AAC: An Acoustic Actor-Critic Trajectory Planning and Correction System for Stable Multi-Particle Levitation Displays

Paper Title

AAC: An Acoustic Actor-Critic Trajectory Planning and Correction System for Stable Multi-Particle Levitation Displays

Publication Info

• Topic area: Stability optimization for multi-particle acoustic levitation displays.
• Keywords: Acoustic levitation, multi-particle displays, trajectory planning, stability constraints, anomaly detection, path refinement, Actor-Critic framework, Long-Short Transformer-VAE, acoustic interference, Human-Computer Interaction.

Background and Problem

• Problem / challenge: Multi-particle acoustic levitation displays face significant stability challenges, including particle drops and positional deviations, which limit animation complexity and duration. Existing methods lack systematic guidance for stability and fail to integrate trajectory planning, anomaly detection, and correction.
• Significance: Stability is critical for reliable mid-air displays, enabling longer, more complex animations and reducing trial-and-error for designers. Improved stability enhances applications like storytelling, data physicalization, and interactive games.
• Motivation and related work: Prior work has focused on single-particle stability or acoustic feature adjustments. Multi-particle displays remain underexplored, particularly regarding trajectory optimization. Existing methods like StableLev detect instabilities but rely on manual corrections, leaving a gap in automated, closed-loop systems for trajectory planning and repair.

Solution

• Proposed approach: Acoustic Actor-Critic (AAC), a closed-loop system for trajectory planning, stability evaluation, and localized repair, following a plan-detect-repair strategy.
• Novelty:
  1. Empirical derivation of stability constraints, including a scaling law for particle count vs. velocity and a generalized minimum safe volume.
  2. Introduction of a Long-Short Transformer-VAE (LST-VAE) for anomaly detection, capturing both long-term and short-term instabilities.
  3. Closed-loop integration of trajectory planning, anomaly detection, and localized repair, automating stability optimization.
  4. Modular design applicable to diverse trajectory sources, including human-designed and motion-captured paths.
• Procedure and key techniques:
  1. Plan: Generate initial trajectories using a Conflict-Based Search planner, ensuring compliance with velocity and safe volume constraints.
  2. Detect: Evaluate trajectory stability using LST-VAE, which identifies anomalies in acoustic features (e.g., pressure amplitude, phase change) via reconstruction errors.
  3. Repair: Perform localized trajectory refinement by sampling alternative segments, selecting the most stable replacement, and integrating it into the original path.

Results

• Concrete findings:
  • Stability improved from 79% to 94% for 8-particle trajectories.
  • Anomaly detection achieved an F1 score of 0.88, with 83.3% success in repairing unstable trajectories.
  • Empirical scaling law: Maximum stable velocity (Vm) decreases with particle count (N) as Vm = 4519.97·N^-2.7294 + 20.17.
  • Minimum safe volume defined as a rectangular prism (14 mm × 14 mm × 25 mm) or an ellipsoid (14 mm × 14 mm × 28 mm).
• Advantage over baselines:
  • Outperformed StableLev’s LSTM-VAE in anomaly detection (F1 score: 0.88 vs. 0.74).
  • Automated trajectory refinement reduced manual trial-and-error and preserved visual content with minimal distortion (average path deviation: 3.8 mm).
• Experiments / evaluation:
  • Tested on 100 trajectories with 8 particles using a real acoustic levitation system.
  • Evaluated anomaly detection against baselines (LSTM-VAE, Transformer-VAE) and path refinement on detected unstable trajectories.
  • Quantified stability improvements via trajectory success rates, anomaly detection metrics, and acoustic feature analysis.
• Limitations and future work:
  • Current system is offline and not integrated with real-time content creation tools.
  • Constraints and findings are specific to the tested hardware and configurations (e.g., 8-particle limit, top-bottom levitator).
  • Future work includes real-time streaming, dynamic safe volume estimation, and adaptation to larger levitators or different media.

Summary

This paper presents AAC, a closed-loop system that enhances the stability of multi-particle acoustic levitation displays by combining empirically derived physical constraints with automated trajectory planning, anomaly detection, and localized repair. The system achieved a 15% improvement in trajectory success rates (from 79% to 94%) and demonstrated superior anomaly detection (F1 = 0.88) and repair (83.3% success). By enabling stable, minute-long animations and reducing manual corrections, AAC advances levitation displays toward practical, interactive applications. Future directions include real-time integration and adaptation to broader configurations.