Splat-MOVER: Multi-Stage, Open-Vocabulary Robotic Manipulation via Editable Gaussian Splatting

Authors: ola  shorinwa
johnathan  tucker
aliyah  smith
aiden  swann
timothy  chen
roya  firoozi
monroe  kennedy
mac  schwager
a  neill
a  rehman
a  maddukuri
a  gupta
a  padalkar
a  lee
a  pooley
a  mandlekar
a  jain
a  tung
a  bewley
a  herzog
a  irpan
a  khazatsky
a  rai
a  wang
a  kolobov
a  singh
a  garg
a  kembhavi
a  xie
a  brohan
a  raffin
a  sharma
a  yavary
a  balakrishna
b  wahid
b  burgess- limerick
b  kim
b  schölkopf
c  wulfe
c  lu
c  xu
c  le
c  finn
c  wang
c  chi
c  huang
c  chan
c  agia
c  pan
c  fu
d  devin
d  xu
d  morton
d  driess
d  chen
d  pathak
d  shah
d  büchler
d  jayaraman
d  kalashnikov
e  sadigh
e  johns
f  foster
f  liu
f  ceola
f  xia
f v zhao
f  frujeri
g  stulp
g s zhou
g  sukhatme
g  salhotra
g  yan
g  feng
g  schiavi
g  berseth
g  kahn
g  yang
h  wang
h.-s  su
h  fang
h  shi
h b bao
h i amor
h  christensen
h  furuta
h  walke
i  ha
i  mordatch
i  radosavovic
j  leal
j  liang
j  abou-chakra
j  kim
j  drake
j  peters
j  schneider
j  hsu
j  bohg
j  bingham
j  wu
j  gao
j  hu
j  sun
j  luo
j  gu
j  tan
j  oh
j  lu
j  yang
j  malik
j  silvério
j  hejna
j  booher
j  tompson
j j salvador
j  lim
k  han
k  wang
k  rao
k  pertsch
k  hausman
k  go
k  gopalakrishnan
k  goldberg
k  byrne
k  oslund
k  kawaharazuka
k  black
k  lin
k  zhang
k  ehsani
k  lekkala
k  ellis
k  rana
k  srinivasan
k p fang
k.-h  singh
k  zeng
k  hatch
l  hsu
l y itti
l  chen
l  pinto
l  fei-fei
l j tan
l  fan
l  ott
l  lee
m  weihs
m  chen
m  lepert
m  memmel
m  tomizuka
m g itkina
m  castro
m  spero
m  du
m c ahn
m  yip
m  zhang
m  ding
m k heo
m  srirama
m j sharma
n  kim
n  kanazawa
n  hansen
n j heess
n  joshi
n  suenderhauf
n d liu
n m m palo
o  shafiullah
o  mees
o  kroemer
p r bastani
p t sanketi
p  miller
p  yin
p  wohlhart
p d xu
p  fagan
p  mitrano
p  sermanet
p  abbeel
q  sundaresan
q  chen
r  vuong
r  rafailov
r  tian
r  doshi
r  mart'in-mart'in
r  baijal
r  scalise
r  hendrix
r  lin
r  qian
r  zhang
r  mendonca
r  shah
  hoque
t  gupta
t  harada
t  matsushima
t  xiao
t  kollar
t  yu
t  ding
t  davchev
t z zhao
t  armstrong
t  darrell
t  chung
v  jain
v  vanhoucke
w  zhan
w  zhou
w  burgard
x  chen
x  wang
x  zhu
x  geng
x  liu
x  liangwei
x  li
y  pang
y  lu
y j ma
y  kim
y  chebotar
y  zhou
y  zhu
y.-h  wu
y  xu
y  wang
y  bisk
y  dou
y  cho
y  lee
y  cui
y  cao
y  tang
y  zhang
y  jiang
y  li
y  iwasawa
y  matsuo
z  ma
z  xu
z j cui
z  zhang
z  fu
z  lin
Venue: robot-learning_org_CoRL_2024_Conference
Published: 2024-06-04 06:34:40

Abstract: We present Splat-MOVER, a modular robotics stack for open-vocabulary
robotic manipulation, which leverages the editability of Gaussian Splatting (GSplat)
scene representations to enable multi-stage manipulation tasks. Splat-MOVER
consists of: (i) ASK-Splat, a GSplat representation that distills semantic and grasp
affordance features into the 3D scene. ASK-Splat enables geometric, semantic,
and affordance understanding of 3D scenes, which is critical for many robotics
tasks; (ii) SEE-Splat, a real-time scene-editing module using 3D semantic masking
and infilling to visualize the motions of objects that result from robot interactions
in the real-world. SEE-Splat creates a “digital twin” of the evolving environment
throughout the manipulation task; and (iii) Grasp-Splat, a grasp generation module
that uses ASK-Splat and SEE-Splat to propose affordance-aligned candidate grasps
for open-world objects. ASK-Splat is trained in real-time from RGB images
in a brief scanning phase prior to operation, while SEE-Splat and Grasp-Splat
run in real-time during operation. We demonstrate the superior performance of
Splat-MOVER in hardware experiments on a Kinova robot compared to two recent
baselines in four single-stage, open-vocabulary manipulation tasks. In addition, we
demonstrate Splat-MOVER in four multi-stage manipulation tasks, using the edited
scene to reflect changes due to prior manipulation stages, which is not possible
with existing baselines. Video demonstrations and the code for the project are 
available at https://splatmover.github.io.

Main paper: 
 introduction: 
 Open-world robotic manipulation requires spatial and semantic understanding of the scene in which a robot is operating. In particular, a robot must be able to identify the location and geometry of objects in its environment based on their semantic attributes. However, spatial and semantic scene understanding alone is often inadequate in robotic manipulation. In many cases, it is critical for the robot to know the best place to grasp the object to perform the required task, that is, to be able to detect and localize grasp affordances on the object [1, 2] . Furthermore, for multi-stage manipulation tasks, where the pre-conditions for the next stage are met through the success of a previous stage, it is essential to continually update the 3D scene model to reflect the objects' motions due to the robot's previous actions, to have an accurate scene representation that is useful for subsequent stages.Consequently, in this work, we introduce Splat-MOVER, a modular robotics stack for Multi-Stage, Open-Vocabulary Robotic Manipulation via Editable Gaussian Splatting. Splat-MOVER consists of three modules: (i) a 3D Affordance-and-Semantic Knowledge Gaussian Splatting scene representation (ASK-Splat), (ii) a Scene-Editing-Enabled module for Gaussian Splatting scenes (SEE-Splat), and (iii) a grasp generation module (Grasp-Splat) that uses ASK-Splat and SEE-Splat to plan grasps in multi-stage manipulation tasks. These three modules together make up Splat-MOVER, illustrated in Fig. 1 . In a brief pre-scanning phase, we train the ASK-Splat model from posed RGB images of the workspace, simultaneously embedding CLIP and grasp affordance features from the images into the 3D scene model. Then, given a natural language prompt of a multi-stage manipulation task, Splat-MOVER uses ASK-Splat to localize and mask the objects from the prompt in the 3D scene, providing the object's 3D initial and target configurations at each stage of the task. Subsequently, SEE-Splat edits the ASK-Splat scene, reflecting the dynamic poses of the objects throughout the manipulation task. Finally, Grasp-Splat uses the pre-trained GraspNet model [3] to generate candidate grasps, which are then re-ranked based on their affordance scores from ASK-Splat, to obtain grasp poses for each object, at each stage of the manipulation task. Point-to-point motion planning for the robot arm is accomplished with standard off-the-shelf planning tools, e.g., MoveIt [4] .We showcase Splat-MOVER's effectiveness through hardware experiments on a Kinova robot, where Splat-MOVER achieves significantly improved success rates across four single-stage open-vocabulary manipulation tasks compared to two recent baseline methods: LERF-TOGO [5] and F3RM* [6] . In three single-stage manipulation tasks, Splat-MOVER improves the success rate of LERF-TOGO by a factor of at least 2.4, while achieving similar success rates in a fourth task (95% compared to LERF-TOGO's 100%). Likewise, Splat-MOVER outperforms F3RM* by a factor ranging from 1.2 to 3.3, across the four tasks. In addition, we demonstrate the performance of Splat-MOVER in four multi-stage manipulation tasks, where we leverage SEE-Splat to reflect the updates in the scene resulting from prior manipulation stages, a capability absent in existing baseline approaches. 
preliminaries: 
 We introduce notation relevant to this paper, before presenting Gaussian Splatting. We denote a 2D feature embedding as f ∈ R a×b×c , where the first-two dimensions (a, b) represent the spatial dimensions, while the last dimension c represents the dimension of the embedding. Similarly, we denote 1D feature embeddings as f ∈ R c . We provide a brief review of Gaussian Splatting, which we build upon to obtain a affordance-and-semantic-aware scene representation. We direct interested readers to [7] for a more in-depth discussion of Gaussian Splatting. In Gaussian Splatting, the scene is represented using 3D Gaussians, each parameterized by a mean µ ∈ R 3 and covariance Σ ∈ R 3×3 , which is represented as the product of a scaling (diagonal) matrix S ∈ R 3×3 and a rotation matrix R ∈ R 3×3 . Each Guassian has an opacity parameter α ∈ R and spherical harmonics parameters for view-dependent visual properties. Tile-based rasterization with α-blending is utilized for rendering the Gaussians. The parameters of each Gaussian are optimized through stochastic gradient descent, leveraging the differentiability of the tile-based rasterization procedure to compute the gradients of the loss function L, which consists of an ℓ 1 -photometric loss and a similarity (SSIM) loss [8] . 
affordance-and-semantic-knowledge gaussian splatting: 
 Given a dataset D of RGB images, given by D = {I 1 , . . . , I N }, ASK-Splat embeds: (1) CLIP features, and (2) grasp affordance features in the GSplat scene. Using the CLIP features, ASK-Splat generates a 3D heatmap given an open-vocabulary text prompt, which denotes the semantic relevance to the prompt. E.g., the prompt "apple" will give a 3D heat map that is hottest over the apple, but also somewhat hot over the pear and orange (which are semantically "close" to apple). Although the affordance feature field cannot be queried directly in natural language, it provides information on the graspability of all points in the scene. We use the CLIP features to mask out relevant objects and the affordance features to highlight graspable locations, as illustrated in Fig. 2 .Grounding Language Semantics in 3D Gaussian Splatting. We distill ground-truth image embeddings from the vision-language foundation model CLIP, denoted by f gt ∈ R H f ×W f ×C , extracted from D via MaskCLIP [9] , into the 3D scene. To preserve the real-time rendering speed of Gaussian Splatting, we learn a latent space for the CLIP embeddings with an autoencoder, consisting of an encoder g enc ϕ : R H f ×W f ×C → R H f ×W f ×l and a decoder g dec θ : R H f ×W f ×l → R H f ×W f ×C , compressing the semantic feature space of dimension C to the semantic latent space of dimension l and vice-versa, with parameters ϕ and θ, respectively, depicted in Fig. 2 . We set l = 3 ≪ C. The autoencoder is trained to minimize the reconstruction loss.We distill the latent CLIP features into the GSplat scene, by augmenting the attributes of each Gaussian with an additional parameter f s ∈ R l , denoting the semantic feature of the Gaussian, which are optimized via gradient descent on the loss function:EQUATIONwhere Îs i ∈ R H×W ×l denotes the 2D semantic feature map rendered from the Gaussian Splats, ψ : R U ×V ×C × R U ×V ×C → R denotes the cosine-similarity function (where we note that ψ applies to inputs of arbitrary height and width), and κ s ∈ R ++ denotes the constant term in the mean-squarederror (MSE) loss. To generate a semantic similarity map given a natural-language query (positive query), we compute the cosine-similarity between the CLIP embedding associated with the query and the distilled semantic embeddings associated with each Gaussian in the scene. We transform the computed cosine-similarity to a probability using the pairwise softmax function (given a negative query), which is thresholded to generate the semantic similarity map. We describe the distillation and optimization procedures in greater detail in Appendix A.Grounding Affordance in 3D Gaussian Splatting. ASK-Splat embeds object-specific grasp affordances directly within the 3D Gaussian Splatting environment, yielding a heat map over objects in the scene relating to the graspability. We distill visual grasp affordances from a vision-affordance foundation model trained on large human-object interaction datasets, VRB [10] , into the scene representation, although we note that other vision-affordance foundation models can also be used. The distilled affordance endows robots with the ability to identify the parts of an object that a human is more likely to grasp, capturing common-sense human knowledge and experience in interacting with objects. We obtain the ground-truth affordance score by evaluating the training dataset D using VRB and leverage the 3D Gaussian primitives in embedding the 2D visual grasp affordance scores in 3D. By augmenting the attributes of each Gaussian in the scene with an additional parameter β ∈ [0, 1], representing the score of the Gaussian affording the task of grasping, we ground the grasp affordances within the geometric primitives representing the occupied regions of the scene. We enforce the box constraints on β using the sigmoid activation function to provide smooth gradients during the training procedure. We provide additional details in Appendix A.4 Scene-Editing-Enabled Gaussian Splatting SEE-Splat consists of three components: (i) a semantic component utilizing natural-language queries to generate a relevancy map based on semantic similarity; (ii) a Gaussian masking module that generates a sparse point cloud of the relevant objects, comprising of all semantically-relevant Gaussians; and (iii) a scene transformation component that edits the 3D scene by inserting, removing, or modifying the geometric, spatial, or visual properties of the Gaussians. Together, these components enable robots to visualize the effects of their interactions with other objects in a virtual 3D scene, prior to executing these actions in the real-world. In Fig. 2 , we illustrate each component of SEE-Splat by editing a real-world cooking scene to visualize the action of moving the saucepot from the table to the electric stove, showing localization of the saucepot, extraction of the semantically-relevant Gaussians, and transformation of the relevant Gaussians.Semantic Localization via ASK-Splat. Given a natural-language query specifying an object of interest, SEE-Splat leverages ASK-Splat to identify semantically relevant Gaussians, generating a semantic similarity map. To improve the localization accuracy, the text prompt can include the geometric and visual properties of the object, such as its color, in addition to its semantic class.Masking the Gaussians in SEE-Splat. Given a semantic similarity map of the scene, SEE-Splat generates a mask identifying the Gaussians relevant to the specified object. Given a threshold for semantic relevancy, SEE-Splat removes dissimilar Gaussians from the scene, creating a sparse point cloud of the relevant Gaussians, constructed from the means of these Gaussians. However, photorealistic rendering of Gaussian environments require denser point clouds. To densify the point cloud, SEE-Splat lifts the features of the point cloud from the 3D Euclidean space to a 7D feature space, by augmenting each point in the point cloud with its RGB color and semantic score, and subsequently identifies all neighboring Gaussians in the scene within a specified distance of the point cloud in the 7D feature space using an efficient KD-tree query. SEE-Splat incorporates these points into the point cloud to create a denser point cloud, comprising of all semantically-relevant Gaussians, while removing outliers from the set of points.Editing the Gaussians in SEE-Splat. To edit ASK-Splat, SEE-Splat applies a transform ξ : G s → G s to the relevant Gaussians to update their spatial and geometric attributes, where G s represents the space of the Gaussian primitives. The transform ξ, which is not limited to rigid transformations, can be generated via heuristics, a large language model (LLM), a human, or computed from the observations collected by onboard sensors. With these capabilities, SEE-Splat provides a digital twin of the scene. Moreover, provided sensor feedback is available, SEE-Splat enables real-time visualization of the real-world in a virtual environment, enabling the Gaussian primitives to accurately reflect the real-time geometry and visual properties of objects in the real-world. Although, we do not consider physics-based simulations in this work, we note that physics can be incorporated into SEE-Splat to achieve greater realism. We expound on this point in our discussion on the limitations of SEE-Splat. In addition, while editing the scene, SEE-Splat removes visual and geometric artifacts through 3D Gaussian infilling, shown in Fig. 8 , which we discuss in detail in Appendix B. 5 : Grasp-Splat generates affordance-aligned grasps using the semantic and grasp-affordance knowledge in ASK-Splat. Qualitatively, the proposed grasps lie in regions where a human is more likely to grasp (e.g., the handle of the saucepot and the center of the fruit) and are more likely to result in stable grasps, when executed by a robot. 
affordance-aligned grasp generation: 
 Grasp-Splat utilizes the dense point cloud of the object generated by SEE-Splat to propose grasp configurations for grasping the object, while harnessing the grasp affordance knowledge in ASK-Splat to identify generally more stable grasp configurations associated with the specified object. The proposed grasps are generated from the point cloud using a deep-learned model GraspNet [3] , that estimates 6D grasp poses for a parallel-jaw gripper from a point cloud of the object, along with estimated grasp-quality scores associated with these grasp poses. We note that the grasps generated by GraspNet are not always ideal (see Fig. 4 ). Consequently, Grasp-Splat executes a grasp selection procedure to identify more-promising candidate grasps. We hypothesize that leveraging grasp affordance of each part of the object when generating candidate grasps could be essential to identifying better candidate grasps. As a result, we introduce the grasp metric ν : SE(3) → R, which computes the grasp affordance at a specified grasp pose X ∈ SE(3). Grasp-Splat ranks the candidate grasps generated by GraspNet based on the grasp scores given by ν(X), leveraging the affordance associated with each grasp pose to identify grasp configurations that are more likely to succeed, depicted in Fig. 9 . Moreover, since GraspNet does not consider the position of the robot relative to the object, the proposed grasps might require post-processing to account for the relative position of the robot. We provide additional discussion in Appendix C. 
experiments: 
 We compare Splat-MOVER to the existing open-vocabulary robotic manipulation methods LERF-TOGO [5] and F3RM [6] in four tasks: the Cooking task, Chopping task, Cleaning task, and Workshop task, illustrated in Table 2 , executed on a Kinova robot. We utilize the implementation of LERF-TOGO provided by the authors. We refer to our implementation of F3RM [6] using GraspNet for grasp generation in place of the virtual-reality-collected task demonstrations as F3RM*. We summarize the capabilities of each method in Table 1 and provide additional results in Appendix D. ✓ ✗ ✗ F3RM* [6] ✓ ✗ ✗ Splat-MOVER (ours) ✓ ✓ ✓Table 1 : Representation Capabilities of LERF-TOGO [5] , F3RM* [6] , and Splat-MOVER ASK-Splat Representation. We evaluate the grasp affordance and semantic knowledge embedded in ASK-Splat. In Figure 10 , we show the RGB image, grasp affordance heatmap computed by VRB, and the grasp affordance heatmap rendered from ASK-Splat composited with the rendered RGB image, in addition to the semantic similarity map for a salt shaker and a pair of scissors. The affordance heatmap shows the regions in each object amenable to grasping. Qualitatively, from Figure 10 , ASK-Splat encodes the grasp affordance given by VRB, identifying reasonable regions on each object for grasping. Although VRB provides the 2D motion direction associated with each grasp affordance region, we do not distill this knowledge into ASK-Splat, as we found the 2D motion directions to be quite noisy and relatively uninformative.Single-Stage Manipulation. We consider grasping a saucepan, knife in a knife guard, cleaning spray, and power drill. We show the grasps proposed by each method for a power drill in Fig. 12 .In the hardware experiments on the robot, we describe a candidate grasp as being feasible if the MoveIt planner successfully finds a plan to execute the grasp. We execute 20 feasible trials for each object, and in Table 2 , provide the grasping success rate of each method, as well as the percentage of grasps that lie within the affordance region of the object (AGSR), where the affordance region of each object is defined as follows: the entire handle of the saucepan, the entire knife with the guard on, the region of the cleaning spray excluding its cap, and the middle region of the power drill below its top compartment and above its battery compartment.From Table 2 , Splat-MOVER achieves the best grasping success rates and the highest percentage of grasps in the affordance region in grasping the saucepan, knife, and cleaning spray. LERF-TOGO attains a perfect success rate in grasping the power drill; however, LERF-TOGO always grasped the top of the drill, outside its affordance region, shown in Appendix D. In contrast, Splat-MOVER achieves a 95% success rate, grasping the object within its affordance region. Splat-MOVER outperforms the other methods in the first stage of the task likely due to the embedded grasp affordance in ASK-Splat. To generate grasps, Splat-MOVER exploits the distilled grasp affordance in ASK-Splat, which encodes common-sense knowledge of more suitable grasp locations on an object, drawn from human experience. In contrast, LERF-TOGO generates candidate grasp conditioned on a text prompt identifying the region to grasp the object (such as its handle) provided by a human operator or an LLM, while and F3RM* does so from a dataset of human demonstrations. We note that the semantic part description can introduce ambiguity in tasks where the "handle" of the object is not well-defined, such as the cleaning spray.In addition, we evaluate the pick-and-place success rate of all the methods in each manipulation task, where the place success rate is conditioned on the number of successful trials in picking the object. The publicly-available implementation of LERF-TOGO does not support the specification of a place location. Hence, we do not evaluate its place success rate. In Table 2 , we present the pick-and-place success rates in the four tasks. In the Cooking task, Splat-MOVER achieves a perfect success rate in picking up the saucepan, with a place success rate of 60%. We note that the place step involves placing the saucepan on an electric burner, which is quite challenging, potentially explaining the lower place success rate. Nonetheless, Splat-MOVER outperforms LERF-TOGO and F3RM* in the first stage of the task, the only stage of the task that both methods can perform.Multi-Stage Manipulation. Since the NeRF-based methods LERF-TOGO and F3RM* are not amenable to multi-stage manipulation, we cannot evaluate the success rate of these methods for the entire manipulation task. In contrast, Splat-MOVER enables multi-stage robotic manipulation, achieving minimum pick-and-place success rates of 50% and 80%, respectively, across the Cooking, Chopping, Cleaning, and Workshop tasks, as shown in Table 2 . Language-Embedded NeRFs and Gaussian Splats. Neural radiance fields (NeRFs) [16] have enabled high-fidelity scene representations, with view-consistent 3D geometry, yielding photorealistic renderings, with many robotic applications [17, 18, 19, 20, 21, 22, 23] . Many works [24, 25, 26, 9, 25] have leveraged NeRFs to ground semantic knowledge from 2D vision-language foundation models [27, 28, 29] in 3D to enable consistent object masking via natural-language queries. More recently, Gaussian Splatting [7] has emerged as an effective 3D scene representation, providing notable competitive advantages compared to NeRFs, including real-time rendering speeds and greater flexibility for dynamic scene-editing. Splat-MOVER leverages these competitive features to provide a digital twin of a scene, enabling multi-stage manipulation. As in the case with NeRFs, recent works [30, 31, 32, 33, 34] have embedded semantic features into 3D Gaussian Splatting, often requiring comparatively intensive training procedures. In comparison, Splat-MOVER introduces a lightweight technique for semantic distillation and applies the resulting model specifically to robotic manipulation. We provide a more extensive discussion of the related work in Appendix E.Grasp Generation in Gaussian Splatting Scenes. In concurrent work, GaussianGrasper [35] leverages the deep-learned model AnyGrasp [36] to generate robotic grasps from GSplat environments. However, GaussianGrasper does not embed grasp affordances or consider scene editing for multistage tasks, as we do. ManiGaussian [37] uses a GSplat scene to represent the robot arm itself, and predicts optimal arm actions for grasping, given this representation. The method is shown in simulation only. In addition, the workshop paper [38] considers a GSplat method for tracking objects during robot manipulation motions, but does not consider robotic planning or distilled affordances, as is our focus here. Finally, GraspSplats [39] utilizes the sampling-based grasp-generation method GPG [40] to propose grasp configurations and utilizes RGB-D inputs for depth supervision and real-time object tracking, whereas our work focuses on multi-stage robotic manipulation. 
conclusion: 
 We present Splat-MOVER, a robotics stack for multi-stage open-vocabulary robotic manipulation, consisting of three modules: ASK-Splat, SEE-Splat, and Grasp-Splat. ASK-Splat enables semantic and affordance queries via natural-language interaction to identify relevant objects within 3D scenes, while SEE-Splat provides real-time, dynamic scene editing, enabling visualization of the evolution of the real-world scene due to the robot's interaction with objects within the scene. Grasp-Splat builds upon these two modules for affordance-aware grasp generation, necessary for effective multi-stage robotic manipulation. We demonstrate the effectiveness of Splat-MOVER in real-world experiments in comparison to two recent baseline methods. Compared to the existing works, Splat-MOVER endows robots with the unique capability for multi-stage, open-vocabulary manipulation with minimal human inputs, by leveraging distilled grasp affordance knowledge and real-time dynamic scene editing, which are essential to multi-stage manipulation. 
limitations and future work: 
 We present a few limitations of Splat-MOVER and provide directions for future work. ASK-Splat distills grasp affordance knowledge from foundation models into 3D Gaussian Splatting scenes. We note that the effectiveness of the distilled grasp affordances and the generalization capability of our model is highly dependent on that of the affordance foundation model. For example, when trained using the VRB foundation model, an ASK-Splat scene may not generalize notably well to markedly-different objects outside of those seen in the EPIC-KITCHENS dataset. Future work will examine enhancing the generalization capability of the proposed ASK-Splat module by training and employing diverse cross-environment, cross-task, vision-affordance foundation models, rather than relying on VRB, which is specifically trained for kitchen tasks. Further, in its current form, the distilled visual grasp affordance does not depend on the orientation of the candidate grasp, limiting Grasp-Splat from fully harnessing grasp affordances in identifying better grasp configurations in SE(3). Future work will consider extending the computation of grasp affordance to SE(3). We present additional directions for future work in Appendix F. score between a feature point p and the positive query is given by:EQUATIONwhere Q denotes the set of positive queries,Q ′ s = {q ′ s,i , ∀i ∈ [|Q ′ s |]} denotes the set of negative queries, ν a : S → R computes the average semantic embedding of a set of text prompts s ∈ S, ν b (q ′ s,i ) represents the semantic embedding of the negative query q ′ s,i , and γ : R 3 × R C × R C → R represents the pairwise softmax function over the positive query embedding and the ith negative query embedding at the 3D feature point, outputting the probability associated with the positive query embedding. In general, when rendering the semantic similarity maps, we apply a threshold of 0.5 to the similarity score computed in (3) to distinguish feature points associated with the query from dissimilar ones. 
 
 Appendix: We embed grasp affordances in ASK-Splat. During training, we utilize the same tile-based rasterization procedure discussed in Section A.1 in rendering the 2D visual grasp affordance of the scene and optimize the grasp affordance parameter β using the loss function:L β = κ β |D| i=1 Îβ i -I β i 2 2, which represents the MSE loss between the ground-truth 2D visual grasp affordance I β i ∈ R H×W ×1 and the rendered visual grasp affordance Îβ i ∈ R H×W ×1 . We optimize the affordance parameters concurrently with the non-semantic parameters of each Gaussian. From a trained ASK-Splat scene, we can generate dense 2D visual grasp affordance maps, as well as sparser 3D visual grasp affordance maps, by directly evaluating the affordance score associated with each Gaussian.With 3D Gaussian Infilling language model (LLM). In the case where the natural-language description of the task does not specify the stages involved in the task, we query an LLM for the stages required to complete the manipulation task. For each stage in the manipulation task, we utilize ASK-Splat, SEE-Splat, and Grasp-Splat to identify the relevant object and generate candidate grasp poses. Likewise, query ASK-Splat for the target location for placing the object. We evaluate the feasibility of each candidate grasp using an off-the-shelf motion planner for the robotic manipulator, inputting the point cloud of the scene, extracted from ASK-Splat and SEE-Splat, into the motion planner, which the motion planner uses for collision detection during motion planning. We execute the top candidate grasps, moving on to the next if the robot motion planner fails to compute a solution to execute the selected grasp.We execute the motion plan returned by the motion planner on the robotic manipulator. We note that the end-effector trajectory can be published to SEE-Splat for real-time visualization of the task in the virtual scene. In this case, we can apply the relative transformation between consecutive end-effector poses to the spatial attributes of the Gaussian associated with the object being manipulated. In addition, we note that alternative approaches exist for computing the relative transformations of the object between consecutive frames. For example, if object-tracking information is available from sensors in the scene, SEE-Splat could leverage this information to update the spatial attributes of the Gaussians, rendering a video showing the real-time changes in the scene of the manipulator, including the motion of the object, as the manipulation task progresses. We proceed to the next stage in the manipulation task at the conclusion of the current stage, repeating the same procedures with the updated representation of the scene provided by SEE-Splat. We consider the multi-stage robotic manipulation task where the robot must sequentially pick and place two different objects and move them to a common goal location. The task is specified by a user that provides an open-vocabulary command, e.g., "Pick up the saucepan and move it to the burner, then pick up the lid and put it on the saucepan." For simplicity, we limit the task to two sequential pick-and-place maneuvers. However, we note that Splat-MOVER does not impose this limitation and is amenable to longer multi-stage manipulation tasks. Furthermore, we consider three adjacency goal location primitives ("on", "next to", and "inside") for the second object where each primitive is defined based on the geometry of the first object.Specifically, we evaluate Splat-MOVER in four multi-stage manipulation tasks across three scenes: the Kitchen, Cleaning, and Workshop scenes. In the Kitchen scene, we consider a Cooking task where the robot is asked to place a saucepan on an electric burner (Stage 1) and subsequently place a fruit inside the saucepan (Stage 2). Further, in the Kitchen scene, we consider a Chopping task where the robot is asked to place a knife on a chopping board (Stage 1) and subsequently place a fruit next to the knife (Stage 2). We consider a Cleaning task (in the Cleaning scene), where the robot is asked to place a cleaning spray in a bin (Stage 1) and subsequently place a sponge next to the cleaning spray (Stage 2). Lastly, in the Workshop scene, the robot is asked to place a power drill on a work mat (Stage 1) and subsequently place a wooden block next to the drill (Stage 2), which we refer to as the Workshop task.We implement Splat-MOVER in grasping and placing tasks on a Kinova Gen3 robot, equipped with a Robotiq parallel-jaw gripper. The Kinova robot is a 7-DoF robot with a maximum reach of 902 mm. We interface with the robot using the Robot Operating System (ROS), through which we send waypoints, which are tracked by the default low-level controllers provided by the robot. We utilize the MoveIt ROS package [48] for motion planning for the Kinova robot given a specified grasp pose. At each stage of the manipulation task, we extract a point cloud and a mesh from ASK-Splat and SEE-Splat, reflecting the progress in the task up to that stage, which we use as the environment representation within MoveIt for collision avoidance during planning.We provide additional results showing the quality of affordance and semantic knowledge in ASK-Splat. In Figure 10 , we show the RGB image, grasp affordance heatmap computed by VRB, and the grasp affordance heatmap rendered from ASK-Splat composited with the rendered RGB image.We compute the Structural Similarity Index (SSIM) for each scene to assess the quality of the distilled affordance compared to the VRB-generated grasp affordance. The SSIM metric ranges between -1 (indicating greater dissimilarity) to 1 (indicating greater similarity). As expected, the Workshop scene yields the smallest SSIM value of 0.592 ± 7.20e -2 , recalling that the objects in this scene, such as the power drill and the scraper, are outside the training distribution of the VRB model. Nevertheless, the model shows relatively-good generalization performance, given that the grasp affordance region lies around the handle of the drill, shown in Figure 10 (bottom row). Likewise, the Meal scene achieves the highest SSIM score of 0.681 ± 8.91e -2 , noting that the objects in the scene can be found in the dataset used in training the VRB model. Further, the Cleaning, Kitchen, and Random scenes achieve SSIM scores of 0.648 ± 9.06e -2 , 0.647 ± 1.30e -1 , and 0.614 ± 8.37e -2 , respectively.Figure 11 shows the semantic masks generated by ASK-Splat in the Cleaning scenes. Given a naturallanguage query, ASK-Splat localizes the relevant object in the scene based on the cosine-similarity of the Gaussians to the query. In Figure 11 , ASK-Splat identifies the flower. However, the success of robotic manipulation tasks depend on the integration of semantic scene understanding with grasp affordance. As such, we show the semantic-affordance masks generated by ASK-Splat in Figure 11 .With the semantic-affordance masks, a robot not only has the ability to identify a relevant object to grasp, the robot can also identify where on the relevant object to grasp. We examine the grasps proposed by Splat-MOVER compared to those proposed by prior work LERF-TOGO [5] and F3RM [6] . Figure 12 shows a few candidate grasps proposed by GraspNet, F3RM, LERF-TOGO, and Grasp-Splat for each of these objects. GraspNet does not consider the semantic features of the object in generating candidate grasps; as a result, the proposed grasps are not localized in regions where a human might grasp the object, unlike the candidate grasps proposed by F3RM, LERF-TOGO, and Grasp-Splat, which generate grasps closer to the handle of the respective objects. For example, the proposed grasps lie relatively close to the handle of the saucepan and the knife. Whereas LERF-TOGO and F3RM require guidance from a human operator or an LLM (in LERF-TOGO) or from a dataset of human demonstrations (in F3RM), Grasp-Splat does not require any external guidance to generate candidate grasps of similar quality, harnessing the grasp affordances provided by ASK-Splat.We neither perform a head-to-head comparison nor an ablation study against classic geometric representations, such as point clouds and voxels, noting the advantages of Gaussian Splatting (and more generally, radiance field) over these classic representations, among other reasons, which have been discussed in prior work, e.g., [7] . Here, we summarize a few of these advantages. Gaussian Splatting enables high-fidelity rendering in contrast to point-based representations, which suffer from missing geometry and aliasing, due to the limited resolution power of these methods. SEE-Splat leverages this high-fidelity rendering capability to provide a realistic digital twin for visualizing the evolution of the scene as the manipulation task unfolds. Moreover, Gaussian Splatting (and radiance fields in general) enables more effective language grounding in 3D, unlike point-based representations, as discussed in [26] . ASK-Splat exploits semantic distillation to enable semantic localization of the relevant objects given a language-guided task. Lastly, point-based representations Although LERF-TOGO and F3RM require the specification of a grasp location from an operator, an LLM, or via human demonstrations to generate more-promising candidate grasps, Grasp-Splat generates candidate grasps of similar or better quality without requiring external guidance.generally require a depth sensor to backproject a point cloud from each camera view, e.g., [49] . Our work does not require an RGBD sensor; the scene representation is constructed entirely from monocular images, which hinders a direct implementation of a point-based representation. Notably, under appropriate assumptions, Gaussian Splatting representations can be interpreted as a point-cloud, by reducing the ellipsoidal primitives to a point primitive given by the center of the ellipsoid. Hence, we can extract a point-cloud from a Gaussian Splatting representation, loosely demonstrating that the benefits of Gaussian Splatting encompass those of point-based representations.Generalist robot policies such as OpenVLA [15] and Octo [14] seek to enable versatile and adaptive behaviors across a wide range of tasks, environments, and natural language instructions. In contrast with specialized policies such as Diffusion Policy [50] , these generalist policies are trained via imitation learning on mixtures of the Open-X Embodiment dataset [13]. We do not perform head-tohead comparisons with these methods for the following reasons: 1. These policies use very different data from ours, and are trained in quite a different manner from our method making a performance comparison problematic. They are based on VLM foundation models trained on vast data sets with vast resources. E.g., OpenVLA was finetuned for specific tasks using 8 A100 GPUs trained for 5 to 15 hours per task. This is just for fine tuning. Pre-training required full industrial scale foundation model training on vast internet-scale data in a large GPU cluster. Few academic labs have access to such resources. By comparison, our method was trained on a single 3090 desktop machine for 25 minutes.2. These methods have access to real-time camera views (typically from multiple cameras) at execution time, while we do not require a camera at execution time. Conversely, we require a multi-view scanning phase prior to execution to build the map, while these policies require no such scanning phase, and do not use a map. Thus, it is difficult to make a fair comparison based on runtime data. While the real-time camera images enable robust control (e.g., to unmodeled disturbances) in generalist policies, the map enables global scene-understanding in Splat-MOVER, supporting a larger spatial context for task specification. Figure 13 depicts sample observations and tasks from the BridgeData V2 dataset used in fine-tuning generalist policies, showing that the goal and target object are always in frame, highlighting the relatively limited spatial-context required by these generalist policies.3. Finally, these methods are, fundamentally, policies that are conditioned on images. Our method is not a policy. It is a scene representation and understanding framework. The actual motion policy we use is an off-the-shelf MoveIt implementation using a classical RRT planner. We do not claim this is the best option, or even a good option. Rather, the planning was not the focus of our contribution. Therefore, again, a performance comparison is problematic. We instead compare with LERF-TOGO and F3RM, which are generally methods of the same kind of architecture as our method, using similar amounts of data in a similar fashion.In lieu of a head-to-head comparison, we provide existing results on the performance of generalist policies, as stated in [15] , where Octo, RT-1-X, RT-2-X, and OpenVLA are evaluated on a subset of the BridgeData V2 dataset. For each evaluation, OpenVLA and Octo are fully fine-tuned on a subset of 10-150 demonstrations for each task. The results for these evaluations, presented in Table 3 , show that OpenVLA achieves a 70.6% average success rate across the 17 different tasks. This represents a 20 percent increase in average success rate over the next best generalist policy RT-2-X. While we recognize the strengths of these generalist policies, we do not consider them to be direct competitors to Splat-MOVER. Rather, we believe that integrating a generalist policy into the Splat-MOVER framework would result in a superior robotic manipulation system. Such a system would be compatible with a vast array of tasks specified over a large spatial range given natural language descriptions and robust to disturbances, e.g., in the object location, blending the global scene knowledge of Splat-MOVER with the closed-loop control of generalist policies.Open-World Robotic Manipulation. Advances in foundation models [51] have enabled the development of open-world robotic manipulation methods, where robots manipulate objects given natural-language task instructions at runtime, without being trained on those specific objects or tasks.Existing methods fall into one of two categories: (i) ("smart policy") end-to-end visuo-motor policies based on a pre-trained large vision-language model [11, 12, 13] , or (ii) ("smart map") methods that use a rich 3D scene representation that embeds features from a vision-language foundation model, interfacing with a traditional manipulation planning stack to drive robot motion. Our method is of the "smart map" variety. Two other recent methods also take this general approach: LERF-TOGO [5] and F3RM [6] . LERF-TOGO [5] builds upon the semantic NeRF representation in LERF [26] , coupled with GraspNet [3] for grasp generation. Similarly, F3RM [6] uses the NeRF-based distilled feature field from [9] to embed task-relevant features learned from human demonstrations into the 3D scene model, which are used to generate and optimize candidate grasps. We compare against LERF-TOGO and F3RM as baselines.Despite their effectiveness, these methods still face a number of challenges. LERF-TOGO [5] requires the specification of a grasp location on an object by a human operator or a large language model, which might not be readily available. Likewise, F3RM [6] requires human demonstrations, which might be difficult to collect. Both methods rely on NeRFs as the underlying scene representation, which can be time-consuming to train and is not easily edited to represent changes in the environment (e.g., due to manipulation actions by the robot). In this paper, we embed affordance features from a pre-trained 2D affordance model VRB [10] into the 3D scene, thereby avoiding the need for human demonstrations or human specification of grasp locations. We also build our scene on the Gaussian Splatting representation, which is faster to train and render than NeRF, and easier to edit to reflect object motions. We introduce a novel GSplat scene editing algorithm specifically designed for the tabletop, object-centric edits needed in robotic manipulation.Language-Embedded NeRFs and Gaussian Splats. The core enabling technology behind the "smart map" variety of open-world manipulation methods is the neural feature field concept, which distills information from 2D data sources into a view-consistent 3D field by back-propagating through a differentiable image renderer. Neural Radiance Field (NeRF) [16] represents one of the earliest high-fidelity instance of this concept, distilling the 2D color information from RGB images into a 3D color and density field. NeRFs have been integrated into a number of robotics tasks, spanning navigation [17, 18] , SLAM [19, 20, 21] , and manipulation [22, 23] . Recent works have distilled semantic features from vision-language foundation models (such as CLIP [27] , DINO [28] , or LSeg [29] ) into NeRFs [24, 25, 26] , yielding a rich visual-semantic 3D scene representation. These methods were designed to highlight 3D semantic relevance to a text query (e.g., MaskCLIP [9] and LERF 


Decision: # Strengths
1. Utilizing the scene editability of 3DGS in robotics is novel.
1. The paper shows promising results for robotic manipulation tasks.
1. The real-world demonstrations showcase the effectiveness of the approach.
1. The paper is well-written.

# Weaknesses
1. The main body sometimes lacks necessary information about the method and experiments. Instead, the information is explained in Appendix. This is critical because the instructions for authors clearly state that "reviewers are not required to read the appendix." 
1. Baseline comparison is insufficient.

### Post-rebuttal comment 
Although the reviewers initially raised a few concerns, they agree that most of them have been addressed. As one of the reviewers pointed out, this paper could be one of the earliest works using 3DGS with feature distillation in robotic manipulation tasks. In the discussion between the Area Chair and the reviewers, they are in agreement on the quality and acceptance. I support their shared opinion.

Reviews: review: title: title: Details in Appendix
paper_summary: paper_summary: The paper leverages the Gaussian Splatting representation with affordance and semantics to locate grasp points corresponding to a task expressed as natural language.
main_review: main_review: The overall quality of the paper is moderate to high. With 20 trials per task there is a clear improvement over baseline methods.

The idea of using the GS over NeRFs is an obvious win for robotics which this paper capitalizes on. However it is not necessarily true that GS is slower than NeRFs (i.e. mip-Nerf and zip-Nerf) especially when considering the presented work suggests training and auto-encoder in series (Appendix).

Strengths:
- An exciting use of GS for robotics with clear improvements over NeRF based models. This novel direction deserves more attention with regards to the context of robotics.
- Well written with clear notation.

Weaknesses:
- The a lot of the details were left to the appendix which was required to read to understand the method beyond the surface level. The appendix reads something like what the main paper should include.
- Would like to put the success rates into perspective compared to a smart-policy method that uses a foundational method as discusses in the early part of the related work.
- Not clear on how SEE-spalt models or reacts to un-expected dynamics such as slippage or errors in grasping.

The paper motivates the editability of GS but the evaluation appears limiting with regards to how this benefits long horizon tasks. This is partially due to the evaluation limiting to map/NeRF. Extending the evaluation to include smart-policies using an pre-trained open-vocab VLA model could help here (SayCan, RT-1 or more recently OpenVLA).

[Edit post-rebuttal]:
The the authors have reworked the structure and included more details in the main paper. The overall idea is interesting and novel. With this improved clarification the revised version I consider borderline accept to encourage more exploration of the GS approach to representations for robotics.
questions: questions: Please provide some additional details on data used for training the autoencoder to compress the semantic embeddings to 3 dimensions. Is this using only data from a single experimental scene? If not what training data is used? Is this slower than the GS optimization?

Practical challenges of collecting enough posed views are not well discussed. How many views are required and do the image poses extend beyond the reachability of a wrist mounted camera? If so please update the limitation section. Also how often would the scene need to be re-scanned in a multistage task. I.e.  under what conditions does the SEE-slpat not keep up with scene dynamics?

Do you have a data point for "smart-policy" methods on the evaluation tasks to better gauge the difficulty of the tasks beyond comparing to map based methods?
limitations: limitations: 2
review_summary: review_summary: Scope of paper and/or division of content between main paper and appendix should be revised. Otherwise this is a great direction and could be highly impactful over the next two or more generations of papers in this direction.
title: title: Review and comments on Splat-MOVER
paper_summary: paper_summary: This paper proposes Splat-MOVER, a 3DGS-based representation for open-vocabulary robotic manipulation.  It consists of ASK-Splat, SEE-Splat and Grasp-Splat.  ASK-Splat distills VLM features (CLIP) into 3GDS which enables open-set language query and scene/object understanding. SEE-Splat leverages the editability of 3DGS scene representations to enable multi-stage manipulation tasks. Grasp-Splat uses off-the-shelf grasping and motion planning modules to achieve manipulation. In the real-robot experiments, Splat-MOVER shows improvement comparing with the NeRF-based baselines.
main_review: main_review: Overall, this paper show promising results of applying 3DGS-based representation for robotic manipulation tasks. The distillation of semantic feature and affordance features into 3DGS, utilizing scene editability of 3DGS in robotics are innovative. However, a few more points need to be improved in this paper:

The qualitative results of the feature distillation of Gaussian splatting used in this paper should be improved in the future.

The author should provide more justifications why 3DGS-based representation is chosen over classic geometric representation in the robotic manipulation task.

In real robot experiment, the author should also consider adding classic geometric baseline comparison, such as voxel-based representation.  In a relatively small scale environment, the requirement of 3DGS-based representation over pointcloud/voxel need to be justified in the experiments.

In the experiments, the author shows improved performance of NeRF-based baseline approaches, which is great. However, the authors are encouraged to add more explanations on why better results are achieved.
questions: questions: Provide more justification that 3DGS-based representation is chosen over classic geometric representation such as voxel/pointcloud. More experiments should also be conducted to provide justifications.

Provide explanations why 3DGS-based representation performs better than NeRF-based representations in the conducted experiments.
limitations: limitations: 3
review_summary: review_summary: This paper is among one of the earliest works using 3DGS with feature distillation in robotic manipulation tasks. Experiments show promising results comparing with NeRF-based baselines. However, more justifications need to be discussed to indicate why 3DGS representation is chosen and performs better than other representations in the particular robotic tasks.
title: title: Good paper but need refinement
paper_summary: paper_summary: This paper leverages Gaussian Splatting and foundational model to enable multi-stage manipulation tasks. Authors introduce three modules, including ASK-Splat, SEE-Splat, and Grasp-Splat to approach this problem.
main_review: main_review: - strength:
  - The discussion of failure case and limitation is sufficient
  - This paper is clearly presented and easy to follow
  - Introducing the scene editing stage is novel and enables interesting downstream tasks.
- weakness:
  - Although it is understandable that authors have to cut down experiment section in the main paper due to page limitation, I suggest authors to make the method section more concise and expand more on the experiment section. Current experiment section is short and not thorough enough. I think authors could consider to break down the experiment section into several questions they want to answer.
  - Authors mention that F3RM requires collecting human demo in VR. I believe the demo can also be collected using robot's teacher's mode or other teleop interface. Authors might need to put more efforts into constructing baselines for fair comparisons.
  - For experiments, authors compare with LERF-TOGO and F3RM for grasping quality and success rate. Maybe authors want to include GaussianGrasper for comparison to be more convincing.
- comments:
  - This paper can be improved by introducing more tasks in the video, since the whole pipeline seems to use foundational models directly without more tuning. 
  - It could be a minor issue, but the IK solver of the robot seems to be not optimal. For example, when grasping the pot, the robot end-effector finds a long path from its current position to the goal position.
  - I think more works can be included in "Open-World Robotic Manipulation". Here is a non-exhaustive list:
    - Wang, Yixuan, et al. "D $^ 3$ Fields: Dynamic 3D Descriptor Fields for Zero-Shot Generalizable Robotic Manipulation." arXiv preprint arXiv:2309.16118 (2023).
    - Ye, Jianglong, Naiyan Wang, and Xiaolong Wang. "Featurenerf: Learning generalizable nerfs by distilling foundation models." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023.
    - Qiu, Ri-Zhao, et al. "Learning generalizable feature fields for mobile manipulation." arXiv preprint arXiv:2403.07563 (2024).
    - Ke, Tsung-Wei, Nikolaos Gkanatsios, and Katerina Fragkiadaki. "3d diffuser actor: Policy diffusion with 3d scene representations." arXiv preprint arXiv:2402.10885 (2024).
  - In addition, StructDiffusion has similar scene editting process. Authors might consider compare them in the related works or experiments.
  - L237: Repeated image captions.

### Post-rebuttal comment 
I keep my original rating. Overall, the authors answer my questions. However, the current experiment organization seems scattered and not well-organized.
questions: questions: - L38: As far as I understand, the scene should be represented as $\mu \in \mathbb{R}^{N\time 3}$, where $N$ is the number of Gaussian splats. Or you could say "each Gaussian is parameterized ..." Correct me if I am wrong.
- L208: Main paper and supplementary material mention that we could transform Gaussians. However, it is still not clear how this transformation is generated. Is it generated by LLM, human instructions, or some heuristics?
limitations: limitations: 3
review_summary: review_summary: This is overall a good paper. But it needs to modify its presentation and refine experiment section.