## 2 Methods
### Experimental Protocol  
Participants were instructed to walk 1.5 laps of a 65 m x 2.5 m corridor while wearing an head-mounted display (HMD). Each trial was split into 5 sections within 3 phases separated by turns at the ends of the corridor, as illustrated in Figure 4.  
1. Phase 1--Base section: No avatar or auditory cue is presented to the participant as they walk down the corridor wearing the HMD. 2. Phase 2--conditioned: The avatar appears after the first turn and synchronizes its steps with the participant, playing auditory cues in sync with the foot contacts of the avatar. In the middle of this phase, there is a gradual 12 s change in either the distance or phase difference between the participant and avatar. This phase can be further split into 3 sections: 1. Before--The time between the first turn and the beginning of the gradual change. 2. Change--The gradual 12 s change in either the distance or phase difference between the participant and avatar. 3. After--The time following the end of the gradual change and the beginning of the second turn. 3. Phase 3--Post section: Following the second turn, similar to the Base section, the participant walks with no avatar nor auditory cues presented while wearing the headset until the end of the corridor. Distance changes provided the spatial cues and consisted of gradual increases or decreases of 3 m between the participant and the avatar, where the initial distance was 5 m, resulting in final distances of 8 m and 2 m, respectively. Similarly, target-phase changes provided the temporal cueing and consisted of a \(\frac{\pi}{4}\)-rad difference from an initial phase difference of 0 rad. Increases and decreases in the two changing parameters resulted in four distinct conditions that were tested as follows:  
* Distance decrease (Spatial Decrease, \(S_{D}\)): This condition features a 3 m decrease in the distance between the avatar and the user from 5 m to 2 m over a 12 s period. The expected outcome is a decrease in the stride length of the user. Figure 4: Figure showing the sections and phases of each trial conducted by the participants. The phases are separated by turns at the ends of the corridor. The base section is shown before the first turn, and no avatar is shown. Phase 2 is split into before, change, and after sections in relation to the gradual change. Finally, the post section is after the final turn, with again no avatar shown. * Distance increase (Spatial Increase, \(S_{I}\)): This condition uses a gradual increase of 3 m in the distance between the avatar and the user from 5 m to 8 m over a 12 s period. The expected outcome is an increase in the stride length of the user. * Phase difference decrease (Phase Decrease, \(P_{D}\)): This condition modifies the phase difference between the user and avatar. A gradual decrease in phase difference from 0 rad to \(-\frac{\pi}{4}\) is used as the cue to the user. This difference can be seen in the avatar's step timing being slightly advanced with respect to the user's. The expected result is a decrease in the cycle time of the user's gait. * Phase difference increase (Phase Increase \(P_{I}\)): This condition modifies the phase difference between the user and the avatar. A gradual increase in phase difference from 0 rad to \(\frac{\pi}{4}\) is used as the temporal cue to the user. This difference can be seen in the avatar's step timing being slightly delayed with respect to the user's. The expected result is an increase in the cycle time of the user's gait. For each participant, each condition was randomly conducted twice. The order was counterbalanced among the participants. Two practice trials were conducted at the beginning of the experiment. The participants used the system, walking with the avatar, but there was no change in the distance or phase difference. These practice trials allowed the participants to get accustomed to using the system and walking with the avatar. Following the practice trials, two straight-line (65 m) baseline trials without the HMD were conducted to record normal gait values.