Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions

We study the problem of certifying the stability of closed-loop systems under control policies derived from optimal control or reinforcement learning (RL). Classical Lyapunov methods require a strict step-wise decrease in the Lyapunov function but such a certificate is difficult to construct for a learned control policy. The value function associated with an RL policy is a natural Lyapunov function candidate but it is not clear how it should be modified. To gain intuition, we first study the linear quadratic regulator (LQR) problem and make two key observations. First, a Lyapunov function can be obtained from the value function of an LQR policy by augmenting it with a residual term related to the system dynamics and stage cost. Second, the classical Lyapunov decrease requirement can be relaxed to a generalized Lyapunov condition requiring only decrease on average over multiple time steps. Using this intuition, we consider the nonlinear setting and formulate an approach to learn generalized Lyapunov functions by augmenting RL value functions with neural network residual terms. Our approach successfully certifies the stability of RL policies trained on Gymnasium and DeepMind Control benchmarks. We also extend our method to jointly train neural controllers and stability certificates using a multi-step Lyapunov loss, resulting in larger certified inner approximations of the region of attraction compared to the classical Lyapunov approach. Overall, our formulation enables stability certification for a broad class of systems with learned policies by making certificates easier to construct, thereby bridging classical control theory and modern learning-based methods.

Learned IMU Bias Prediction for Invariant Visual Inertial Odometry

Autonomous mobile robots operating in novel environments depend critically on accurate state estimation, often utilizing visual and inertial measurements. Recent work has shown that an invariant formulation of the extended Kalman filter improves the convergence and robustness of visual-inertial odometry by utilizing the Lie group structure of a robot's position, velocity, and orientation states. However, inertial sensors also require measurement bias estimation, yet introducing the bias in the filter state breaks the Lie group symmetry. In this paper, we design a neural network to predict the bias of an inertial measurement unit (IMU) from a sequence of previous IMU measurements. This allows us to use an invariant filter for visual inertial odometry, relying on the learned bias prediction rather than introducing the bias in the filter state. We demonstrate that an invariant multi-state constraint Kalman filter (MSCKF) with learned bias predictions achieves robust visual-inertial odometry in real experiments, even when visual information is unavailable for extended periods and the system needs to rely solely on IMU measurements.

Variational Formulation of the Particle Flow Particle Filter

This paper provides a formulation of the particle flow particle filter from the perspective of variational inference. We show that the transient density used to derive the particle flow particle filter follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density.

MISO: Multiresolution Submap Optimization for Efficient Globally Consistent Neural Implicit Reconstruction

Neural implicit representations have had a significant impact on simultaneous localization and mapping (SLAM) by enabling robots to build continuous, differentiable, and high-fidelity 3D maps from sensor data. However, as the scale and complexity of the environment increase, neural SLAM approaches face renewed challenges in the back-end optimization process to keep up with runtime requirements and maintain global consistency. We introduce MISO, a hierarchical optimization approach that leverages multiresolution submaps to achieve efficient and scalable neural implicit reconstruction. For local SLAM within each submap, we develop a hierarchical optimization scheme with learned initialization that substantially reduces the time needed to optimize the implicit submap features. To correct estimation drift globally, we develop a hierarchical method to align and fuse the multiresolution submaps, leading to substantial acceleration by avoiding the need to decode the full scene geometry. MISO significantly improves computational efficiency and estimation accuracy of neural signed distance function (SDF) SLAM on large-scale real-world benchmarks.

Learning Scene-Level Signed Directional Distance Function with Ellipsoidal Priors and Neural Residuals

Dense geometric environment representations are critical for autonomous mobile robot navigation and exploration. Recent work shows that implicit continuous representations of occupancy, signed distance, or radiance learned using neural networks offer advantages in reconstruction fidelity, efficiency, and differentiability over explicit discrete representations based on meshes, point clouds, and voxels. In this work, we explore a directional formulation of signed distance, called signed directional distance function (SDDF). Unlike signed distance function (SDF) and similar to neural radiance fields (NeRF), SDDF has a position and viewing direction as input. Like SDF and unlike NeRF, SDDF directly provides distance to the observed surface along the direction, rather than integrating along the view ray, allowing efficient view synthesis. To learn and predict scene-level SDDF efficiently, we develop a differentiable hybrid representation that combines explicit ellipsoid priors and implicit neural residuals. This approach allows the model to effectively handle large distance discontinuities around obstacle boundaries while preserving the ability for dense high-fidelity prediction. We show that SDDF is competitive with the state-of-the-art neural implicit scene models in terms of reconstruction accuracy and rendering efficiency, while allowing differentiable view prediction for robot trajectory optimization.

DynaGSLAM: Real-Time Gaussian-Splatting SLAM for Online Rendering, Tracking, Motion Predictions of Moving Objects in Dynamic Scenes

Simultaneous Localization and Mapping (SLAM) is one of the most important environment-perception and navigation algorithms for computer vision, robotics, and autonomous cars/drones. Hence, high quality and fast mapping becomes a fundamental problem. With the advent of 3D Gaussian Splatting (3DGS) as an explicit representation with excellent rendering quality and speed, state-of-the-art (SOTA) works introduce GS to SLAM. Compared to classical pointcloud-SLAM, GS-SLAM generates photometric information by learning from input camera views and synthesize unseen views with high-quality textures. However, these GS-SLAM fail when moving objects occupy the scene that violate the static assumption of bundle adjustment. The failed updates of moving GS affects the static GS and contaminates the full map over long frames. Although some efforts have been made by concurrent works to consider moving objects for GS-SLAM, they simply detect and remove the moving regions from GS rendering ("anti'' dynamic GS-SLAM), where only the static background could benefit from GS. To this end, we propose the first real-time GS-SLAM, "DynaGSLAM'', that achieves high-quality online GS rendering, tracking, motion predictions of moving objects in dynamic scenes while jointly estimating accurate ego motion. Our DynaGSLAM outperforms SOTA static & "Anti'' dynamic GS-SLAM on three dynamic real datasets, while keeping speed and memory efficiency in practice.

LATMOS: Latent Automaton Task Model from Observation Sequences

Robot task planning from high-level instructions is an important step towards deploying fully autonomous robot systems in the service sector. Three key aspects of robot task planning present challenges yet to be resolved simultaneously, namely, (i) factorization of complex tasks specifications into simpler executable subtasks, (ii) understanding of the current task state from raw observations, and (iii) planning and verification of task executions. To address these challenges, we propose LATMOS, an automata-inspired task model that, given observations from correct task executions, is able to factorize the task, while supporting verification and planning operations. LATMOS combines an observation encoder to extract the features from potentially high-dimensional observations with automata theory to learn a sequential model that encapsulates an automaton with symbols in the latent feature space. We conduct extensive evaluations in three task model learning setups: (i) abstract tasks described by logical formulas, (ii) real-world human tasks described by videos and natural language prompts and (iii) a robot task described by image and state observations. The results demonstrate the improved plan generation and verification capabilities of LATMOS across observation modalities and tasks.

LTLCodeGen: Code Generation of Syntactically Correct Temporal Logic for Robot Task Planning

This paper focuses on planning robot navigation tasks from natural language specifications. We develop a modular approach, where a large language model (LLM) translates the natural language instructions into a linear temporal logic (LTL) formula with propositions defined by object classes in a semantic occupancy map. The LTL formula and the semantic occupancy map are provided to a motion planning algorithm to generate a collision-free robot path that satisfies the natural language instructions. Our main contribution is LTLCodeGen, a method to translate natural language to syntactically correct LTL using code generation. We demonstrate the complete task planning method in real-world experiments involving human speech to provide navigation instructions to a mobile robot. We also thoroughly evaluate our approach in simulated and real-world experiments in comparison to end-to-end LLM task planning and state-of-the-art LLM-to-LTL translation methods.

Neural Configuration-Space Barriers for Manipulation Planning and Control

Planning and control for high-dimensional robot manipulators in cluttered, dynamic environments require both computational efficiency and robust safety guarantees. Inspired by recent advances in learning configuration-space distance functions (CDFs) as robot body representations, we propose a unified framework for motion planning and control that formulates safety constraints as CDF barriers. A CDF barrier approximates the local free configuration space, substantially reducing the number of collision-checking operations during motion planning. However, learning a CDF barrier with a neural network and relying on online sensor observations introduce uncertainties that must be considered during control synthesis. To address this, we develop a distributionally robust CDF barrier formulation for control that explicitly accounts for modeling errors and sensor noise without assuming a known underlying distribution. Simulations and hardware experiments on a 6-DoF xArm manipulator show that our neural CDF barrier formulation enables efficient planning and robust real-time safe control in cluttered and dynamic environments, relying only on onboard point-cloud observations.

SplatSDF: Boosting Neural Implicit SDF via Gaussian Splatting Fusion

A signed distance function (SDF) is a useful representation for continuous-space geometry and many related operations, including rendering, collision checking, and mesh generation. Hence, reconstructing SDF from image observations accurately and efficiently is a fundamental problem. Recently, neural implicit SDF (SDF-NeRF) techniques, trained using volumetric rendering, have gained a lot of attention. Compared to earlier truncated SDF (TSDF) fusion algorithms that rely on depth maps and voxelize continuous space, SDF-NeRF enables continuous-space SDF reconstruction with better geometric and photometric accuracy. However, the accuracy and convergence speed of scene-level SDF reconstruction require further improvements for many applications. With the advent of 3D Gaussian Splatting (3DGS) as an explicit representation with excellent rendering quality and speed, several works have focused on improving SDF-NeRF by introducing consistency losses on depth and surface normals between 3DGS and SDF-NeRF. However, loss-level connections alone lead to incremental improvements. We propose a novel neural implicit SDF called "SplatSDF" to fuse 3DGSandSDF-NeRF at an architecture level with significant boosts to geometric and photometric accuracy and convergence speed. Our SplatSDF relies on 3DGS as input only during training, and keeps the same complexity and efficiency as the original SDF-NeRF during inference. Our method outperforms state-of-the-art SDF-NeRF models on geometric and photometric evaluation by the time of submission.