Abstract-- There are many challenges in bimanual assembly, including high-level sequencing, multi-robot coordination, and low-level, contact-rich operations such as component mating. T ask and motion planning (T AMP) methods, while effective in this domain, may be prohibitively slow to converge when adapting to disturbances that require new task sequencing and optimisation. These events are common during tight-tolerance assembly, where difficult-to-model dynamics such as friction or deformation require rapid replanning and reat-tempts. Moreover, defining explicit task sequences for assembly can be cumbersome, limiting flexibility when task replanning is required. T o simplify this planning, we introduce BGBG, a decentralised gradient-based framework that uses a piecewise continuous energy function through the automatic composition of adaptive potential functions. This approach generates sub-goals using only myopic optimisation, rather than long-horizon planning. It demonstrates effectiveness at solving long-horizon tasks due to the structure and adaptivity of the energy function. We show that our approach scales to physical bimanual assembly tasks for constructing tight-tolerance assemblies. In these experiments, we discover that our gradient-based rapid replanning framework generates automatic retries, coordinated motions and autonomous handovers in an emergent fashion. Bimanual assembly is an inherently sequential planning problem that demands reasoning over tasks and motions. The challenge is further amplified in contact-rich settings or when collaborating with humans, making efficient and robust planning essential for reliable execution.

Clustering non-independent and identically distributed (non-IID) data under local differential privacy (LDP) in federated settings presents a critical challenge: preserving privacy while maintaining accuracy without iterative communication. Existing one-shot methods rely on unstable pairwise centroid distances or neighborhood rankings, degrading severely under strong LDP noise and data heterogeneity. We present Gravitational Federated Clustering (GFC), a novel approach to privacy-preserving federated clustering that overcomes the limitations of distance-based methods under varying LDP. Addressing the critical challenge of clustering non-IID data with diverse privacy guarantees, GFC transforms privatized client centroids into a global gravitational potential field where true cluster centers emerge as topologically persistent singularities. Our framework introduces two key innovations: (1) a client-side compactness-aware perturbation mechanism that encodes local cluster geometry as "mass" values, and (2) a server-side topological aggregation phase that extracts stable centroids through persistent homology analysis of the potential field's superlevel sets. Theoretically, we establish a closed-form bound between the privacy budget $ε$ and centroid estimation error, proving the potential field's Lipschitz smoothing properties exponentially suppress noise in high-density regions. Empirically, GFC outperforms state-of-the-art methods on ten benchmarks, especially under strong LDP constraints ($ε< 1$), while maintaining comparable performance at lower privacy budgets. By reformulating federated clustering as a topological persistence problem in a synthetic physics-inspired space, GFC achieves unprecedented privacy-accuracy trade-offs without iterative communication, providing a new perspective for privacy-preserving distributed learning.

Personal use of this material is permitted. Abstract-- Motivated by the problem of pursuit-evasion, we present a motion planning framework that combines energy-based diffusion models with artificial potential fields for robust real time trajectory generation in complex environments. Our approach processes obstacle information directly from point clouds, enabling efficient planning without requiring complete geometric representations. The framework employs classifier-free guidance training and integrates local potential fields during sampling to enhance obstacle avoidance. In dynamic scenarios, the system generates initial trajectories using the diffusion model and continuously refines them through potential field-based adaptation, demonstrating effective performance in pursuit-evasion scenarios with partial pursuer observability. This paper is motivated by the problem of using robots to guide crowds to safety in scenarios involving rapidly evolving threats, such as an active shooter or a forest fire.

Teleoperated ultrasound can improve diagnostic medical imaging access for remote communities. Having accurate force feedback is important for enabling sonographers to apply the appropriate probe contact force to optimize ultrasound image quality. However, large time delays in communication make direct force feedback impractical. Prior work investigated using point cloud-based model-mediated teleoperation and internal potential field models to estimate contact forces and torques. We expand on this by introducing a method to update the internal potential field model of the patient with measured positions and forces for more transparent model-mediated tele-ultrasound. We first generate a point cloud model of the patient's surface and transmit this to the sonographer in a compact data structure. This is converted to a static voxelized volume where each voxel contains a potential field value. These values determine the forces and torques, which are rendered based on overlap between the voxelized volume and a point shell model of the ultrasound transducer. We solve for the potential field using a convex quadratic that combines the spatial Laplace operator with measured forces. This was evaluated on volunteer patients ($n=3$) by computing the accuracy of rendered forces. Results showed the addition of measured forces to the model reduced the force magnitude error by an average of 7.23 N and force vector angle error by an average of 9.37$^{\circ}$ compared to using only Laplace's equation.

-- Deep generative models, particularly diffusion and flow matching models, have recently shown remarkable potential in learning complex policies through imitation learning. However, the safety of generated motions remains overlooked, particularly in complex environments with inherent obstacles. In this work, we address this critical gap by proposing Potential Field-Guided Flow Matching Policy (PF2MP), a novel approach that simultaneously learns task policies and extracts obstacle-related information, represented as a potential field, from the same set of successful demonstrations. During inference, PF2MP modulates the flow matching vector field via the learned potential field, enabling safe motion generation. By leveraging these complementary fields, our approach achieves improved safety without compromising task success across diverse environments, such as navigation tasks and robotic manipulation scenarios. We evaluate PF2MP in both simulation and real-world settings, demonstrating its effectiveness in task space and joint space control. Experimental results demonstrate that PF2MP enhances safety, achieving a significant reduction of collisions compared to baseline policies. This work paves the way for safer motion generation in unstructured and obstacle-rich environments.

Robotic trajectory planning in dynamic and cluttered environments remains a critical challenge, particularly when striving for both time efficiency and motion smoothness under actuation constraints. Traditional path planner, such as Artificial Potential Field (APF), offer computational efficiency but suffer from local minima issue due to position-based potential field functions and oscillatory motion near the obstacles due to Newtonian mechanics. To address this limitation, an Energy-based Artificial Potential Field (APF) framework is proposed in this paper that integrates position and velocity-dependent potential functions. E-APF ensures dynamic adaptability and mitigates local minima, enabling uninterrupted progression toward the goal. The proposed framework integrates E-APF with a hybrid trajectory optimizer that jointly minimizes jerk and execution time under velocity and acceleration constraints, ensuring geometric smoothness and time efficiency. The entire framework is validated in simulation using the 7-degree-of-freedom Kinova Gen3 robotic manipulator. The results demonstrate collision-free, smooth, time-efficient, and oscillation-free trajectory in the presence of obstacles, highlighting the efficacy of the combined trajectory optimization and real-time obstacle avoidance approach. This work lays the foundation for future integration with reactive control strategies and physical hardware deployment in real-world manipulation tasks.

Reactive intelligence remains one of the cornerstones of versatile robotics operating in cluttered, dynamic, and human-centred environments. Among reactive approaches, potential fields (PF) continue to be widely adopted due to their simplicity and real-time applicability. However, existing PF methods typically oversimplify environmental representations by relying on isotropic, point- or sphere-based obstacle approximations. In human-centred settings, this simplification results in overly conservative paths, cumbersome tuning, and computational overhead -- even breaking real-time requirements. In response, we propose the Geometric Potential Field (GeoPF), a reactive motion-planning framework that explicitly infuses geometric primitives -- points, lines, planes, cubes, and cylinders -- their structure and spatial relationship in modulating the real-time repulsive response. Extensive quantitative analyses consistently show GeoPF's higher success rates, reduced tuning complexity (a single parameter set across experiments), and substantially lower computational costs (up to 2 orders of magnitude) compared to traditional PF methods. Real-world experiments further validate GeoPF reliability, robustness, and practical ease of deployment, as well as its scalability to whole-body avoidance. GeoPF provides a fresh perspective on reactive planning problems driving geometric-aware temporal motion generation, enabling flexible and low-latency motion planning suitable for modern robotic applications.

This paper presents a multi-agent reinforcement learning (MARL) framework for cooperative collision avoidance of UA V swarms leveraging domain knowledge-driven reward. The reward is derived from knowledge in the domain of image processing, approximating contours on a two-dimensional field. By modeling obstacles as maxima on the field, collisions are inherently avoided as contours never go through peaks or intersect. Additionally, counters are smooth and energy-efficient. Our framework enables training with large swarm sizes as the agent interaction is minimized and the need for complex credit assignment schemes or observation sharing mechanisms in state-of-the-art MARL approaches are eliminated. Moreover, UA Vs obtain the ability to adapt to complex environments where contours may be nonviable or non-existent through intensive training. Extensive experiments are conducted to evaluate the performances of our framework against state-of-the-art MARL algorithms.

Safe navigation within a workspace is a fundamental skill for autonomous robots to accomplish more complex tasks. Harmonic potentials are artificial potential fields that are analytical, globally convergent and provably free of local minima. Thus, it has been widely used for generating safe and reliable robot navigation control policies. However, most existing methods do not allow customization of the harmonic potential fields nor the resulting paths, particularly regarding their topological properties. In this paper, we propose a novel method that automatically finds homotopy classes of paths that can be generated by valid harmonic potential fields. The considered complex workspaces can be as general as forest worlds consisting of numerous overlapping star-obstacles. The method is based on a hybrid optimization algorithm that searches over homotopy classes, selects the structure of each tree-of-stars within the forest, and optimizes over the continuous weight parameters for each purged tree via the projected gradient descent. The key insight is to transform the forest world to the unbounded point world via proper diffeomorphic transformations. It not only facilitates a simpler design of the multi-directional D-signature between non-homotopic paths, but also retain the safety and convergence properties. Extensive simulations and hardware experiments are conducted for non-trivial scenarios, where the navigation potentials are customized for desired homotopic properties. Project page: https://shuaikang-wang.github.io/CustFields.

--Navigation of UA Vs in unknown environments with obstacles is essential for applications in disaster response and infrastructure monitoring. However, existing obstacle avoidance algorithms such as Artificial Potential Field (APF) are unable to generalize across environments with different obstacle configurations. Furthermore, the precise location of the final target may not be available in applications such search and rescue, in which case approaches such as RF source seeking can be used to align towards the target location. This paper proposes a real-time trajectory planning method, which involves real time adaptation of APF through a sampling-based approach. The proposed approach utilizes only the bearing angle of the target without its precise location, and adjusts the potential field parameters according to the environment with new obstacle configurations in real time. The main contributions of the article are i) RF source seeking algorithm to provide a bearing angle estimate using RF signal calculations based on antenna placement, and ii) modified APF for adaptable collision avoidance in changing environments, which are evaluated separately in the simulation software Gazebo, using ROS2 for communication. Simulation results show that the RF source-seeking algorithm achieves high accuracy, with an average angular error of just 1.48 degrees, and with this estimate, the proposed navigation algorithm improves the success rate of reaching the target by 46% and reduces the trajectory length by 1.2% compared to standard potential fields. The increasing use of drones in various applications has been facilitated by advancements in sensor technology, enabling better localization and obstacle detection methods. These technologies allow drones to effectively navigate through complex environments, avoiding obstacles in real time. The demand for autonomous drone navigation is growing in sectors like search and rescue [1], inspection of unknown areas [2], and other critical applications requiring drones to operate in unfamiliar and potentially hazardous environments. In these scenarios, drones must autonomously identify and locate targets, update environmental maps in real time, detect obstacles, and plan safe trajectories. The variability of these environments, such as changes in obstacle sizes, distances, and spatial constraints, poses a significant challenge to creating a unified navigation system that can adapt to such differing conditions.