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An end-to-end (E2E) visuomotor policy is typically treated as a unified whole, but recent approaches using out-of-domain (OOD) data to pretrain the visual encoder have cleanly separated the visual encoder from the network, with the remainder referred to as the policy. We propose Visual Alignment Testing, an experimental framework designed to evaluate the validity of this functional separation. Our results indicate that in E2E-trained models, visual encoders actively contribute to decision-making resulting from motor data supervision, contradicting the assumed functional separation. In contrast, OOD-pretrained models, where encoders lack this capability, experience an average performance drop of 42% in our benchmark results, compared to the state-of-the-art performance achieved by E2E policies. We believe this initial exploration of visual encoders' role can provide a first step towards guiding future pretraining methods to address their decision-making ability, such as developing task-conditioned or context-aware encoders.

Inherent robustness in manipulation is prevalent in biological systems and critical for robotic manipulation systems due to real-world uncertainties and disturbances. This robustness relies not only on robust control policies but also on the design characteristics of the end-effectors. This paper introduces a bi-level optimization approach to co-designing tools and control policies to achieve robust manipulation. The approach employs reinforcement learning for lower-level control policy learning and multi-task Bayesian optimization for upper-level design optimization. Diverging from prior approaches, we incorporate caging-based robustness metrics into both levels, ensuring manipulation robustness against disturbances and environmental variations. Our method is evaluated in four non-prehensile manipulation environments, demonstrating improvements in task success rate under disturbances and environment changes. A real-world experiment is also conducted to validate the framework's practical effectiveness.

Useful robot control algorithms should not only achieve performance objectives but also adhere to hard safety constraints. Control Barrier Functions (CBFs) have been developed to provably ensure system safety through forward invariance. However, they often unnecessarily sacrifice performance for safety since they are purely reactive. Receding horizon control (RHC), on the other hand, consider planned trajectories to account for the future evolution of a system. This work provides a new perspective on safety-critical control by introducing Forward Invariance in Trajectory Spaces (FITS). We lift the problem of safe RHC into the trajectory space and describe the evolution of planned trajectories as a controlled dynamical system. Safety constraints defined over states can be converted into sets in the trajectory space which we render forward invariant via a CBF framework. We derive an efficient quadratic program (QP) to synthesize trajectories that provably satisfy safety constraints. Our experiments support that FITS improves the adherence to safety specifications without sacrificing performance over alternative CBF and NMPC methods., Comment: 8 pages, 4 figures

The term safety in robotics is often understood as a synonym for avoidance. Although this perspective has led to progress in path planning and reactive control, a generalization of this perspective is necessary to include task semantics relevant to contact-rich manipulation tasks, especially during teleoperation and to ensure the safety of learned policies. We introduce the semantics-aware distance function and a corresponding computational method based on the Kelvin Transformation. The semantics-aware distance generalizes signed distance functions by allowing the zero level set to lie inside of the object in regions where contact is allowed, effectively incorporating task semantics -- such as object affordances and user intent -- in an adaptive implicit representation of safe sets. In validation experiments we show the capability of our method to adapt to time-varying semantic information, and to perform queries in sub-microsecond, enabling applications in reinforcement learning, trajectory optimization, and motion planning., Comment: 8 pages, 6 figures, submitted to IEEE/RSJ IROS 2024

In this paper, we investigate the Walk on Spheres algorithm (WoS) for motion planning in robotics. WoS is a Monte Carlo method to solve the Dirichlet problem developed in the 50s by Muller and has recently been repopularized by Sawhney and Crane, who showed its applicability for geometry processing in volumetric domains. This paper provides a first study into the applicability of WoS for robot motion planning in configuration spaces, with potential fields defined as the solution of screened Poisson equations. The experiments in this paper empirically indicate the method's trivial parallelization, its dimension-independent convergence characteristic of $O(1/N)$ in the number of walks, and a validation experiment on the RR platform., Comment: 10 pages, 13 figures

To develop robust manipulation policies, quantifying robustness is essential. Evaluating robustness in general dexterous manipulation, nonetheless, poses significant challenges due to complex hybrid dynamics, combinatorial explosion of possible contact interactions, global geometry, etc. This paper introduces ``caging in motion'', an approach for analyzing manipulation robustness through energy margins and caging-based analysis. Our method assesses manipulation robustness by measuring the energy margin to failure and extends traditional caging concepts for a global analysis of dynamic manipulation. This global analysis is facilitated by a kinodynamic planning framework that naturally integrates global geometry, contact changes, and robot compliance. We validate the effectiveness of our approach in the simulation and real-world experiments of multiple dynamic manipulation scenarios, highlighting its potential to predict manipulation success and robustness., Comment: 8 pages

Even though large-scale text-to-image generative models show promising performance in synthesizing high-quality images, applying these models directly to image editing remains a significant challenge. This challenge is further amplified in video editing due to the additional dimension of time. This is especially the case for editing real-world videos as it necessitates maintaining a stable structural layout across frames while executing localized edits without disrupting the existing content. In this paper, we propose RealCraft, an attention-control-based method for zero-shot real-world video editing. By swapping cross-attention for new feature injection and relaxing spatial-temporal attention of the editing object, we achieve localized shape-wise edit along with enhanced temporal consistency. Our model directly uses Stable Diffusion and operates without the need for additional information. We showcase the proposed zero-shot attention-control-based method across a range of videos, demonstrating shape-wise, time-consistent and parameter-free editing in videos of up to 64 frames.

As model and dataset sizes continue to scale in robot learning, the need to understand how the composition and properties of a dataset affect model performance becomes increasingly urgent to ensure cost-effective data collection and model performance. In this work, we empirically investigate how physics attributes (color, friction coefficient, shape) and scene background characteristics, such as the complexity and dynamics of interactions with background objects, influence the performance of Video Transformers in predicting planar pushing trajectories. We investigate three primary questions: How do physics attributes and background scene characteristics influence model performance? What kind of changes in attributes are most detrimental to model generalization? What proportion of fine-tuning data is required to adapt models to novel scenarios? To facilitate this research, we present CloudGripper-Push-1K, a large real-world vision-based robot pushing dataset comprising 1278 hours and 460,000 videos of planar pushing interactions with objects with different physics and background attributes. We also propose Video Occlusion Transformer (VOT), a generic modular video-transformer-based trajectory prediction framework which features 3 choices of 2D-spatial encoders as the subject of our case study. The dataset and source code are available at https://cloudgripper.org., Comment: IEEE/RSJ IROS 2024

We present CloudGripper, an open source cloud robotics testbed, consisting of a scalable, space and cost-efficient design constructed as a rack of 32 small robot arm work cells. Each robot work cell is fully enclosed and features individual lighting, a low-cost custom 5 degree of freedom Cartesian robot arm with an attached parallel jaw gripper and a dual camera setup for experimentation. The system design is focused on continuous operation and features a 10 Gbit/s network connectivity allowing for high throughput remote-controlled experimentation and data collection for robotic manipulation. CloudGripper furthermore is intended to form a community testbed to study the challenges of large scale machine learning and cloud and edge-computing in the context of robotic manipulation. In this work, we describe the mechanical design of the system, its initial software stack and evaluate the repeatability of motions executed by the proposed robot arm design. A local network API throughput and latency analysis is also provided. CloudGripper-Rope-100, a dataset of more than a hundred hours of randomized rope pushing interactions and approximately 4 million camera images is collected and serves as a proof of concept demonstrating data collection capabilities. A project website with more information is available at https://cloudgripper.org., Comment: Under review at IEEE ICRA 2024

We present a sampling-based approach to reasoning about the caging-based manipulation of rigid and a simplified class of deformable 3D objects subject to energy constraints. Towards this end, we propose the notion of soft fixtures extending earlier work on energy-bounded caging to include a broader set of energy function constraints and settings, such as gravitational and elastic potential energy of 3D deformable objects. Previous methods focused on establishing provably correct algorithms to compute lower bounds or analytically exact estimates of escape energy for a very restricted class of known objects with low-dimensional C-spaces, such as planar polygons. We instead propose a practical sampling-based approach that is applicable in higher-dimensional C-spaces but only produces a sequence of upper-bound estimates that, however, appear to converge rapidly to actual escape energy. We present 8 simulation experiments demonstrating the applicability of our approach to various complex quasi-static manipulation scenarios. Quantitative results indicate the effectiveness of our approach in providing upper-bound estimates for escape energy in quasi-static manipulation scenarios. Two real-world experiments also show that the computed normalized escape energy estimates appear to correlate strongly with the probability of escape of an object under randomized pose perturbation., Comment: Paper submitted to ICRA 2024

We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence properties. Due to its radial definition RVDE is continuous and computable in linear time with respect to the dataset size. This amends for the main shortcomings of previously studied VDEs, which are highly discontinuous and computationally expensive. We provide a theoretical study of the modes of RVDE as well as an empirical investigation of its performance on high-dimensional data. Results show that RVDE outperforms other non-parametric density estimators, including recently introduced VDEs., Comment: 13 pages

We introduce an algorithm for active function approximation based on nearest neighbor regression. Our Active Nearest Neighbor Regressor (ANNR) relies on the Voronoi-Delaunay framework from computational geometry to subdivide the space into cells with constant estimated function value and select novel query points in a way that takes the geometry of the function graph into account. We consider the recent state-of-the-art active function approximator called DEFER, which is based on incremental rectangular partitioning of the space, as the main baseline. The ANNR addresses a number of limitations that arise from the space subdivision strategy used in DEFER. We provide a computationally efficient implementation of our method, as well as theoretical halting guarantees. Empirical results show that ANNR outperforms the baseline for both closed-form functions and real-world examples, such as gravitational wave parameter inference and exploration of the latent space of a generative model., Comment: Accepted at the International Conference on Machine Learning (ICML) 2022

The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because Voronoi cells rapidly increase in complexity as dimensions grow, making the necessary explicit computations infeasible. We define a variant of the VDE deemed Compactified Voronoi Density Estimator (CVDE), suitable for higher dimensions. We propose computationally efficient algorithms for numerical approximation of the CVDE and formally prove convergence of the estimated density to the original one. We implement and empirically validate the CVDE through a comparison with the Kernel Density Estimator (KDE). Our results indicate that the CVDE outperforms the KDE on sound and image data., Comment: Accepted at the Conference on Uncertainty in Artificial Intelligence (UAI) 2022. This version contains erratas of the published material

Optimal sampling based motion planning and trajectory optimization are two competing frameworks to generate optimal motion plans. Both frameworks have complementary properties: Sampling based planners are typically slow to converge, but provide optimality guarantees. Trajectory optimizers, however, are typically fast to converge, but do not provide global optimality guarantees in nonconvex problems, e.g. scenarios with obstacles. To achieve the best of both worlds, we introduce a new planner, BITKOMO, which integrates the asymptotically optimal Batch Informed Trees (BIT*) planner with the K-Order Markov Optimization (KOMO) trajectory optimization framework. Our planner is anytime and maintains the same asymptotic optimality guarantees provided by BIT*, while also exploiting the fast convergence of the KOMO trajectory optimizer. We experimentally evaluate our planner on manipulation scenarios that involve high dimensional configuration spaces, with up to two 7-DoF manipulators, obstacles and narrow passages. BITKOMO performs better than KOMO by succeeding even when KOMO fails, and it outperforms BIT* in terms of convergence to the optimal solution., Comment: 6 pages, Accepted at IROS 2022

In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path optimization problem. This is important to compress path databases, as contingencies for replanning and as source of symbolic representations. Following ideas from Morse theory, we define modes as paths invariant under optimization of a cost functional. We develop a multi-mode estimation algorithm which approximately finds all modes of a given motion optimization problem and asymptotically converges. This is made possible by integrating sparse roadmaps with an existing single-mode optimization algorithm. Initial evaluation results show the multi-mode estimation algorithm as a promising direction to study path spaces from a topological point of view., Comment: 5 pages, Extended Abstract for RSS Workshop on Geometry and Topology in Robotics

In this work we propose algorithms to explicitly construct a conservative estimate of the configuration spaces of rigid objects in 2D and 3D. Our approach is able to detect compact path components and narrow passages in configuration space which are important for applications in robotic manipulation and path planning. Moreover, as we demonstrate, they are also applicable to identification of molecular cages in chemistry. Our algorithms are based on a decomposition of the resulting 3 and 6 dimensional configuration spaces into slices corresponding to a finite sample of fixed orientations in configuration space. We utilize dual diagrams of unions of balls and uniform grids of orientations to approximate the configuration space. We carry out experiments to evaluate the computational efficiency on a set of objects with different geometric features thus demonstrating that our approach is applicable to different object shapes. We investigate the performance of our algorithm by computing increasingly fine-grained approximations of the object's configuration space., Comment: submitted to IJRR

In this paper, we compute a conservative approximation of the path-connected components of the free space of a rigid object in a 2D workspace in order to solve two closely related problems: to determine whether there exists a collision-free path between two given configurations, and to verify whether an object can escape arbitrarily far from its initial configuration -- i.e., whether the object is caged. Furthermore, we consider two quantitative characteristics of the free space: the volume of path-connected components and the width of narrow passages. To address these problems, we decompose the configuration space into a set of two-dimensional slices, approximate them as two-dimensional alpha-complexes, and then study the relations between them. This significantly reduces the computational complexity compared to a direct approximation of the free space. We implement our algorithm and run experiments in a three-dimensional configuration space of a simple object showing runtime of less than 2 seconds.

We present a novel approach and database which combines the inexpensive generation of 3D object models via monocular or RGB-D camera images with 3D printing and a state of the art object tracking algorithm. Unlike recent efforts towards the creation of 3D object databases for robotics, our approach does not require expensive and controlled 3D scanning setups and enables anyone with a camera to scan, print and track complex objects for manipulation research. The proposed approach results in highly detailed mesh models whose 3D printed replicas are at times difficult to distinguish from the original. A key motivation for utilizing 3D printed objects is the ability to precisely control and vary object properties such as the mass distribution and size in the 3D printing process to obtain reproducible conditions for robotic manipulation research. We present CapriDB - an extensible database resulting from this approach containing initially 40 textured and 3D printable mesh models together with tracking features to facilitate the adoption of the proposed approach.

Autonomous robots operating in dynamic environments must maintain beliefs over a hypothesis space that is rich enough to represent the activities of interest at different scales. This is important both in order to accommodate the availability of evidence at varying degrees of coarseness, such as when interpreting and assimilating natural instructions, but also in order to make subsequent reactive planning more efficient. We present an algorithm that combines a topology-based trajectory clustering procedure that generates hierarchically-structured spatial abstractions with a bank of particle filters at each of these abstraction levels so as to produce probability estimates over an agent's navigation activity that is kept consistent across the hierarchy. We study the performance of the proposed method using a synthetic trajectory dataset in 2D, as well as a dataset taken from AIS-based tracking of ships in an extended harbour area. We show that, in comparison to a baseline which is a particle filter that estimates activity without exploiting such structure, our method achieves a better normalised error in predicting the trajectory as well as better time to convergence to a true class when compared against ground truth., Comment: 16 pages

Reinforcement Learning (RL) struggles in problems with delayed rewards, and one approach is to segment the task into sub-tasks with incremental rewards. We propose a framework called Hierarchical Inverse Reinforcement Learning (HIRL), which is a model for learning sub-task structure from demonstrations. HIRL decomposes the task into sub-tasks based on transitions that are consistent across demonstrations. These transitions are defined as changes in local linearity w.r.t to a kernel function. Then, HIRL uses the inferred structure to learn reward functions local to the sub-tasks but also handle any global dependencies such as sequentiality. We have evaluated HIRL on several standard RL benchmarks: Parallel Parking with noisy dynamics, Two-Link Pendulum, 2D Noisy Motion Planning, and a Pinball environment. In the parallel parking task, we find that rewards constructed with HIRL converge to a policy with an 80% success rate in 32% fewer time-steps than those constructed with Maximum Entropy Inverse RL (MaxEnt IRL), and with partial state observation, the policies learned with IRL fail to achieve this accuracy while HIRL still converges. We further find that that the rewards learned with HIRL are robust to environment noise where they can tolerate 1 stdev. of random perturbation in the poses in the environment obstacles while maintaining roughly the same convergence rate. We find that HIRL rewards can converge up-to 6x faster than rewards constructed with IRL., Comment: 12 pages

In many applications data is naturally presented in terms of orderings of some basic elements or symbols. Reasoning about such data requires a notion of similarity capable of handling sequences of different lengths. In this paper we describe a family of Mercer kernel functions for such sequentially structured data. The family is characterized by a decomposable structure in terms of symbol-level and structure-level similarities, representing a specific combination of kernels which allows for efficient computation. We provide an experimental evaluation on sequential classification tasks comparing kernels from our family of kernels to a state of the art sequence kernel called the Global Alignment kernel which has been shown to outperform Dynamic Time Warping

Let $(L, h)\to (X, \omega)$ denote a polarized toric K\"ahler manifold. Fix a toric submanifold $Y$ and denote by $\hat{\rho}_{tk}:X\to \mathbb{R}$ the partial density function corresponding to the partial Bergman kernel projecting smooth sections of $L^k$ onto holomorphic sections of $L^k$ that vanish to order at least $tk$ along $Y$, for fixed $t>0$ such that $tk\in \mathbb{N}$. We prove the existence of a distributional expansion of $\hat{\rho}_{tk}$ as $k\to \infty$, including the identification of the coefficient of $k^{n-1}$ as a distribution on $X$. This expansion is used to give a direct proof that if $\omega$ has constant scalar curvature, then $(X, L)$ must be slope semi-stable with respect to $Y$. Similar results are also obtained for more general partial density functions. These results have analogous applications to the study of toric K-stability of toric varieties., Comment: Accepted by Mathematische Annalen on 13 September 2013