1. Bibliographic Information

1.1. Title

ManiGaussian: Dynamic Gaussian Splatting for Multi-task Robotic Manipulation

1.2. Authors

The paper is co-authored by:

• Guanxing Lu

• Shiyi Zhang

• Ziwei Wang

• Changliu Liu

• Jiwen Lu

• Yansong Tang

  Their affiliations include:

• Tsinghua University (Shenzhen Key Laboratory of Ubiquitous Data Enabling, Shenzhen International Graduate School, Department of Automation)

• Nanyang Technological University

• Carnegie Mellon University

1.3. Journal/Conference

The paper was published on arXiv, a preprint server. Its current status is $v2$, published on 2024-03-13T08:06:41.000Z. While arXiv is not a peer-reviewed journal or conference in itself, it is a widely recognized platform for rapid dissemination of research in physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics. Papers posted on arXiv often undergo subsequent peer review and publication in prestigious conferences (e.g., NeurIPS, ICCV, CoRL) or journals. Given the topic, it is likely intended for a top-tier robotics or computer vision conference.

1.4. Publication Year

2024 (specifically, March 13, 2024).

1.5. Abstract

The paper addresses the challenge of performing language-conditioned robotic manipulation tasks in unstructured environments, a critical demand for general intelligent robots. Conventional methods typically learn semantic representations for action prediction, but they often overlook scene-level spatiotemporal dynamics essential for completing human goals. To overcome this, the authors propose ManiGaussian, a dynamic Gaussian Splatting method designed for multi-task robotic manipulation. This method mines scene dynamics by reconstructing future scenes.

Specifically, ManiGaussian formulates a dynamic Gaussian Splatting framework that infers the semantics propagation within the Gaussian embedding space. This semantic representation is then used to predict optimal robot actions. To parameterize the distribution within this framework, a Gaussian world model is built, which provides informative supervision through future scene reconstruction in interactive environments. The ManiGaussian method was evaluated on 10 RLBench tasks, encompassing 166 variations. The results indicate that ManiGaussian outperforms state-of-the-art methods by 13.1% in average success rate.

1.6. Original Source Link

Official Source: https://arxiv.org/abs/2403.08321v2 PDF Link: https://arxiv.org/pdf/2403.08321v2.pdf Publication Status: Preprint on arXiv.

2. Executive Summary

2.1. Background & Motivation

The core problem the paper aims to solve is enabling robots to perform language-conditioned robotic manipulation tasks in unstructured environments. This is a crucial step towards developing general intelligent robots.

The problem is important because real-world robotic applications often involve diverse, unpredictable settings and require robots to understand and execute human instructions. Current challenges and gaps in prior research include:

• Reliance on Semantic Representation: Many conventional robotic manipulation methods focus on learning semantic representations from observations (e.g., images, point clouds, voxels) to predict actions. While effective for basic recognition, these methods often ignore scene-level spatiotemporal dynamics, which are the physical interactions and changes over time between objects during manipulation.

• Occlusion Handling: Perceptive methods (which directly use visual input) often require multi-view or gripper-mounted cameras to comprehensively cover the workspace and handle occlusion (when one object hides another), limiting their deployment in diverse unstructured environments.

• Lack of Dynamics Understanding in Generative Models: Generative methods (which reconstruct 3D scene structures) capture geometric information well but frequently fail to comprehend spatiotemporal dynamics. This leads to incorrect object interactions and subsequent task failures, even with accurate scene reconstruction. For example, a robot might understand the visual layout but fail to predict how objects will move or react when manipulated, leading to picking up the wrong part of an object or performing an ineffective action.

• Data Intensive World Models: While world models have shown promise in encoding scene dynamics by predicting future states, learning accurate future predictions in latent spaces can be data-intensive and limited to simpler tasks due to weak implicit feature representation.

  The paper's entry point or innovative idea is to explicitly model scene dynamics by integrating a dynamic Gaussian Splatting framework with a world model that reconstructs future scenes. By representing scenes as dynamic Gaussian primitives that propagate over time, the method can capture the physical interactions between objects, thereby improving action prediction for complex manipulation tasks.

2.2. Main Contributions / Findings

The primary contributions of this paper are:

• Dynamic Gaussian Splatting Framework: The authors propose ManiGaussian, a novel dynamic Gaussian Splatting framework tailored for robotic manipulation. This framework models the propagation of diverse semantic features within a Gaussian embedding space, explicitly learning scene-level spatiotemporal dynamics crucial for accurate action prediction in unstructured environments.

• Gaussian World Model: They introduce a Gaussian world model that parameterizes the distributions within the dynamic Gaussian Splatting framework. This world model provides informative supervision by reconstructing future scenes based on current observations and robot actions, enforcing consistency between predicted and realistic future scenes to effectively mine scene dynamics.

• Superior Performance on RLBench: ManiGaussian was rigorously evaluated on 10 challenging RLBench tasks (with 166 variations). The results demonstrate that the proposed method achieves a state-of-the-art average success rate, outperforming existing methods by 13.1%.

• Efficiency: The method not only performs better but also trains faster, achieving 1.18x better performance and 2.29x faster training compared to GNFactor, indicating the efficiency of explicit Gaussian scene reconstruction over implicit approaches like NeRF.

  These findings collectively address the limitation of previous methods that neglect scene dynamics, leading to a more robust and effective robotic manipulation agent capable of comprehending physical interactions and completing complex human goals.

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

Robotic Manipulation

Robotic manipulation refers to the field of robotics concerned with controlling robot arms or manipulators to interact with objects in a physical environment. This often involves tasks like picking and placing, assembly, tool use, and rearrangement. The goal is to enable robots to perform these tasks autonomously, often based on sensory input and high-level instructions.

Language-Conditioned Tasks

In language-conditioned tasks, robots receive instructions in natural language (e.g., "stack the red block on the blue block," "open the drawer"). The robot must then parse these instructions, understand the desired goal, and translate them into a sequence of physical actions. This requires a robust vision-language understanding component that links linguistic commands to visual perceptions and robotic actions.

Gaussian Splatting

Gaussian Splatting (GS) is a novel 3D scene representation and rendering technique introduced by Kerbl et al. (2023). Unlike Neural Radiance Fields (NeRF) which use implicit neural representations, GS explicitly models a 3D scene as a collection of 3D Gaussian primitives. Each Gaussian is defined by parameters such as its position (mean), covariance (scale and rotation), color, and opacity.

When rendering a novel view, these 3D Gaussians are projected onto a 2D image plane. The colors and opacities of overlapping Gaussians are then blended using an alpha-blending process to form the final pixel color. The key advantages of GS include:

• High Fidelity: Produces high-quality, photorealistic renderings.
• Fast Rendering: Achieves real-time rendering speeds, significantly faster than traditional NeRF methods.
• Editability: The explicit representation of Gaussians makes it easier to edit and manipulate scene elements.

Neural Radiance Fields (NeRF)

Neural Radiance Fields (NeRF) (Mildenhall et al., 2021) is an implicit 3D scene representation technique. It uses a multi-layer perceptron (MLP) to map 3D coordinates (x, y, z) and viewing direction $(\theta, \phi)$ to a color (RGB) and volume density value. To render an image from a novel viewpoint, rays are cast through the pixels, and points along each ray are sampled. The MLP then predicts color and density for these points, which are integrated using volume rendering techniques to produce the final pixel color. While NeRF produces highly photorealistic novel views, it is typically slow to render and train compared to Gaussian Splatting.

World Models

A world model in reinforcement learning and robotics is a computational model that learns to simulate the dynamics of an environment. Given a current state and an action, the world model predicts the next state and potentially the reward. By learning an internal model of the world, an agent can plan actions by mentally simulating their consequences without needing to interact with the real environment. This can significantly improve sample efficiency and enable agents to learn complex behaviors. World models often comprise a representation network to encode observations into a latent state, a dynamics model to predict future latent states, and a reconstruction model to decode latent states back into observable forms (e.g., images).

PerceiverIO

PerceiverIO (Jaegle et al., 2021) is a transformer-based architecture designed for general perception across various modalities and tasks. It addresses the quadratic complexity of standard transformers with respect to input size by using a latent bottleneck. Instead of attending over all input tokens directly, PerceiverIO projects high-dimensional inputs (e.g., images, audio, video) into a much smaller, fixed-size latent array. This latent array then cross-attends to the original input and self-attends among its own elements. The output is generated by cross-attending from the latent array to a task-specific query. This architecture allows PerceiverIO to handle diverse and very large inputs efficiently, making it suitable for multi-modal problems like robotic manipulation where visual inputs are combined with language instructions.

3.2. Previous Works

The paper categorizes previous works into three main areas: Visual Representations for Robotic Manipulation (further divided into perceptive and generative methods), World Models, and Gaussian Splatting.

Visual Representations for Robotic Manipulation

Perceptive Methods

These methods directly extract semantic features from visual inputs (2D images, 3D point clouds, or voxels) to predict robot actions.

• 2D Vision: InstructRL [40] and Hiveformer [15] use 2D visual tokens with multi-modal transformers for gripper action decoding. They struggle with complex tasks due to a lack of geometric understanding.
• 3D Vision (Point Clouds): PolarNet [7] used a PointNeXt [49]-based architecture, and Act3D [13] designed a ghost point sampling mechanism to decode actions from point cloud representations.
• 3D Vision (Voxels): PerAct [60] fed voxel tokens into a PerceiverIO [26]-based transformer policy, showing strong performance.
• Limitation: Perceptive methods heavily rely on seamless camera overlay for comprehensive 3D understanding, limiting their effectiveness in unstructured environments with occlusions.

Generative Methods

These methods learn 3D geometry through self-supervised novel view reconstruction, aiming to capture scene structure.

• Li et al. [36] combined NeRF and time contrastive learning to embed 3D geometry and fluid dynamics within an autoencoder.
• GNFactor [76] optimized a generalizable NeRF with a reconstruction loss and behavior cloning, improving performance in simulated and real scenarios.
• Limitation: Conventional generative methods, including GNFactor, typically ignore scene-level spatiotemporal dynamics (how objects interact physically), leading to failed actions due to incorrect interaction understanding.

World Models

World models predict future states based on current state and actions, encoding scene dynamics.

• Early Works: Dreamer [18, 19, 20] and related works [16, 21, 54, 55, 73] learned latent spaces for future prediction through autoencoding. While effective in some tasks, they require large amounts of data and have weak representative ability for complex tasks.
• Explicit Representations:
  • Image Domain: UniPi [9] reconstructed future images using a text-conditional video generation model and inverse dynamics.
  • Language Domain: Dynalang [38] predicted future text representations for navigation.
• Differentiation: ManiGaussian generalizes the world model concept to the embedding space of dynamic Gaussian Splatting, predicting future states in a richer, more explicit representation for learning scene-level dynamics.

Gaussian Splatting

Gaussian Splatting (GS) [32] models scenes with 3D Gaussians for efficient novel view synthesis, outperforming NeRF in speed and fidelity.

• Generalization: Works like PixelSplat [4] and COLMAP-Free 3D Gaussian Splatting [10] aim for higher generalization across diverse scenes.
• Semantic Information: LangSplat [50], Feature 3DGS [81], and FMGS [84] integrate semantic information by distilling features from foundation models like CLIP [51] or Stable Diffusion [53].
• Deformable Scenes / Dynamic GS: Time-variant Gaussian radiance fields [1, 37, 44, 66, 69, 71, 72] reconstruct from videos to model deformation. Luiten et al. [44] proposed Dynamic 3D Gaussians for tracking.
• Differentiation: While existing dynamic GS focuses on reconstruction from past videos, ManiGaussian extends this to extrapolation to future states conditioned on previous states and actions, which is crucial for scene-level dynamics modeling for interactive agents.

3.3. Technological Evolution

The evolution of visual representations for robotic manipulation has moved from simple 2D image processing to sophisticated 3D scene understanding. Initially, methods relied on 2D visual features for action prediction, but these proved insufficient for complex tasks requiring geometric reasoning. The introduction of 3D representations like point clouds and voxels marked a significant step, enabling better spatial understanding. However, these perceptive methods still faced issues with occlusion and the need for extensive camera setups.

The rise of generative methods, particularly those based on implicit representations like NeRF, allowed for the reconstruction of full 3D scenes from limited views. This offered an advantage in handling occlusions and learning generalizable 3D geometry. However, NeRF-based approaches were computationally intensive for rendering and often lacked an explicit understanding of spatiotemporal dynamics—how objects physically interact and change over time under manipulation.

More recently, Gaussian Splatting emerged as a powerful alternative to NeRF, offering superior rendering speed and quality with an explicit representation that is more amenable to editing and manipulation. Concurrently, world models gained prominence, providing a framework for agents to learn and predict environmental dynamics.

This paper's work (ManiGaussian) fits within this timeline by addressing the limitations of prior generative methods. It leverages the efficiency and explicit nature of Gaussian Splatting and combines it with the predictive power of a world model. By making the Gaussian representation dynamic and using a world model to reconstruct future scenes in the Gaussian embedding space, ManiGaussian explicitly learns the scene-level spatiotemporal dynamics that were previously ignored, enabling more robust and accurate action prediction.

3.4. Differentiation Analysis

Compared to the main methods in related work, ManiGaussian offers several core differences and innovations:

• Explicit Scene Dynamics Modeling: The most significant innovation is its explicit focus on learning scene-level spatiotemporal dynamics.

  • Perceptive methods (e.g., PerAct) focus on semantic feature extraction for action prediction but lack 3D geometric and dynamic understanding.
  • Generative methods (e.g., GNFactor based on NeRF) reconstruct 3D geometry well but largely ignore object interactions and how scenes evolve physically. ManiGaussian directly addresses this by formulating dynamic Gaussian Splatting where Gaussian primitives (representing objects/parts) can move and rotate over time, reflecting physical interactions.

• Dynamic Gaussian Splatting Framework:

  • While Gaussian Splatting [32] and its dynamic variants [44, 66] exist for reconstruction, ManiGaussian is the first to formulate it specifically for robotic manipulation by modeling the propagation of diverse semantic features in the Gaussian embedding space. It extends vanilla GS by enabling Gaussian primitives to move and rotate in response to robot actions, which represents physical interaction.
  • Crucially, ManiGaussian uses this dynamic representation not just for interpolation (reconstructing observed dynamic scenes) but for extrapolation (predicting future states conditioned on actions), which is vital for interactive agents.

• Gaussian World Model for Dynamics Mining:

  • Existing world models (e.g., Dreamer, UniPi) typically operate in implicit latent spaces or image/language domains. ManiGaussian introduces a novel Gaussian world model that parameterizes the dynamic Gaussian Splatting framework directly.
  • This world model learns environmental dynamics by predicting future Gaussian parameters (positions, rotations) based on current scene state and robot actions. It then enforces consistency between the reconstructed future scene (from predicted Gaussians) and the realistic future scene, providing a powerful, explicit supervision signal for learning dynamics.

• Integration of Geometric, Semantic, and Dynamic Information:

  • ManiGaussian integrates geometric information (from Gaussian positions, scales), semantic information (distilled from foundation models like Stable Diffusion into Gaussian features), and dynamic information (from the deformation predictor and future scene consistency) into a unified representation. This holistic representation, unlike previous methods that might focus on one or two aspects, allows for more comprehensive scene understanding and action prediction.

  • The use of PerceiverIO as an action decoder leverages this rich, multi-modal representation effectively.

    In essence, ManiGaussian innovates by creating an explicit, dynamic, and physically grounded 3D scene representation using Gaussian Splatting and then training a world model on this representation to predict how the scene will evolve under robotic actions, thereby mastering scene-level spatiotemporal dynamics for manipulation.

4. Methodology

4.1. Principles

The core idea behind ManiGaussian is to explicitly model scene-level spatiotemporal dynamics for robotic manipulation tasks. The intuition is that for a robot to effectively interact with objects and complete complex instructions, it must not only understand the static appearance and geometry of the scene but also predict how objects will move and interact physically when acted upon.

ManiGaussian achieves this by extending Gaussian Splatting into a dynamic framework. Instead of treating the 3D Gaussians as static scene primitives, ManiGaussian allows them to propagate (change positions and rotations) over time, reflecting the movement and interaction of objects during manipulation. This dynamic representation is then learned and controlled by a Gaussian world model. The world model predicts the future state of these dynamic Gaussians based on current observations and robot actions. By comparing the reconstructed future scene (from predicted Gaussians) with the actual future scene, the model receives informative supervision to learn the underlying physical dynamics. This allows the robot to acquire a robust understanding of geometric, semantic, and dynamic properties of the scene, which are then used by an action decoder (PerceiverIO) to predict optimal manipulation actions.

4.2. Core Methodology In-depth (Layer by Layer)

4.2.1. Problem Formulation

The paper frames the language-conditioned robotic manipulation task as predicting robot arm poses based on observations to complete human instructions.

The visual input at the $t$-th step is defined as $o^{(t)} = (\mathbf{C}^{(t)}, \mathbf{D}^{(t)}, \mathbf{P}^{(t)})$.

• $\mathbf{C}^{(t)}$: Single-view RGB images (color information).

• $\mathbf{D}^{(t)}$: Depth images (distance information, crucial for 3D reconstruction).

• $\mathbf{P}^{(t)} \in \mathbb{R}^4$: Proprioception matrix, which includes the gripper state (end-effector position, openness) and the current timestep.

  Based on this visual input $o^{(t)}$ and language instructions, the agent needs to generate an optimal action $\mathbf{a}^{(t)}$. This action is discretized into several components:

• $\mathbf{a}_{\mathrm{trans}}^{(t)} \in \mathbb{R}^{100^3}$: Translation (position) action, typically represented as a discretized 3D grid, where each cell corresponds to a possible target 3D position for the gripper. The $100^3$ indicates a $100 \times 100 \times 100$ voxel grid.

• $\mathbf{a}_{\mathrm{rot}}^{(t)} \in \mathbb{R}^{(360/5) \times 3}$: Rotation action, represented as discretized rotations around three axes (e.g., yaw, pitch, roll), with $360/5 = 72$ discrete orientations for each axis, totaling $72^3$ possibilities.

• $\mathbf{a}_{\mathrm{open}}^{(t)} \in [0, 1]$: Gripper openness, a scalar indicating how open or closed the gripper should be.

• $\mathbf{a}_{\mathrm{col}}^{(t)} \in [0, 1]$: Collision avoidance, a binary or continuous value indicating a collision-aware action.

  Expert demonstrations provide offline datasets containing triplets of (visual input, language instruction, expert actions) for imitation learning. The goal is to predict these optimal actions while overcoming the limitations of prior methods in understanding spatiotemporal dynamics.

4.2.2. Overall Pipeline

The ManiGaussian pipeline (illustrated in Figure 2) consists of two main components: a dynamic Gaussian Splatting framework and a Gaussian world model.

The overall pipeline of ManiGaussian is shown in Figure 2:

该图像是论文中图2的示意图，展示了ManiGaussian整体框架，包含动态高斯散点动态传播与高斯世界模型。高斯混合物通过变形场预测位置与旋转，未来场景重建提供监督，促进场景级动态挖掘。

• Data Preprocessing: Visual input from RGB-D cameras is transformed into a volumetric representation through lifting (converting 2D pixels to 3D points) and voxelization (discretizing the 3D space into a grid of voxels).
• Dynamic Gaussian Splatting Framework:
  • A Gaussian regressor infers the Gaussian distribution of geometric and semantic features based on the volumetric representation.
  • These Gaussians are then propagated along time steps, capturing rich scene-level spatiotemporal dynamics. This propagation models how objects (represented by Gaussians) move and interact.
• Gaussian World Model:
  • This model instantiates a deformation field that reconstructs the future scene by predicting changes in Gaussian parameters based on the current scene and the robot actions.
  • It enforces consistency between the reconstructed and realistic future scenes to mine scene dynamics. This means the representation learned by the dynamic Gaussian Splatting framework now encodes the object correlations and physical properties.
• Action Prediction: A multi-modal transformer (PerceiverIO) takes the learned geometric, semantic, and dynamic information (from the dynamic Gaussian Splatting framework) along with human instructions to predict the optimal robot actions.

4.2.3. Dynamic Gaussian Splatting for Robotic Manipulation

The paper adapts the vanilla Gaussian Splatting to capture scene-level dynamics.

Vanilla Gaussian Splatting

In vanilla Gaussian Splatting [32], a 3D scene is represented by $N$ Gaussian primitives. The $i$-th Gaussian is parameterized by $\theta_i = (\mu_i, c_i, r_i, s_i, \sigma_i)$.

• $\mu_i$: Position (3D mean) of the Gaussian.

• $c_i$: Color of the Gaussian (e.g., an RGB value or coefficients for spherical harmonics).

• $r_i$: Rotation (e.g., quaternion) of the Gaussian.

• $s_i$: Scale (e.g., 3D vector for semi-axes lengths) of the Gaussian.

• $\sigma_i$: Opacity of the Gaussian.

  To render a pixel $\mathbf{p}$ in a novel 2D view, the Gaussians are projected onto the 2D plane and blended using alpha-blending. The rendered color $C(\mathbf{p})$ is given by: $$C(\mathbf{p}) = \sum_{i=1}^N \alpha_i c_i \prod_{j=1}^{i-1} (1 - \alpha_j) \quad { \mathrm{ ~ where, ~ } } \alpha_i = \sigma_i e^{-{\frac{1}{2}} \left( \mathbf{p} - { \boldsymbol{\mu}_i} \right)^T { \boldsymbol{\Sigma}}_i^{-1} \left( \mathbf{p} - { \boldsymbol{\mu}_i} \right)}$$

• $C(\mathbf{p})$: The rendered color at pixel $\mathbf{p}$.

• $N$: The number of Gaussians in the tile contributing to pixel $\mathbf{p}$.

• $\alpha_i$: The 2D density (or alpha value) of the $i$-th Gaussian at pixel $\mathbf{p}$ in the splatting process. It's calculated based on its opacity $\sigma_i$ and a 2D Gaussian function.

• $c_i$: The color of the $i$-th Gaussian.

• $\mathbf{p}$: The 2D projection of the Gaussian's mean onto the image plane.

• $\boldsymbol{\Sigma}_i$: The 2D covariance matrix of the $i$-th Gaussian, derived from its 3D rotation $r_i$ and scale $s_i$.

• $\prod_{j=1}^{i-1} (1 - \alpha_j)$: This term accounts for the transparency of Gaussians farther away, ensuring correct alpha-blending order (typically front-to-back).

  Vanilla Gaussian Splatting struggles with dynamic scenes. ManiGaussian extends this by enabling the Gaussian primitives to move over time to capture spatiotemporal dynamics.

Dynamic Gaussian Splatting

The parameters of the $i$-th Gaussian primitive at the $t$-th step are extended to include semantic features: $$\boldsymbol{\theta}_i^{(t)} = (\mu_i^{(t)}, c_i^{(t)}, r_i^{(t)}, s_i^{(t)}, \sigma_i^{(t)}, f_i^{(t)})$$

• $\mu_i^{(t)}$: Position at time $t$.

• $c_i^{(t)}$: Color at time $t$.

• $r_i^{(t)}$: Rotation at time $t$.

• $s_i^{(t)}$: Scale at time $t$.

• $\sigma_i^{(t)}$: Opacity at time $t$.

• $f_i^{(t)}$: High-level semantic feature for the $i$-th Gaussian at time $t$, distilled from a visual encoder (e.g., Stable Diffusion [53]) based on RGB images.

  For robotic manipulation, objects are typically treated as rigid bodies. This implies that their intrinsic properties like colors ($c_i$), scales ($s_i$), opacities ($\sigma_i$), and semantic features ($f_i$) are considered time-independent. The changes during manipulation primarily affect their positions and rotations due to physical interactions with the robot gripper. These changes are formulated as: $$(\mu_i^{(t+1)}, r_i^{(t+1)}) = (\mu_i^{(t)} + \Delta\mu_i^{(t)}, r_i^{(t)} + \Delta r_i^{(t)})$$

• $\mu_i^{(t+1)}$: Position of the $i$-th Gaussian at the next step $t+1$.

• $r_i^{(t+1)}$: Rotation of the $i$-th Gaussian at the next step $t+1$.

• $\Delta\mu_i^{(t)}$: The change in position from step $t$ to $t+1$ for the $i$-th Gaussian primitive.

• $\Delta r_i^{(t)}$: The change in rotation from step $t$ to $t+1$ for the $i$-th Gaussian primitive.

  With these time-dependent position and rotation parameters, the pixel values in 2D views can still be rendered using the alpha-blend rendering formula (Equation 1), but now reflecting the dynamic state of the scene.

4.2.4. Gaussian World Model

The Gaussian world model is responsible for parameterizing the Gaussian mixture distribution in the dynamic Gaussian Splatting framework. Its primary role is to enable future scene reconstruction via parameter propagation, providing informative supervision by ensuring consistency between reconstructed and realistic future scenes.

The Gaussian world model consists of four key components:

1. Representation Network ($q_\phi$): Learns high-level visual features with rich semantics from the input observation.

2. Gaussian Regressor ($g_\phi$): Predicts the Gaussian parameters of different primitives based on these visual features.

3. Deformation Predictor ($p_\phi$): Infers the changes (difference) in Gaussian parameters (specifically positions and rotations) during propagation from one time step to the next.

4. Gaussian Renderer ($\mathcal{R}$): Generates RGB images for the predicted future state using the propagated Gaussian parameters (as described in Equation 1).

   The process within the Gaussian world model is summarized by the following system of equations: $$\left\{ \begin{array}{ll} \mathrm{Representation ~ model:} & {\mathbf{v}^{(t)} = q_\phi \left( o^{(t)} \right),} \\ \mathrm{Gaussian ~ regressor:} & {\theta^{(t)} = g_\phi \left( \mathbf{v}^{(t)} \right),} \\ \mathrm{Deformation ~ predictor:} & {\Delta\theta^{(t)} = p_\phi \left( \theta^{(t)}, a^{(t)} \right),} \\ \mathrm{Gaussian ~ renderer:} & {o^{(t+1)} = \mathcal{R} \left( \theta^{(t+1)}, w \right),} \end{array} \right.$$

• $o^{(t)}$: The visual observation at the $t$-th step.

• $\mathbf{v}^{(t)}$: The high-level visual features extracted by the representation network $q_\phi$ from $o^{(t)}$.

• $\theta^{(t)}$: The Gaussian parameters (e.g., positions, rotations, colors, scales, opacities, semantic features) predicted by the Gaussian regressor $g_\phi$ from $\mathbf{v}^{(t)}$.

• $a^{(t)}$: The robot action taken at the $t$-th step.

• $\Delta\theta^{(t)}$: The change in Gaussian parameters (specifically $\Delta\mu_i^{(t)}$ and $\Delta r_i^{(t)}$ for all $i$ Gaussians, combined as $\Delta\theta^{(t)}$ for simplicity in this equation) predicted by the deformation predictor $p_\phi$ based on current Gaussian parameters $\theta^{(t)}$ and action $a^{(t)}$. This $\Delta\theta^{(t)}$ is then used to update $\theta^{(t)}$ to $\theta^{(t+1)}$ (as per Equation 3).

• $\theta^{(t+1)}$: The propagated Gaussian parameters for the future step $t+1$.

• $o^{(t+1)}$: The predicted future visual scene rendered by the Gaussian renderer $\mathcal{R}$ using $\theta^{(t+1)}$.

• $w$: The camera pose for the view from which the Gaussians are projected.

  The Gaussian regressor is implemented as a multi-head neural network, where each head is specialized to predict a specific component of the Gaussian parameters (position, color, rotation, scale, opacity, semantic feature). The deformation predictor infers changes in positions and rotations, allowing for the calculation of propagated Gaussian parameters for the next step. The Gaussian renderer then projects these propagated Gaussians into a specified view to reconstruct the future scene.

4.2.5. Learning Objectives

The ManiGaussian agent is trained using a combination of four loss terms, ensuring consistency in current scene reconstruction, semantic features, action prediction, and future scene prediction.

Current Scene Consistency Loss

This loss ensures that the Gaussian regressor accurately reconstructs the current scene based on the current Gaussian parameters. It compares the ground truth observed image with the image rendered from the predicted current Gaussians. $$\mathcal{L}_{\mathrm{Geo}} = \| \mathbf{C}^{(t)} - \hat{\mathbf{C}}^{(t)} \|_2^2$$

• $\mathcal{L}_{\mathrm{Geo}}$: The geometric consistency loss.
• $\mathbf{C}^{(t)}$: The ground truth observation image from a specific view at step $t$.
• $\hat{\mathbf{C}}^{(t)}$: The predicted observation image rendered from the current Gaussian parameters $\theta^{(t)}$ (output of $g_\phi$) at step $t$.
• $\|\cdot\|_2^2$: The squared L2 norm, measuring the pixel-wise difference between the images.

Semantic Feature Consistency Loss

This loss distills knowledge from large pre-trained foundation models (e.g., Stable Diffusion) into the Gaussian parameters' semantic features. It enforces that the projected semantic features from the Gaussians mimic those extracted by the pre-trained model. $$\mathcal{L}_{\mathrm{Sem}} = 1 - \sigma_{\mathrm{cos}} (\mathbf{F}^{(t)}, \hat{\mathbf{F}}^{(t)})$$

• $\mathcal{L}_{\mathrm{Sem}}$: The semantic feature consistency loss.
• $\mathbf{F}^{(t)}$: The feature map extracted by a pre-trained foundation model from the ground truth image $\mathbf{C}^{(t)}$.
• $\hat{\mathbf{F}}^{(t)}$: The projected map of semantic features from the Gaussian parameters $f_i^{(t)}$ (part of $\theta^{(t)}$).
• $\sigma_{\mathrm{cos}}(\cdot, \cdot)$: The cosine similarity function, which measures the cosine of the angle between two vectors, indicating their similarity. A value of 1 means perfect similarity. The loss aims to minimize $1 - \text{cosine similarity}$, so that maximizing similarity minimizes the loss.

Action Prediction Loss

This loss guides the PerceiverIO action decoder to predict the optimal robot actions. It uses cross-entropy to compare the predicted action probabilities with the ground truth actions from expert demonstrations. $$\mathcal{L}_{\mathrm{Act}} = CE(p_{\mathrm{trans}}, p_{\mathrm{rot}}, p_{\mathrm{open}}, p_{\mathrm{col}})$$

• $\mathcal{L}_{\mathrm{Act}}$: The action prediction loss.
• $CE(\cdot)$: The cross-entropy loss function, typically used for classification tasks.
• $p_{\mathrm{trans}}$: The probability distribution over possible translation actions (e.g., target voxel) predicted by the model, or the probability of the ground truth translation action.
• $p_{\mathrm{rot}}$: The probability distribution over possible rotation actions, or the probability of the ground truth rotation action.
• $p_{\mathrm{open}}$: The probability distribution over possible gripper openness states, or the probability of the ground truth openness action.
• $p_{\mathrm{col}}$: The probability distribution over collision avoidance states, or the probability of the ground truth collision avoidance action. This loss is applied to the output of the action decoder, which takes the Gaussian parameters and human instructions as input.

Future Scene Consistency Loss

This is a critical loss for dynamics mining. It enforces consistency between the predicted future scene (rendered from propagated Gaussians) and the actual observed future scene. $$\mathcal{L}_{\mathrm{Dyna}} = \Vert \hat{\mathbf{C}}^{(t+1)} (a^{(t)}, o^{(t)}) - \mathbf{C}^{(t+1)} \Vert_2^2$$

• $\mathcal{L}_{\mathrm{Dyna}}$: The dynamic consistency loss or future scene consistency loss.
• $\hat{\mathbf{C}}^{(t+1)}(a^{(t)}, o^{(t)})$: The predicted future image of the scene at step $t+1$. This image is rendered by the Gaussian renderer using the future Gaussian parameters $\theta^{(t+1)}$ that were propagated from $\theta^{(t)}$ using action $a^{(t)}$ (as defined in Equation 4).
• $\mathbf{C}^{(t+1)}$: The ground truth realistic observation image at the next step $t+1$.
• $\|\cdot\|_2^2$: The squared L2 norm, measuring the pixel-wise difference. By minimizing this loss, the model is compelled to encode the physical properties and dynamics of the scene into its representation, allowing the action decoder to predict more effective actions.

Overall Objective

The overall objective function for training ManiGaussian is a weighted sum of these four loss terms: $$\mathcal{L} = \mathcal{L}_{\mathrm{Act}} + \lambda_{\mathrm{Geo}} \mathcal{L}_{\mathrm{Geo}} + \lambda_{\mathrm{Sem}} \mathcal{L}_{\mathrm{Sem}} + \lambda_{\mathrm{Dyna}} \mathcal{L}_{\mathrm{Dyna}}$$

• $\mathcal{L}$: The total loss to be minimized during training.
• $\mathcal{L}_{\mathrm{Act}}$: Action prediction loss.
• $\mathcal{L}_{\mathrm{Geo}}$: Geometric consistency loss.
• $\mathcal{L}_{\mathrm{Sem}}$: Semantic feature consistency loss.
• $\mathcal{L}_{\mathrm{Dyna}}$: Dynamic consistency loss.
• $\lambda_{\mathrm{Geo}}, \lambda_{\mathrm{Sem}}, \lambda_{\mathrm{Dyna}}$: Hyperparameters that control the relative importance of the geometric, semantic, and dynamic loss terms, respectively. These are tuned during training to balance the different objectives.

Training Procedure: The training process involves a warm-up phase during the first 3,000 iterations. In this phase, the deformation predictor ($p_\phi$) is frozen, allowing the representation network ($q_\phi$) and the Gaussian regressor ($g_\phi$) to learn a stable initial representation. After the warm-up, the entire Gaussian world model (including the deformation predictor) and the action decoder are jointly trained.

5. Experimental Setup

5.1. Datasets

The experiments are conducted using the RLBench [27] simulated task suite.

• Curated Subset: A subset of 10 challenging language-conditioned manipulation tasks was selected from RLBench.
• Variations: These 10 tasks include 166 variations in object properties (e.g., colors, sizes, counts) and scene arrangement.
  • Color Palette: 20 shades are used (red, maroon, lime, green, blue, navy, yellow, cyan, magenta, silver, gray, orange, olive, purple, teal, azure, violet, rose, black, white).
  • Object Size: Two types: short and tall.
  • Object Count: 1, 2, or 3 objects.
  • Placement: Objects are randomly arranged on the tabletop within a certain range.
  • Task-specific variations: Other properties vary based on the task (e.g., category for "meat off grill", keyframes for stack blocks).
• Goal: The diversity of tasks requires agents to acquire generalizable knowledge about intrinsical scene-level spatial-temporal dynamics rather than just mimicking demonstrations.
• Visual Observation:
  • RGB-D images are captured by a single front camera.
  • Resolution: $128 \times 128$.
  • For fair comparison with GNFactor, 20 cameras are used to provide multi-view supervision during training, but inference uses a single front camera.
• Training Data: 20 expert demonstrations are used for each task during the training phase.
• Task Classification (for Ablation Study): The 10 RLBench tasks are grouped into 6 categories based on their main challenges, following [15]:

  • Planning Group: Tasks with multiple subtasks (e.g., "meat off grill", "push buttons").

  • Long Group: Long-term tasks requiring more than 10 keyframes (e.g., "put in drawer", "stack blocks").

  • Tools Group: Tasks requiring grasping an object to interact with a target object (e.g., "slide block", "drag stick", "sweep to dustpan").

  • Motion Group: Tasks requiring precise control, often challenging due to predefined motion planners (e.g., "turn tap").

  • Screw Group: Tasks requiring gripper rotation to screw an object (e.g., "close jar").

  • Occlusion Group: Tasks with severe occlusion problems from certain views (e.g., "open drawer").

    The following are the selected tasks from Table 3 of the original paper:

    Task	Type	Variations	Keyframes	Instruction Template
    close jar	color	20	6.0	"close the _ jar"
    open drawer	placement	3	3.0	"open the _ drawer"
    sweep to dustpan	size	2	4.6	"sweep dirt to the _ dustpan"
    meat off grill	category	2	5.0	"take the _ off the grill"
    turn tap	placement	2	2.0	“turn _ tap"
    slide block	color	4	4.7	"slide the block to _ target"
    put in drawer	placement	3	12.0	"put the item in the _ drawer"
    drag stick	color	20	6.0	"use the stick to drag the cube onto the _ target"
    push buttons	color	50	3.8	"push the _ button, [then the _ button]"
    stack blocks	color, count	60	14.6	"stack blocks"

5.2. Evaluation Metrics

The primary evaluation metric used is the task success rate.

• Conceptual Definition: The task success rate quantifies the percentage of completed episodes out of the total number of evaluation episodes. An episode is considered successful if the robot agent achieves the goal specified in natural language within a predefined maximum number of steps (25 steps in this case). This metric directly measures the overall effectiveness and reliability of the robotic manipulation policy.
• Mathematical Formula: The task success rate is calculated as: $ \text{Success Rate} = \frac{\text{Number of Successful Episodes}}{\text{Total Number of Evaluation Episodes}} \times 100% $
• Symbol Explanation:

  • Number of Successful Episodes: The count of episodes where the robot successfully completes the task as defined by the language instruction and within the step limit.

  • Total Number of Evaluation Episodes: The total number of episodes the robot was tested on.

  • $100\%$: Conversion factor to express the rate as a percentage.

    For evaluation, 25 episodes are tested for each task to ensure statistical reliability and avoid bias.

5.3. Baselines

The paper compares ManiGaussian against state-of-the-art methods representing both perceptive and generative approaches:

• PerAct [60]: A prominent perceptive method that feeds voxel tokens into a PerceiverIO-based transformer policy. This baseline represents the cutting edge in directly learning from 3D visual input.

• PerAct (4 cameras): A modified version of PerAct that uses 4 camera inputs to achieve better coverage of the workbench, addressing one of the key limitations of single-camera perceptive methods. This helps to gauge the impact of increased visual information for perceptive models.

• GNFactor [76]: A state-of-the-art generative method that optimizes a generalizable NeRF representation. It learns informative latent representations for action prediction by reconstructing 3D scenes. This baseline is particularly relevant as it shares the generative approach of 3D scene representation but ManiGaussian argues that it lacks explicit scene dynamics understanding.

  These baselines are representative because they cover the two main paradigms (perceptive and generative) in general manipulation policy learning and include methods that have shown strong performance on RLBench tasks.

5.4. Implementation Details

• Data Augmentation: $SE(3)$ [60, 76] augmentation is applied to expert demonstrations in the training set to enhance the generalizability of the agents. $SE(3)$ refers to the special Euclidean group, representing rigid body transformations (rotations and translations) in 3D space.

• Action Decoder: The PerceiverIO [26] multi-modal transformer is used as the action decoder across all baselines for a fair comparison, ensuring that performance differences are due to the scene representation and dynamics modeling, not the action prediction architecture itself.

• Computational Resources: Training is performed on two NVIDIA RTX 4090 GPUs.

• Training Iterations: 100,000 iterations.

• Batch Size: 2.

• Optimizer: LAMB optimizer [74].

• Learning Rate: Initial learning rate of $5 \times 10^{-4}$.

• Scheduler: A cosine scheduler with a warm-up phase for the first 3,000 steps.

• Loss Hyperparameters:

  • $\lambda_{\mathrm{Geo}} = 0.01$
  • $\lambda_{\mathrm{Sem}} = 0.0001$
  • $\lambda_{\mathrm{Dyna}} = 0.001$ These values are chosen to prioritize action prediction ($\mathcal{L}_{\mathrm{Act}}$ has an implicit weight of 1) while balancing the contributions of geometric, semantic, and dynamic consistency.

• Image Resolution: $128 \times 128$.

• Voxel Resolution: $100 \times 100 \times 100$ (for the volumetric representation).

• Number of Gaussian points: 16,384.

  The following are the hyperparameters from Table 4 of the original paper:

  Hyperparameter	Value
  training iteration	100k
  image resolution	128 × 128
  voxel resolution	100 × 100 × 100
  batch size	2
  optimizer	LAMB
  learning rate	0.0005
  weight decay	0.000001
  Number of Gaussian points	16384
  $\lambda_{\mathrm{Geo}}$	0.01
  $\lambda_{\mathrm{Sem}}$	0.0001
  $\lambda_{\mathrm{Dyna}}$	0.001

6. Results & Analysis

6.1. Core Results Analysis

The experimental results demonstrate that ManiGaussian significantly outperforms state-of-the-art methods in multi-task robotic manipulation. On the RLBench task suite, ManiGaussian achieves an average success rate of 44.8%, which is a substantial improvement over previous approaches.

The following are the results from Table 1 of the original paper:

Comparison with Baselines:

• Perceptive Methods (PerAct, PerAct (4 cameras)): These methods perform poorly, especially on tasks requiring intricate spatial or dynamic understanding (e.g., "sweep to dustpan" with 0.0% success rate for both, "put in drawer" with 2.7% and 6.7%). PerAct (4 cameras) shows marginal improvement in some tasks ("meat off grill") but also degradation in others ("open drawer"), indicating that simply adding more cameras doesn't fundamentally solve the lack of dynamic understanding. Their average success rates are 20.4% and 22.7%.
• Generative Method (GNFactor): As a NeRF-based generative method, GNFactor shows significant improvement over PerAct, achieving an average success rate of 31.7%. It performs particularly well on "open drawer" (76.0%). However, it still struggles with tasks like "put in drawer" (0.0%) and "stack blocks" (4.0%), highlighting its limitations in complex, multi-step, or physically interactive scenarios.
• ManiGaussian (Ours): ManiGaussian surpasses GNFactor by a relative improvement of 41.3% (from 31.7% to 44.8% average success rate), which is an absolute 13.1% increase.

  • It matches GNFactor on "open drawer" (76.0%).

  • It shows dramatic improvements in tasks requiring explicit dynamic understanding:

    • "sweep to dustpan": 64.0% (vs. 28.0% for GNFactor)
    • "drag stick": 92.0% (vs. 37.3% for GNFactor)
    • "put in drawer": 16.0% (vs. 0.0% for GNFactor)
    • "stack blocks": 12.0% (vs. 4.0% for GNFactor)

  • Even on "meat off grill" where PerAct (4 cameras) achieved a higher score, ManiGaussian still maintains a respectable 60.0%.

    The results strongly validate ManiGaussian's effectiveness. The significant gains, particularly in tasks involving tools, multiple objects, or long-horizon planning (sweep to dustpan, drag stick, put in drawer, stack blocks), directly support the paper's central hypothesis: explicitly modeling scene-level spatiotemporal dynamics via dynamic Gaussian Splatting and a Gaussian world model is crucial for successful robotic manipulation in complex, unstructured environments. The ability to predict how objects interact and change position/orientation is key to these improvements, overcoming the incorrect interaction issue faced by GNFactor.

6.2. Ablation Studies / Parameter Analysis

Effectiveness of Different Components

The paper conducts an ablation study to verify the contribution of each proposed component, grouping tasks into 6 categories (Planning, Long, Tools, Motion, Screw, Occlusion) for analysis.

The following are the results from Table 2 of the original paper:

• Vanilla Baseline (Geo: X, Sem: X, Dyna: X): This baseline directly trains a representation model and action decoder without Gaussian Splatting, semantic features, or dynamic modeling. It achieves an average success rate of 23.6%.
• Adding Gaussian Regressor (Geo: ✓, Sem: X, Dyna: X): By incorporating the Gaussian regressor to predict Gaussian parameters (which inherently provides geometric information), the average performance jumps by 15.6% to 39.2%. This is a significant gain and highlights the importance of an explicit 3D geometric representation. Tasks requiring strong geometric reasoning like Occlusion (28.0% to 60.0%), Tools (25.3% to 52.0%), and Screw (4.0% to 24.0%) see substantial improvements. This confirms the ability of Gaussian Splatting to model spatial information effectively.
• Adding Semantic Features (Geo: ✓, Sem: ✓, Dyna: X): Including semantic features (distilled from pretrained foundation models) and their corresponding consistency loss ($\mathcal{L}_{\mathrm{Sem}}$) further boosts the average success rate by 2.4% to 41.6%. This demonstrates the benefit of high-level semantic information in understanding and manipulating objects, especially in tasks like Motion (52.0% to 64.0%).
• Adding Deformation Predictor and Future Scene Consistency (Geo: ✓, Sem: ✓, Dyna: ✓): Finally, integrating the deformation predictor and the future scene consistency loss ($\mathcal{L}_{\mathrm{Dyna}}$) yields another substantial improvement of 3.2% (from 41.6% to 44.8%). This component is crucial for explicitly learning scene-level dynamics. Its impact is particularly noticeable in 4 out of 6 task types, especially Long-horizon tasks (Long category, 8.0% to 14.0%), where understanding how the scene evolves over time is paramount. This validates the core hypothesis that modeling dynamics is essential for robust manipulation. The overall gain from the vanilla baseline to the full ManiGaussian is from 23.6% to 44.8%, highlighting the necessity of combining geometric, semantic, and dynamic understanding.

Learning Curve and Efficiency

The learning curve (Figure 3) provides insights into the training efficiency and performance convergence.

该图像是图表，展示了ManiGaussian与GNFactor在训练时间与平均成功率上的对比学习曲线。ManiGaussian在相同训练时间内成功率显著高于GNFactor，提升比例分别为1.18倍和2.29倍，灰色虚线代表移动平均结果。

The plot compares the average success rate over training iterations for ManiGaussian and GNFactor.

• Both methods converge within 100k training steps.
• ManiGaussian consistently outperforms GNFactor across the entire training duration.
• The paper reports that ManiGaussian achieves 1.18x better performance (higher success rate) and 2.29x faster training compared to GNFactor. This indicates that the explicit Gaussian scene reconstruction approach is not only more effective but also more computationally efficient than implicit approaches like NeRF, which GNFactor uses. This efficiency gain is a significant practical advantage.

Impact of Balance Hyperparameters

An additional ablation study (Table 5 in supplementary materials) examines the impact of the loss function hyperparameters ($\lambda_{\mathrm{Geo}}, \lambda_{\mathrm{Sem}}, \lambda_{\mathrm{Dyna}}$) on overall performance.

The following are the results from Table 5 of the original paper:

The results show that the chosen hyperparameters ($\lambda_{\mathrm{Geo}} = 0.01, \lambda_{\mathrm{Sem}} = 0.0001, \lambda_{\mathrm{Dyna}} = 0.001$) achieve the highest average success rate of 44.8%. Variations in these weights lead to fluctuating performance across different task categories. This confirms that a careful balance of each loss item is crucial for learning an optimal manipulation policy, as different losses contribute to different aspects of scene understanding (geometry, semantics, dynamics). For instance, setting $\lambda_{\mathrm{Sem}}$ or $\lambda_{\mathrm{Dyna}}$ to 0 generally leads to lower average success rates, reinforcing their individual importance.

6.3. Qualitative Analysis

Visualization of Whole Trajectories

Figure 4 provides a case study comparing ManiGaussian with GNFactor on specific tasks, illustrating the impact of dynamics understanding.

该图像是论文中的实验示意图，展示了 ManiGaussian 和 GNFactor 两种方法执行“Turn left tap”任务的机器人操作过程。绿色对勾表示动作成功，红色叉号表示动作失败，结果显示 ManiGaussian 在动态高斯点驱动下具有更高的执行成功率。

• "Slide the block to yellow target" (Top Case):
  • GNFactor attempts to imitate a backward pulling motion, even when the gripper is incorrectly positioned (leaning right of the block). This suggests a lack of understanding of how the gripper interacts physically with the block to achieve the target slide. It fails.
  • ManiGaussian successfully returns the gripper to a correct initial position (red square) and then effectively slides the block to the yellow target. This success is attributed to its ability to correctly understand the scene dynamics of objects in contact, allowing it to predict the consequences of its actions and adjust for optimal interaction.
• "Turn left tap" (Bottom Case):

  • GNFactor misunderstands the instruction "left" and attempts to operate the right tap. Even when operating a tap, it fails to turn it on. This indicates a weakness in semantic understanding and precise control.

  • ManiGaussian successfully identifies and operates the correct (left) tap and turns it on. This demonstrates ManiGaussian's superior comprehension of both semantic information (identifying the correct object instance based on language) and its ability to execute operations accurately based on its understanding of dynamics.

    These qualitative examples strongly support the claim that ManiGaussian's physical understanding of scene-level spatial-temporal dynamics enables it to complete human goals more effectively than previous methods.

Visualization of Novel View Synthesis

Figure 5 showcases ManiGaussian's capabilities in current scene reconstruction and future scene prediction from novel views.

该图像是论文ManiGaussian中的图5，展示了不同方法下的视角合成结果，包括观察图、当前时间步的视角合成和未来时间步的视角合成。对比表明ManiGaussian在PSNR值上优于GNFactor，且能更准确地重建和预测场景细节。

The image shows a "slide block" task, presenting an observation view (front camera) and novel views for both the current and future states, comparing ManiGaussian with GNFactor. The action loss is removed for better visualization, focusing on reconstruction quality.

• Current Scene Reconstruction:
  • From a single front view where the gripper's full shape might be occluded, ManiGaussian (bottom row) offers superior detail in modeling cubes and other scene elements in novel views compared to GNFactor (middle row). This suggests that ManiGaussian's underlying Gaussian representation is more robust and detailed.
• Future Scene Prediction:

  • Crucially, ManiGaussian accurately predicts future states based on these recovered details. In the "slide block" example, it not only predicts the future gripper position that aligns with the instruction but also correctly predicts the future cube location as influenced by the gripper's interaction. This shows an intricate understanding of the physical interaction among objects. GNFactor's future prediction appears less accurate in terms of object placement and gripper pose relative to the expected outcome.

    This qualitative analysis provides visual evidence that ManiGaussian successfully learns intricate scene-level dynamics, which is foundational for its improved manipulation performance.

7. Conclusion & Reflections

7.1. Conclusion Summary

This paper introduces ManiGaussian, a novel agent for language-conditioned robotic manipulation that excels by explicitly encoding scene-level spatiotemporal dynamics. The core of ManiGaussian is a dynamic Gaussian Splatting framework that models the propagation of diverse features within a Gaussian embedding space. This latent representation, enriched with dynamic information, is then leveraged to predict precise robot actions. To facilitate the learning of these dynamics, a Gaussian world model is built. This world model parameterizes the distributions in the dynamic Gaussian Splatting framework, providing crucial supervision by reconstructing future scenes and enforcing consistency with real observations. Extensive experiments on 10 RLBench tasks with 166 variations demonstrate ManiGaussian's superiority, outperforming state-of-the-art methods by 13.1% in average success rate and showing improved training efficiency.

7.2. Limitations & Future Work

The authors acknowledge one key limitation:

• Dependency on Multi-view Supervision: The current Gaussian Splatting framework necessitates multiple view supervision with camera calibration. This means that during training, multiple camera feeds are required to accurately initialize and update the 3D Gaussian representation of the scene. In real-world deployment, obtaining such precise multi-view data and calibration might be challenging or costly, potentially restricting its direct applicability in highly constrained or rapidly changing environments where only a single or uncalibrated camera might be available.

  The paper does not explicitly suggest future work directions beyond implicitly addressing the stated limitation. However, based on the limitation, potential future work could include:

• Single-View Gaussian Splatting Integration: Exploring methods to integrate single-view 3D Gaussian reconstruction techniques (e.g., PixelSplat [4], GaussianCube [78]) into ManiGaussian to reduce its dependency on multi-view setups.

• Robustness to Calibration Errors: Investigating ways to make the framework more robust to noisy or imperfect camera calibrations.

• Longer-Horizon and More Complex Tasks: Extending the framework to even more complex, hierarchical manipulation tasks or those requiring interaction with deformable objects (beyond rigid bodies).

• Real-World Deployment and Generalization: Testing ManiGaussian in real-world robotic setups to assess its generalization capabilities from simulation to reality and address practical challenges like latency and robustness.

• Unsupervised Dynamics Learning: Exploring more unsupervised or self-supervised ways to learn dynamics beyond relying solely on future scene reconstruction loss, perhaps through physical priors or interaction-based learning.

7.3. Personal Insights & Critique

ManiGaussian presents a compelling advancement in robotic manipulation by directly tackling the often-overlooked aspect of scene dynamics. The integration of Dynamic Gaussian Splatting with a Gaussian world model is a highly innovative approach that leverages the strengths of explicit 3D representation and predictive modeling.

Inspirations and Applications:

• Physical Understanding: The explicit modeling of object movement and interaction through dynamic Gaussians provides a more intuitive and physically grounded representation compared to abstract latent codes. This could inspire new directions in robot learning where physical common sense is directly embedded into the scene representation.
• Efficiency of Explicit Models: The reported efficiency gains (2.29x faster training than GNFactor) highlight the practical benefits of Gaussian Splatting over NeRF for robotics. This could accelerate research in sim-to-real transfer and on-robot learning where fast training and inference are critical.
• Beyond Manipulation: The concept of a dynamic 3D representation coupled with a world model could be transferable to other domains requiring complex spatiotemporal reasoning, such as autonomous driving (predicting interactions between vehicles and pedestrians at a fine-grained level), human-robot collaboration (anticipating human movements), or surgical robotics (modeling deformable tissues with dynamic Gaussians).

Potential Issues, Unverified Assumptions, or Areas for Improvement:

• Rigid Body Assumption: The assumption that colors, scales, opacities, and semantic features of Gaussians are time-independent (treating objects as rigid bodies) simplifies the problem significantly. While valid for many manipulation tasks, it limits ManiGaussian's applicability to tasks involving deformable objects (e.g., cloth, soft robots, pouring liquids). Extending the framework to model deformable Gaussians would be a natural next step, though it would introduce considerable complexity.

• Discrete Action Space: The action space is discretized for translation and rotation. While common, this can limit the precision and fluidity of robot movements compared to continuous action spaces. The use of a low-level motion planner (like RRT-Connect) helps, but the action prediction itself is still coarse.

• Reliance on Foundation Models for Semantics: Distilling semantic features from Stable Diffusion is powerful, but the quality of these features depends on the generative capabilities of the foundation model and its relevance to the specific manipulation domain. Any biases or limitations in the foundation model's understanding could propagate.

• Interpretability of Gaussian Embeddings: While Gaussians are explicit, the semantic features $f_i$ within them are still high-dimensional embeddings. Further work could explore how to make these semantic embeddings more interpretable or controllable for specific manipulation attributes.

• Scalability to Complex Scenes: While Gaussian Splatting is efficient, handling very large numbers of dynamically interacting Gaussians in extremely cluttered environments might still pose computational challenges. The fixed number of Gaussians (16,384) might also be a limiting factor for very complex scenes.

• Generalization to Unseen Object Properties: The paper mentions 166 variations in RLBench. While impressive, real-world unstructured environments can present vastly greater novelty in object shapes, textures, and physical properties. The framework's ability to generalize to truly novel objects (not just variations of known categories) would be an important test.

  Overall, ManiGaussian makes a significant contribution by bringing dynamic 3D scene representation to the forefront of robotic manipulation, providing a robust and efficient way to model physical interactions. Its success underscores the importance of explicit dynamics modeling for achieving truly intelligent and adaptable robots.