Graph generation is a critical task across scientific domains. Existing methods fall broadly into two categories: autoregressive models, which iteratively expand graphs, and one-shot models, such as diffusion, which generate the full graph at once. In this work, we provide an analysis of these two paradigms and reveal a key trade-off: autoregressive models stand out in capturing fine-grained local structures, such as degree and clustering properties, whereas one-shot models excel at modeling global patterns, such as spectral distributions. Building on this, we propose LGDC (latent graph diffusion via spectrum-preserving coarsening), a hybrid framework that combines strengths of both approaches. LGDC employs a spectrum-preserving coarsening-decoarsening to bidirectionally map between graphs and a latent space, where diffusion efficiently generates latent graphs before expansion restores detail. This design captures both local and global properties with improved efficiency. Empirically, LGDC matches autoregressive models on locally structured datasets (Tree) and diffusion models on globally structured ones (Planar, Community-20), validating the benefits of hybrid generation.

Data-driven planar pushing methods have recently gained attention as they reduce manual engineering effort and improve generalization compared to analytical approaches. However, most prior work targets narrow capabilities (e.g., side switching, precision, or single-task training), limiting broader applicability. We present a model-based framework for non-prehensile tabletop pushing that uses a single learned model to address multiple tasks without retraining. Our approach employs a recurrent GRU-based architecture with additional non-linear layers to capture object-environment dynamics while ensuring stability. A tailored state-action representation enables the model to generalize across uncertain dynamics, variable push lengths, and diverse tasks. For control, we integrate the learned dynamics with a sampling-based Model Predictive Path Integral (MPPI) controller, which generates adaptive, task-oriented actions. This framework supports side switching, variable-length pushes, and objectives such as precise positioning, trajectory following, and obstacle avoidance. Training is performed in simulation with domain randomization to support sim-to-real transfer. We first evaluate the architecture through ablation studies, showing improved prediction accuracy and stable rollouts. We then validate the full system in simulation and real-world experiments using a Franka Panda robot with markerless tracking. Results demonstrate high success rates in precise positioning under strict thresholds and strong performance in trajectory tracking and obstacle avoidance. Moreover, multiple tasks are solved simply by changing the controller's objective function, without retraining. While our current focus is on a single object type, we extend the framework by training on wider push lengths and designing a balanced controller that reduces the number of steps for longer-horizon goals.

Torsion Resistant Strain Limiting Layers Enable High Grip Strength of Electrically-Driven Handed Shearing Auxetic Grippers Ian Good, Srivatsan Balaji, and Jeffrey I. Lipton Abstract --Soft grippers have demonstrated a strong ability to successfully pick and manipulate many objects. A key limitation to their wider adoption is their inability to grasp larger payloads due to objects slipping out of grasps. We have overcome this limitation by introducing a torsionally rigid strain limiting layer (TR-SLL). This reduces out-of-plane bending while maintaining the gripper's softness and in-plane flexibility. We characterize the design space of the strain limiting layer and Handed Shearing Auxetic (HSA) actuators for a soft gripper using simulation and experiment. The inclusion of the TR-SLL with HSAs enables HSA grippers to be made with a single digit. We found that the use of our TR-SLL HSA gripper enabled pinch grasping of payloads over 1 kg. We demonstrate a lifting capacity of 5 kg when loading using the TR-SLL. We also demonstrate a peak pinch grasp force of 5.8 N, and a peak planar caging force of 14.5 N. Finally, we test the TR-SLL gripper on a suite of 43 YCB objects. We show success on 37 objects demonstrating significant capabilities. I NTRODUCTION Soft robotic fingers have focused on emulating the ability of human and other biotas compliance when bending [1]. However, the key to human's remarkable grip is that our fingers can simultaneously bend while resisting torsion and lateral loading. People rely on a rigid skeleton with discrete joints to provide this selective compliance. We build upon a previous conference paper that introduced the torsion resistant strain limiting layer (TR-SLL) [2]. The TR-SLL provides soft grippers with same torsion resistance of a skeleton without discretization. This work extends this to entirely electrically driven grippers. This allows a single Handed Shearing Auxetic (HSA) to be used in gripper and produce a high holding force. The TR-SLLs constrict bending and serves as a reaction body for the HSA.

Determining the maximal density $m_1(\mathbb{R}^2)$ of planar sets without unit distances is a fundamental problem in combinatorial geometry. This paper investigates lower bounds for this quantity. We introduce a novel approach to estimating $m_1(\mathbb{R}^2)$ by reformulating the problem as a Maximal Independent Set (MIS) problem on graphs constructed from flat torus, focusing on periodic sets with respect to two non-collinear vectors. Our experimental results supported by theoretical justifications of proposed method demonstrate that for a sufficiently wide range of parameters this approach does not improve the known lower bound $0.22936 \le m_1(\mathbb{R}^2)$. The best discrete sets found are approximations of Croft's construction. In addition, several open source software packages for MIS problem are compared on this task.

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.

Non-prehensile planar pushing is a challenging task due to its underactuated nature with hybrid-dynamics, where a robot needs to reason about an object's long-term behaviour and contact-switching, while being robust to contact uncertainty. The presence of clutter in the environment further complicates this task, introducing the need to include more sophisticated spatial analysis to avoid collisions. Building upon prior work on reinforcement learning (RL) with multimodal categorical exploration for planar pushing, in this paper we incorporate location-based attention to enable robust navigation through clutter. Unlike previous RL literature addressing this obstacle avoidance pushing task, our framework requires no predefined global paths and considers the target orientation of the manipulated object. Our results demonstrate that the learned policies successfully navigate through a wide range of complex obstacle configurations, including dynamic obstacles, with smooth motions, achieving the desired target object pose. We also validate the transferability of the learned policies to robotic hardware using the KUKA iiwa robot arm.

We present a method for global motion planning of robotic systems that interact with the environment through contacts. Our method directly handles the hybrid nature of such tasks using tools from convex optimization. We formulate the motion-planning problem as a shortest-path problem in a graph of convex sets, where a path in the graph corresponds to a contact sequence and a convex set models the quasi-static dynamics within a fixed contact mode. For each contact mode, we use semidefinite programming to relax the nonconvex dynamics that results from the simultaneous optimization of the object's pose, contact locations, and contact forces. The result is a tight convex relaxation of the overall planning problem, that can be efficiently solved and quickly rounded to find a feasible contact-rich trajectory. As a first application of this technique, we focus on the task of planar pushing. Exhaustive experiments show that our convex-optimization method generates plans that are consistently within a small percentage of the global optimum. We demonstrate the quality of these plans on a real robotic system.

Developing robot controllers capable of achieving dexterous nonprehensile manipulation, such as pushing an object on a table, is challenging. The underactuated and hybrid-dynamics nature of the problem, further complicated by the uncertainty resulting from the frictional interactions, requires sophisticated control behaviors. Reinforcement Learning (RL) is a powerful framework for developing such robot controllers. However, previous RL literature addressing the nonprehensile pushing task achieves low accuracy, non-smooth trajectories, and only simple motions, i.e. without rotation of the manipulated object. We conjecture that previously used unimodal exploration strategies fail to capture the inherent hybrid-dynamics of the task, arising from the different possible contact interaction modes between the robot and the object, such as sticking, sliding, and separation. In this work, we propose a multimodal exploration approach through categorical distributions, which enables us to train planar pushing RL policies for arbitrary starting and target object poses, i.e. positions and orientations, and with improved accuracy. We show that the learned policies are robust to external disturbances and observation noise, and scale to tasks with multiple pushers. Furthermore, we validate the transferability of the learned policies, trained entirely in simulation, to a physical robot hardware using the KUKA iiwa robot arm. See our supplemental video: https://youtu.be/vTdva1mgrk4.