PMGS: Reconstruction of Projectile Motion across Large Spatiotemporal Spans via 3D Gaussian Splatting

2025-08-04

AI Summary

Reconstructing high-speed, nonlinear rigid-body motion (e.g., projectiles) over large spatiotemporal scales remains challenging due to trade-offs among long-duration modeling, physical consistency, and geometric accuracy. To address this, we propose a physics-driven 3D Gaussian lattice reconstruction framework. First, we incorporate acceleration consistency constraints into SE(3) pose estimation, embedding Newtonian mechanics priors directly. Second, we design a dynamic simulated annealing strategy coupled with Kalman filtering to enhance state estimation robustness. Third, we integrate scene decomposition, adaptive point density control, and joint optimization of multi-source observation errors. Evaluated on mainstream dynamic reconstruction benchmarks, our method significantly improves reconstruction accuracy and physical plausibility for long-duration (>1 s) and high-velocity (>10 m/s) rigid-body motion. To the best of our knowledge, it is the first end-to-end rigid-motion modeling approach that simultaneously achieves high-fidelity geometric reconstruction and dynamical consistency.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Motion & Tracking
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Modeling complex rigid motion across large spatiotemporal spans remains an unresolved challenge in dynamic reconstruction. Existing paradigms are mainly confined to short-term, small-scale deformation and offer limited consideration for physical consistency. This study proposes PMGS, focusing on reconstructing Projectile Motion via 3D Gaussian Splatting. The workflow comprises two stages: 1) Target Modeling: achieving object-centralized reconstruction through dynamic scene decomposition and an improved point density control; 2) Motion Recovery: restoring full motion sequences by learning per-frame SE(3) poses. We introduce an acceleration consistency constraint to bridge Newtonian mechanics and pose estimation, and design a dynamic simulated annealing strategy that adaptively schedules learning rates based on motion states. Futhermore, we devise a Kalman fusion scheme to optimize error accumulation from multi-source observations to mitigate disturbances. Experiments show PMGS's superior performance in reconstructing high-speed nonlinear rigid motion compared to mainstream dynamic methods.

Problem

• Reconstructing projectile motion across large spatiotemporal spans
• Addressing limited physical consistency in dynamic reconstruction
• Improving accuracy in high-speed nonlinear rigid motion reconstruction

Innovation

• 3D Gaussian Splatting for projectile motion
• Dynamic scene decomposition with density control
• Kalman fusion for error optimization