# Subjective Distance Estimates and Sense of Agency in Robotic Wheelchair Control
## Experiment 1
### Materials and Methods
#### 2.1.4 Procedure  
The structure of trials in different experimental conditions is shown in the flowchart (Figure 2). The participant task in the Act condition was to travel in the robotic wheelchair in a straight line until they heard a sound signal to stop. The distance was not known to the participant beforehand and was chosen randomly for each trial from five values: 0.5 m, 1 m, 2 m, 2.5 m and 3 m. The participant started driving by holding the button on the joystick (B in Figure 1a) and tilting the joystick forward up to the limit. The participant was not able to change the direction of the wheelchair movement during the trial. Eventually, a short signal sound (the sound production was implemented as \"dzin\" text read by a text-to-speech device. \"Dzin\" is a standard phonetic imitation of a bell sound in Russian, and by using this text we intended to reproduce a primitive tone as close as possible. The duration of the sound was approximately 200 ms) alerted the participant that the distance had been covered. Figure 1: (a) A photo of the robotic wheelchair with the experimenter, here in a role of a participant. A—a touch monitor used to give distance estimates and sense of agency scores, B—a flight simulator joystick used to steer the wheelchair, C—LEDs involved in Experiment 2; (b) a participant looking at the central LED during control conditions. The exact moment of the signal sounding was not known to the participant, but the sound occurred only after the wheelchair had covered the distance. Since the sound would not have occurred if the participant had not been moving forward in the wheelchair, the sound was (counterfactually [34]) the effect of the participant's actions. According to the instructions, after the signal, the participant was to quickly release the button on the joystic and return the joystic to its initial state. If the participant did not release the button, the wheelchair would stop on its own for safety reasons, but the experimenter made sure that the participant released the button in each trial. The participant was requested to drive until the sound occurred without stopping or varying the speed of the wheelchair. In the Exp condition, it was the experimenter who stopped the wheelchair after the sound, and in the Rem mode, the wheelchair was started by a button press from a different room and stopped on its own in a preprogrammed way. In these two conditions, the subject observed what was happening without having control over the wheelchair. The wheelchair did not stop instantaneously, but with a braking path of (M \(\pm\) SD) 1.22 \(\pm\) 0.14 m in conditions with joystick control (Act, Exp) and 1.21 \(\pm\) 0.13 m when the braking was preprogrammed (Rem). After the wheelchair stopped, in every trial the participant was asked to estimate (in centimeters) the distance covered by the wheelchair from the start of movement to the sound signal onset. The participant was never informed that the distance was chosen from a set of five values. The participant was asked to avoid using spatial reference points and to make estimates based on their internal sense of motion. During wheelchair movement, the participant was asked to look at the tablet placed in front of them on a folding arm (A in Figure 1a). When the wheelchair stopped, they used the tablet to enter the estimated distance via a screen input box and screen number buttons with a backspace and enter buttons. In addition to distance estimates, in each trial we asked the participant to estimate the degree of their control over the movement of the wheelchair. The score was given on a Likert scale from 0 to 9 using the same input box. The  
Figure 2: Flowchart of the experimental procedure in different conditions. The color indicates the degree of the participant’s control over events (green—direct control, orange—no direct control).