SAFER-Splat (Simultaneous Action Filtering and Environment Reconstruction) is a real-time, scalable, and minimally invasive safety filter, based on control barrier functions, for safe robotic navigation in a detailed map constructed at runtime using Gaussian Splatting (GSplat). We propose a novel Control Barrier Function (CBF) that not only induces safety with respect to all Gaussian primitives in the scene, but when synthesized into a controller, is capable of processing hundreds of thousands of Gaussians while maintaining a minimal memory footprint and operating at 15 Hz during online Splat training. Of the total compute time, a small fraction of it consumes GPU resources, enabling uninterrupted training. The safety layer is minimally invasive, correcting robot actions only when they are unsafe. To showcase the safety filter, we also introduce SplatBridge, an open-source software package built with ROS for real-time GSplat mapping for robots. We demonstrate the safety and robustness of our pipeline first in simulation, where our method is 20-50x faster, safer, and less conservative than competing methods based on neural radiance fields. Further, we demonstrate simultaneous GSplat mapping and safety filtering on a drone hardware platform using only on-board perception. We verify that under teleoperation a human pilot cannot invoke a collision. Our videos and codebase can be found at https://chengine.github.io/safer-splat.

Autonomous visual navigation is an essential element in robot autonomy. Reinforcement learning (RL) offers a promising policy training paradigm. However, existing RL methods suffer from high sample complexity, poor sim-to-real transfer, and limited runtime adaptability. These problems are particularly challenging for drones, with complex nonlinear and unstable dynamics, and strong dynamic coupling between control and perception. In this paper, we propose a novel framework that integrates 3D Gaussian Splatting (3DGS) with differentiable deep reinforcement learning (DDRL) to train vision-based drone navigation policies. By leveraging high-fidelity 3D scene representations and differentiable simulation, our method improves sample efficiency and sim-to-real transfer. Additionally, we incorporate a Context-aided Estimator Network (CENet) to adapt to environmental variations at runtime. Moreover, by curriculum training in a mixture of different surrounding environments, we achieve in-task generalization, the ability to solve new instances of a task not seen during training. Drone hardware experiments demonstrate our method’s high training efficiency compared to state-of-the-art RL methods, zero shot sim-to-real transfer for real robot deployment without fine tuning, and ability to adapt to new instances within the same task class (e.g. to fly through a gate at different locations with different distractors in the environment). Our simulator and training framework are open-sourced at: https://github.com/Qianzhong-Chen/grad_nav.

We present Splat-Nav, a real-time robot navigation pipeline for Gaussian splatting (GSplat) scenes, a powerful new 3-D scene representation. Splat-Nav consists of two components: first, Splat-Plan, a safe planning module, and second, Splat-Loc, a robust vision-based pose estimation module. Splat-Plan builds a safe-by-construction polytope corridor through the map based on mathematically rigorous collision constraints and then constructs a Bézier curve trajectory through this corridor. Splat-Loc provides real-time recursive state estimates given only an RGB feed from an on-board camera, leveraging the point-cloud representation inherent in GSplat scenes. Working together, these modules give robots the ability to recursively replan smooth and safe trajectories to goal locations. Goals can be specified with position coordinates, or with language commands by using a semantic GSplat. We demonstrate improved safety compared to point cloud-based methods in extensive simulation experiments. In a total of 126 hardware flights, we demonstrate equivalent safety and speed compared to motion capture and visual odometry, but without a manual frame alignment required by those methods. We show online replanning at more than 2 Hz and pose estimation at about 25 Hz, an order of magnitude faster than neural radiance field-based navigation methods, thereby enabling real-time navigation.

We introduce a transformation of a Neural Radiance Field (NeRF) to an equivalent Poisson Point Process (PPP). This PPP transformation allows for rigorous quantification of uncertainty in NeRFs, in particular, for computing collision probabilities for a robot navigating through a NeRF environment. The PPP is a generalization of a probabilistic occupancy grid to the continuous volume and is fundamental to the volumetric ray-tracing model underlying radiance fields. Building upon this PPP representation, we present a chance-constrained trajectory optimization method for safe robot navigation in NeRFs. Our method relies on a voxel representation called the Probabilistic Unsafe Robot Region (PURR) that spatially fuses the chance constraint with the NeRF model to facilitate fast trajectory optimization. We then combine a graph-based search with a spline-based trajectory optimization to yield robot trajectories through the NeRF that are guaranteed to satisfy a user-specific collision probability. We validate our chance constrained planning method through simulations and hardware experiments, showing superior performance compared to prior works on trajectory planning in NeRF environments. Our code can be found athttps://github.com/chengine/catnips.

Based on this article, a fuzzy NN (neural network) based on the EBA (evolved bat algorithm) was developed to devise adaptive control with gray signal prediction to provide asymptomatic stability and increased driving comfort. The method is used to assess plant nonlinearity and to perform structural tracking of the signal. The set of Gray’s differential equations is applied to Gray’s model (GM) (n, h), which has been an active system model. In the model, n is the order of the Gray’s differential equation and h is the number of variables considered. In this paper, a GM(2.1) has been utilised to achieve advanced nonlinear motion of a system, allowing the controller to demonstrate the efficiency and stability of the whole system in a Lyapunov-like expression. The controller design standard for a MEW (mechanical elastic wheel) is presented, creating a realistic framework in mathematical for practical engineering applications.