Contact Modes Are Strata: What Geometric Structure Buys in Discrete-Continuous Planning

Contact-rich manipulation poses a discrete question and a continuous one at once, namely which contacts are active and how to move while they hold. The two are coupled by a change of dimension, since each contact that a robot maintains confines its motion to a lower-dimensional manifold. We make that coupling the explicit object of planning by observing that a contact mode is not merely analogous to a stratum of the configuration space; it is one. A plan is then a walk over strata whose within-stratum segments are geodesics. On two contact-rich manipulation tasks in simulation, pushing a T-shaped block around obstacles and reorienting a cube in a dexterous hand, our planner returns solutions within seconds with no mode, contact sequence, or stratum given in advance.

Lost in Time? Continuous Symmetry and Identifiability in Aided Inertial Navigation with Unknown Measurement Delays

In many multisensor systems, measurements from different sensors are subject to unknown relative time delays. Accurate state estimation requires that delays be accounted for and, when possible, calibrated online. We consider the case of aided navigation, where measurements from a single aiding sensor are subject to an unknown but constant delay relative to the inertial measurement stream, and study the identifiability of the resulting system. Critically, identifiability depends not only on the temporal structure of the measurements, but also on the shape of the vehicle trajectory: some trajectories are sufficiently informative to support unique recovery of the delay and the navigation state, while others are not. Using the special Galilean group, we characterize these uninformative (or degenerate) trajectories and relate them to a continuous symmetry of the delayed measurement model, providing geometric insight into identifiability failures. We show that the class of trajectories for which identifiability fails is larger than previously reported, and connect our characterization to the familiar linearized, Jacobian-based analysis. Although our development is motivated by aided navigation, the underlying ideas apply more broadly to estimation problems on Lie groups with delayed measurements.

On the Identifiability of Aided Inertial Navigation Under Measurement Delays: A Geometric Approach

In aided inertial navigation, measurements from different sensors are often subject to unknown relative time delays. Consider a single aiding sensor whose measurements have an unknown but constant delay relative to the inertial-measurement data stream. We study the identifiability of the delay and the initial navigation state that parameterizes the trajectory. Identifiability depends on both the temporal structure of the aiding measurements and the form of the trajectory itself. Our geometric analysis shows that, for a larger class of uninformative (i.e., degenerate) trajectories than has previously been reported, the delayed measurement model admits a continuous symmetry that prevents unique delay-and-state recovery.

Exploring the Intrinsic Geometry of Diffusion Models with Constrained Inverse Kinematics

Recent studies suggest that diffusion models can recover geometric structure in the data manifolds they are trained on, yet the supporting evidence has so far come mostly from natural-image data, where the underlying geometry itself is unknown. We study this question in a setting where the geometry is analytically tractable: constrained inverse kinematics (IK). Each task-space constraint defines a configuration-space manifold with known intrinsic dimension, giving direct ground truth for evaluating the geometry learned by the model. For each of the 6-DoF UR5 and 7-DoF Franka, we train a single conditional diffusion model across seven constraint families, spanning solution manifolds from discrete IK branches to self-motion manifolds. Our empirical results reveal that the intrinsic dimension recovered from the model's score function matches the analytical degrees of freedom of the corresponding constraint manifold across both robots. Moreover, linear interpolation in the latent space leads to generated solutions that remain close to the appropriate constraint manifold, indicating that the learned representation further captures geometric structure of the constraint family beyond intrinsic dimension alone. Constrained IK therefore offers a controlled setting for studying the intrinsic geometry learned by diffusion models.

Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds

Informed sampling techniques accelerate sampling-based motion planners by focusing the search on promising regions of the state space, yet most existing methods rely on Euclidean heuristics that become inadmissible under configuration-dependent Riemannian metrics. While scalar eigenvalue bounds restore admissibility by uniformly scaling the Euclidean distance, they discard the directional structure of the metric, producing overly conservative informed sets. We propose a matrix-valued admissible heuristic that exploits the Loewner order on symmetric positive definite matrices to compute the tightest constant lower bound on the metric tensor while preserving its full directional structure. The Cholesky factorization of this bound defines a linear map to an isotropic Euclidean space in which the Riemannian informed set reduces to a standard prolate hyperspheroid, enabling direct, rejection-free sampling using existing algorithms. Experiments on manipulation tasks with a 6-DoF UR5, 7-DoF Franka, and 14-DoF PR2 under three distinct Riemannian metrics show that our heuristic produces consistently tighter informed sets than both the Euclidean and scalar eigenvalue bounds, accelerating convergence across multiple state-of-the-art asymptotically optimal planners.

Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds

In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the problem of planning collision-free motions that minimize length under configuration-dependent Riemannian metrics, corresponding to geodesics on the configuration manifold. Conventional numerical methods for computing such paths do not scale well to high-dimensional systems, while sampling-based planners trade scalability for geometric fidelity. To bridge this gap, we propose a sampling-based motion planning framework that operates directly on Riemannian manifolds. We introduce a computationally efficient midpoint-based approximation of the Riemannian geodesic distance and prove that it matches the true Riemannian distance with third-order accuracy. Building on this approximation, we design a local planner that traces the manifold using first-order retractions guided by Riemannian natural gradients. Experiments on a two-link planar arm and a 7-DoF Franka manipulator under a kinetic-energy metric, as well as on rigid-body planning in $\mathrm{SE}(2)$ with non-holonomic motion constraints, demonstrate that our approach consistently produces lower-cost trajectories than Euclidean-based planners and classical numerical geodesic-solver baselines.

VibES: Induced Vibration for Persistent Event-Based Sensing

Event cameras are a bio-inspired class of sensors that asynchronously measure per-pixel intensity changes. Under fixed illumination conditions in static or low-motion scenes, rigidly mounted event cameras are unable to generate any events, becoming unsuitable for most computer vision tasks. To address this limitation, recent work has investigated motion-induced event stimulation that often requires complex hardware or additional optical components. In contrast, we introduce a lightweight approach to sustain persistent event generation by employing a simple rotating unbalanced mass to induce periodic vibrational motion. This is combined with a motion-compensation pipeline that removes the injected motion and yields clean, motion-corrected events for downstream perception tasks. We demonstrate our approach with a hardware prototype and evaluate it on real-world captured datasets. Our method reliably recovers motion parameters and improves both image reconstruction and edge detection over event-based sensing without motion induction.

Risk-Averse Traversal of Graphs with Stochastic and Correlated Edge Costs for Safe Global Planetary Mobility

In robotic planetary surface exploration, strategic mobility planning is an important task that involves finding candidate long-distance routes on orbital maps and identifying segments with uncertain traversability. Then, expert human operators establish safe, adaptive traverse plans based on the actual navigation difficulties encountered in these uncertain areas. In this paper, we formalize this challenge as a new, risk-averse variant of the Canadian Traveller Problem (CTP) tailored to global planetary mobility. The objective is to find a traverse policy minimizing a conditional value-at-risk (CVaR) criterion, which is a risk measure with an intuitive interpretation. We propose a novel search algorithm that finds exact CVaR-optimal policies. Our approach leverages well-established optimal AND-OR search techniques intended for (risk-agnostic) expectation minimization and extends these methods to the risk-averse domain. We validate our approach through simulated long-distance planetary surface traverses; we employ real orbital maps of the Martian surface to construct problem instances and use terrain maps to express traversal probabilities in uncertain regions. Our results illustrate different adaptive decision-making schemes depending on the level of risk aversion. Additionally, our problem setup allows accounting for traversability correlations between similar areas of the environment. In such a case, we empirically demonstrate how information-seeking detours can mitigate risk.

Learning Cross-Spectral Point Features with Task-Oriented Training

Unmanned aerial vehicles (UAVs) enable operations in remote and hazardous environments, yet the visible-spectrum, camera-based navigation systems often relied upon by UAVs struggle in low-visibility conditions. Thermal cameras, which capture long-wave infrared radiation, are able to function effectively in darkness and smoke, where visible-light cameras fail. This work explores learned cross-spectral (thermal-visible) point features as a means to integrate thermal imagery into established camera-based navigation systems. Existing methods typically train a feature network's detection and description outputs directly, which often focuses training on image regions where thermal and visible-spectrum images exhibit similar appearance. Aiming to more fully utilize the available data, we propose a method to train the feature network on the tasks of matching and registration. We run our feature network on thermal-visible image pairs, then feed the network response into a differentiable registration pipeline. Losses are applied to the matching and registration estimates of this pipeline. Our selected model, trained on the task of matching, achieves a registration error (corner error) below 10 pixels for more than 75% of estimates on the MultiPoint dataset. We further demonstrate that our model can also be used with a classical pipeline for matching and registration.

Structured Pneumatic Fingerpads for Actively Tunable Grip Friction

Grip surfaces with tunable friction can actively modify contact conditions, enabling transitions between higher- and lower-friction states for grasp adjustment. Friction can be increased to grip securely and then decreased to gently release (e.g., for handovers) or manipulate in-hand. Recent friction-tuning surface designs using soft pneumatic chambers show good control over grip friction; however, most require complex fabrication processes and/or custom gripper hardware. We present a practical structured fingerpad design for friction tuning that uses less than \$1 USD of materials, takes only seconds to repair, and is easily adapted to existing grippers. Our design uses surface morphology changes to tune friction. The fingerpad is actuated by pressurizing its internal chambers, thereby deflecting its flexible grip surface out from or into these chambers. We characterize the friction-tuning capabilities of our design by measuring the shear force required to pull an object from a gripper equipped with two independently actuated fingerpads. Our results show that varying actuation pressure and timing changes the magnitude of friction forces on a gripped object by up to a factor of 2.8. We demonstrate additional features including macro-scale interlocking behaviour and pressure-based object detection.