Control  
The adaptive scheme for the semi-autonomous control relies on continuously blending input from the user and input from the computer vision module based on a confidence measure. This confidence measure is based on calculating the similarity of the command received from the user with the intention predicted by the computer vision module. All commands from the user for manually moving the exoskeleton (up, right, forward, and so on) can be described in 3D using the vector \(\vec{U}_{x,y,z}\). As only the direction of the user input is considered for calculating the confidence, the normalized vector, \(\vec{U}\), is used. A similar vector can be formulated for the computer vision module, \(\vec{C}_{x,y,z}\), which describes how the position of the exoskeleton's end-effector should change in order to reach the grasp pose for the predicted target. The direction of this vector from the computer vision module is expressed as the normalized vector, \(\hat{\mathcal{C}}\). The confidence is then measured using the scalar product between these two normalized direction vectors:  
\[\rho(\vec{U},\hat{\mathcal{C}})=\frac{\big{(}\hat{\mathcal{C}}\cdot\vec{U} \big{)}+1}{2}. \tag{1}\]  
The addition and division of the scalar product between the two direction vectors serves to normalize the resulting scalar to a value between 0 and 1. A high confidence indicates that the user and the computer vision want to move in the same direction and vice versa. A confidence measure of 0.5 or below corresponds to an angle of 90\({}^{\circ}\) or more between the direction from the user input, \(\vec{U}\), and the direction from the computer vision module, \(\hat{\mathcal{C}}\). The adaptive semi-autonomous control relies on the above confidence measure to arbitrate the control of the exoskeleton between the user and the computer vision module. This arbitration is performed using a linear blending [26] between the input from the user and the input from the computer vision module:  
\[\vec{E}_{x,y,z,\theta}=(1-\alpha)\vec{U}_{x,y,z,\theta}+\alpha\vec{C}_{x,y,z,\theta} \tag{2}\]  
where \(\alpha\) is the arbitration factor controlling the blending, such that the user is completely in control of the exoskeleton when \(\alpha=0\), and vice versa. \(\vec{E}_{x,y,z,\theta}\) is the output used to actuate the exoskeleton in terms of a linear velocity \(x,y,z\) and an angular velocity \(\theta\) for the wrist rotation. Only the angular movement around the wrist is considered in the above blending because the user is limited to wrist rotation only, as explained earlier in Section 3.1. Lastly, \(\vec{E}\), \(\vec{U}\), and \(\vec{C}\) are velocity vectors and hence not normalized. Finally, the arbitration factor \(\alpha\) for the adaptive semi-autonomous control is dependent on the confidence measure \(\rho\), as shown in Figure 6. The main property of the selected arbitration curve was to ensure that the confidence reached an acceptable level before providing any assistance. No assistance is provided at all until the confidence measure \(\rho>0.5\), which corresponds to an angular difference of less than 90\({}^{\circ}\) between the direction vectors from the user and the computer vision module. The selected arbitration curve is inspired by another study [26] that tested a very aggressive arbitration curve with a sudden jump in the arbitration factor against a more timid one with a gradual change. Their results indicated that the aggressive one worked well in scenarios where the task was difficult and the intent prediction was correct. However, for all other scenarios the timid arbitration curve was to be preferred in terms of task completion time and user preference. The arbitration curve for the adaptive semi-autonomous control was hence designed to be more timid with a gradual change in the arbitration factor.