Towards 3D Proprioception for Supernumerary Robotic Limbs: Design and Validation of a Mixed-Content Audio Feedback Scheme

Supernumerary robotic limbs (SRLs) are extra robotic appendages that require sensory-motor integration for intuitive control, yet most lack proprioceptive feedback. Existing approaches using vibrotactile or electrotactile cues often feel unnatural and offer limited resolution. We present a real-time spatial audio system that provides users with the 3D position of an SRL's end-effector without compromising their native motor or tactile functions. Implemented in ROS2, the system was evaluated for spatial localization error and resolution. Since SRLs are controlled through continuous motion, we prioritized dynamic performance, where the mean localization error was 14.06° in azimuth, 20.49° in elevation, and 0.078 m in distance (with a corresponding dynamic resolution of 4.42°, 2.13°, and 0.044 m). For context, the system's static spatial acuity was also high, achieving a 3AFC success rate of 93.5% in azimuth, 68.0% in elevation, and 87.0% in distance, and a static resolution of 8.43°, 2.59°, and 0.031 m. In the real robotic arm end-effector aiming test, our distance perception error was 0.137 ± 0.046 m. These results demonstrate that the proposed system provides accurate and reliable artificial proprioception for SRLs, offering a promising pathway toward more seamless control.