Obstacle Avoidance

This paper introduces a motion planning framework to plan morphology and trajectory for morphing quadrotors under extremely constrained environments. We develop a novel obstacle avoidance cost function for nonlinear model predictive control (MPC) that enables navigation through extremely narrow gaps under limited perception from a 2D LiDAR. Classical artificial potential field-based costs typically have a high cost in narrow passages, artificially blocking the navigable path. In contrast, we propose a smooth exponential obstacle cost that preserves low traversal cost within narrow gaps while maintaining strong collision avoidance behavior. The formulation avoids hard activation thresholds and introduces a cost reduction factor to reduce the cost within narrow passages. Direct use of 2D LiDAR measurements in MPC allows navigation around arbitrarily shaped obstacles. The method is embedded within an acados-based nonlinear MPC framework. Simulation and experimental results demonstrate successful traversal of narrow corridors where typical repulsive cost functions would fail. The approach provides a computationally efficient and practical solution for navigating through tight spaces while maintaining safety from the obstacles. While we are implementing the framework on the morphing quadrotors, the cost function formulation is general-purpose for any mobile robot application, and is not limited to the morphing quadrotors. The implementation code is available at \href{https://github.com/harshjmodi1996/morphocopter_mpc}{Github Repo} and a short video is available at \href{https://zh.engr.tamu.edu/wp-content/uploads/sites/310/2026/03/MPC_MorphoCopter_video.mp4}{Video Link}.

In this work, we address the problem of ensuring real-time safety in autonomous robot navigation, in spatially constrained dynamic environments, by utilizing only onboard sensors. We present a real-time control architecture that integrates a 3D LIDAR perception-based composite control barrier function(CBF)-based safety filter directly into the autonomy pipeline. The proposed perception-driven framework enforces collision avoidance constraints dynamically from onboard point cloud data, thus allowing a large number of constraints to be handled at the control frequency, while remaining minimally invasive to nominal task execution. The safety region is defined as an ellipsoid in the body-frame, consistent with the geometry of the platform, which induces time-varying constraints in the world frame as the robot rotates; this effect is handled through a dedicated formulation of time-varying (CBF) for each LIDAR point. We validate the system through multiple field experiments in underground environments by utilizing a quadruped platform performing a visual inspection task, demonstrating reliable operation in the presence of dynamic obstacles, unsafe high-level references, abrupt localization anomalies, and while traversing through narrow corridors.

In obstacle avoidance navigation of unmanned aerial vehicles (UAVs), variations in obstacle scale have received strangely less attention than obstacle number or density. Existing methods typically extract purely geometric features from single-frame depth observations. Such representations tend to neglect small obstacles and lose spatial context under occlusions caused by large obstacles, leading to noticeable degradation in environments with multi-scale obstacles. To address this issue, we propose CaMeRL, a Collision-aware and Memory-enhanced Reinforcement Learning framework for UAV navigation. The collision-aware latent representation encodes risk-sensitive depth cues to preserve fine-grained obstacle structures, thereby improving sensitivity to small obstacles. The temporal memory module integrates observations across frames, mitigating partial observability caused by large-obstacle occlusions. We evaluate CaMeRL with multi-scale obstacles, including ultra-small and extra-large obstacle settings. Results show that CaMeRL outperforms state-of-the-art baselines across all scales, with success rate gains of 0.48 and 0.28 in the ultra-small and extra-large settings, respectively. More importantly, CaMeRL achieves reliable navigation in cluttered outdoor environments.

This paper addresses the motion control problem for mobile robots in obstacle-cluttered environments. The mobile robot has partial environment information only, and aims to move from an initial position to a target position without collisions. For this purpose, a reactive planning based control strategy (RPCS) is proposed. First, the initial and target positions are connected as a reference trajectory. Then, a reactive planning strategy (RPS) is developed to ensure the collision avoidance by modifying the reference trajectory locally based on the partial environment information. Next, an adaptive tracking control strategy (ATCS) is proposed to track the reference trajectory with potentially local modifications via the discretization techniques. Finally, the RPS and ATCS are combined to establish the RPCS, whose efficacy and advantages are illustrated by numerical examples.

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

Swarm robotics utilises decentralised self-organising systems to form complex collective behaviours built from the bottom-up using individuals that have limited capabilities. Previous work has shown that simple occlusion-based strategies can be effective in using swarm robotics for the task of transporting objects to a goal position. However, this strategy requires a clear line-of-sight between the object and the goal. In this paper, we extend this strategy by allowing robots to form sub-goals; enabling any member of the swarm to establish a wider range of visibility of the goal, ultimately forming a chain of sub-goals between the object and the goal position. We do so while preserving the fully decentralised and communication-free nature of the original strategy, while maintaining performance in object-free scenarios. In five sets of simulated experiments, we demonstrate the generalisability of our proposed strategy. Our finite-state machine allows a sufficiently large swarm to transport objects around obstacles that block the goal. The method is robust to varying starting positions and can handle both concave and convex shapes.

We study stochastic minimum-cost reach-avoid reinforcement learning, where an agent must satisfy a reach-avoid specification with probability at least $p$ while minimizing expected cumulative costs in stochastic environments. Existing safe and constrained reinforcement learning methods typically fail to jointly enforce probabilistic reach-avoid constraints and optimize cost in the learning setting in stochastic environments. To address this challenge, we introduce reach-avoid probability certificates (RAPCs), which identify states from which stochastic reach-avoid constraints are satisfiable. Building on RAPCs, we develop a contraction-based Bellman formulation that serves as a principled surrogate for integrating reach-avoid considerations into reinforcement learning, enabling cost optimization under probabilistic constraints. We establish almost sure convergence of the proposed algorithms to locally optimal policies with respect to the resulting objective. Experiments in the MuJoCo simulator demonstrate improved cost performance and consistently higher reach-avoid satisfaction rates.

Safe autonomous Uncrewed Aerial Vehicle (UAV) navigation in urban environments requires real-time path planning that avoids obstacles. MaxConvNet is a potential-field planner that leverages properties of Maxwell's equations to generate a path to the goal without local minima. We extend the 2D MaxConvNet magnetic field planner to 3D, using a convolutional autoencoder to predict obstacle-aware potential fields from LiDAR-derived 101^3 voxel grids. Evaluation across 100 randomized closed-loop trials in two distinct Cosys-AirSim urban environments, a dense night-time cityscape and a suburban district shows a 100% path planning success rate on both maps without retraining. In offline path planning, 3DMaxConvNet produces path lengths comparable to A* on unseen maps while reducing runtime from 0.155--0.17s to 0.087--0.089s, or about 1.7--1.95 times faster than A*. Against RRT*(3k), 3DMaxConvNet achieves similar path quality while reducing planning runtime from 17.2--17.5s to about 0.09s, which is roughly 193--201 times faster than RRT*(3k).

Inference-time guidance is essential for steering generative robot policies toward dynamic objectives without retraining, yet existing methods are largely confined to chunk-based architectures that exhibit high latency and lack the reactivity needed for test-time preference alignment or obstacle avoidance. In this work, we formally derive the optimal guidance term for Stochastic Interpolants (SI) by analyzing the value function's time evolution via the Backward Kolmogorov Equation, establishing a modified drift that theoretically guarantees sampling from a target distribution. We apply this framework to real-time control through the Streaming Stochastic Interpolant Policy (SSIP), which generalizes the deterministic Streaming Flow Policy (SFP). Unifying this guidance law with the streaming architecture enables fast and reactive control. To support diverse deployment needs, we propose two complementary mechanisms: training-free Stochastic Trajectory Ensemble Guidance (STEG) that computes gradients on-the-fly for zero-shot adaptation, and training-based Conditional Critic Guidance (CCG) for amortized inference. Empirical evaluations demonstrate that our guided streaming approach significantly outperforms conventional chunk-based policies in reactivity and provides superior, physically valid guidance for dynamic, unstructured environments.

In embodied vision, Goal-Oriented Navigation (GON) requires robots to locate a specific goal within an unexplored environment. The primary challenge of GON arises from the need to construct a Bird's-Eye-View (BEV) map to understand the environment while simultaneously localizing an unobserved goal. Existing map-based methods typically employ self-centered semantic maps, often facing challenges such as reliance on complete maps or inconsistent semantic association. To this end, we propose Plug-and-Play Label Map Diffusion (PLMD), which defines a novel map completion diffusion model based on Denoising Diffusion Probabilistic Models (DDPM). PLMD generates obstacle and semantic labels for unobserved regions through a diffusion-based completion process, thereby enabling goal localization even in partially observed environments. Moreover, it mitigates inconsistent semantic association by leveraging structural consistency between known and unknown obstacle layouts and integrating obstacle priors into the semantic denoising process. By substituting predicted labels for unobserved regions, robots can accurately localize the specified objects. Extensive experiments demonstrate that PLMD \textbf{(I)} effectively expands the region of unknown maps, \textbf{(II)} integrates seamlessly into existing navigation strategies that rely on semantic maps, \textbf{(III)} achieves state-of-the-art performance on three GON tasks.

Offline reference trajectories for active target tracking are needed both for building multi-modal tracking datasets and for benchmarking online tracking planners under repeatable conditions. We present Track A star (TA star), an offline search-based trajectory planner that targets the visibility-aware target tracking objective on a discretized four-dimensional spatio-temporal grid (x, y, z, t). TA star combines a layered Directed Acyclic Graph (DAG) search with three engineering optimizations: cross-time obstacle distance caching against a Bounding Volume Hierarchy (BVH), per-layer beam pruning, and a configurable multi-ray visibility evaluator. TA star employs a beam-pruned heuristic search on this discrete graph to efficiently find high-quality tracking trajectories. While it trades strict theoretical optimality for practical scalability, our empirical results demonstrate robust, near-baseline visibility performance at a fraction of the computational cost. On a 1000-scenario stress test across eight CARLA Optimized maps, TA star converges on all scenarios and completes in 45 s using 32 workers; on a 248-scenario controlled comparison against an unoptimized priority-queue A star baseline (BinaryHeap implementation) under identical scenario inputs and a 5 x 10^6 expansion cap, TA star reduces mean planning time by 23.0x and worst-case planning time by 11.8x, while raising convergence from 56.9% to 100%. On the n=141 baseline-converged subset, TA star changes average visibility by only -0.15 percentage points (pp), with no scenario exceeding a 5 pp drop. We position TA star as a practical offline reference planner under these specific conditions, with limitations and failure cases discussed for environments such as Town07 dense vegetation.

We present a dual-barrier control barrier function (CBF) safety filter for real-time, safety-critical velocity control of holonomic robots operating in incrementally built occupancy grid maps. As a robot explores an unknown environment, unmapped regions introduce irreducible uncertainty, since obstacle geometry beyond the explored frontier is unknown, making entry into such regions a source of collision risk, especially with front-facing sensors. To address this, we enforce two constraints: avoidance of mapped obstacles and restriction from unexplored regions. Both constraints are derived analytically from the occupancy grid's signed distance field, yielding a closed-form safety filter that requires only a small linear system solve per cycle. On resource-constrained platforms such as the Raspberry Pi, where SLAM and planning already consume significant compute, the low overhead of the proposed filter preserves resources. An adaptive gain schedule relaxes the frontier constraint in information-rich regions and tightens it in well-mapped areas, improving exploration efficiency while maintaining safety. The filter operates in velocity space as a minimally invasive correction and composes with arbitrary nominal controllers, including learning-based methods. Hardware flight experiments on a PX4-controlled quadrotor demonstrate zero collisions across multiple indoor runs.

Risk-aware navigation in unknown environments is a fundamental challenge for autonomous vehicles operating in complex urban systems. To address this issue, this paper presents a differentiable optimization layered safety-critical control method based on conformal prediction. First, to handle uncertainties arising from sensor noise, the conformal prediction method is employed to generate risk-aware obstacle ellipsoids around an elliptical-shaped robot. Second, two nested differentiable optimization layers are introduced to build the control barrier functions for obstacle avoidance and feasibility guarantee, respectively. Then, a quadratic program based safety-critical control law is proposed to integrate the above control barrier function constraints as well as input constraints. In the end, the effectiveness of the proposed framework is demonstrated through numerical simulations.

The integration of Large Language Model (LLM) reasoning principles into classical robot path planning represents a rapidly emerging research direction. In this paper, we propose a Semantic Risk-Aware Heuristic (SRAH) planner that encodes LLM-inspired cost functions penalising geometrically cluttered or high-risk zones into an A$^*$ search framework, augmented with closed-loop replanning upon dynamic obstacle detection. We evaluate SRAH against two established baselines Breadth-First Search (BFS) with replanning and a Greedy heuristic without replanning across 200 randomised trials in a $15{\times}15$ grid-world with 20% static obstacle density and stochastic dynamic obstacles. SRAH achieves a task success rate of 62.0%, outperforming BFS (56.5%) by 9.7% relative improvement and Greedy (4.0%) by a large margin. We further analyse the trade-off between planning overhead, path efficiency, and failure-recovery count, and demonstrate via an obstacle-density ablation that semantic cost shaping consistently improves navigation across environments of varying difficulty. Our results suggest that even lightweight, LLM-inspired heuristics provide measurable safety and robustness gains for autonomous robot navigation.

Autonomous driving technology has rapidly evolved over the past decade, offering significant improvements in transportation efficiency, safety, and cost reduction. While much of the progress has focused on highway driving and obstacle avoidance, low-speed maneuvers such as parking remain among the most difficult challenges for autonomous systems. This challenge is especially pronounced in trailer-truck transport vehicles due to their articulated motion and environmental constraints. This paper presents a proposed framework for autonomous truck parking that integrates perception, motion planning, control systems, and infrastructure awareness. By combining sensor fusion, Hybrid A* path planning, nonlinear model predictive control (NMPC), and data-driven parking systems, this work highlights the importance of system-level coordination for reliable and scalable autonomous parking solutions. As a proof-of-concept implementation, we adapted an open-source A* path planning simulation to incorporate a tractor-trailer kinematic model, demonstrating articulated vehicle path planning within a command-line simulation environment, with jackknife prevention identified as an area requiring further development.

This paper addresses the problem of mobile grasping in dynamic, unknown environments where a robot must operate under a limited field-of-view. The fundamental challenge is the inherent trade-off between seeing'' around to reduce environmental uncertainty and moving'' the body to achieve task progress in a high-dimensional configuration space, subject to visibility constraints. Previous approaches often assume known or static environments and decouple these objectives, failing to guarantee safety when unobserved dynamic obstacles intersect the robot's path during manipulation. In this paper, we propose a unified mobile grasping system comprising two core components: (1) an iterative low-level whole-body planner coupled with velocity-aware active perception to navigate dynamic environments safely; and (2) a hierarchical high-level planner based on behavior trees that adaptively generates subgoals to guide the robot through exploration and runtime failures. We provide experimental results across 400 randomized simulation scenarios and real-world deployment on a Fetch mobile manipulator. Results show that our system achieves a success rate of 68.8% and 58.0% in unknown static and dynamic environments, respectively, significantly boosting success rates by 22.8% and 18.0% over the \nam approach in both unknown static and dynamic environments, with improved collision safety.

Autonomous navigation and obstacle avoidance remain a core challenge of modern Unmanned Aerial Vehicles (UAVs). While traditional control methods struggle with the complexity and variability of the environment, reinforcement learning (RL) enables UAVs to learn adaptive behaviors through interaction with the environment. Existing research with RL prioritizes the mission success at the expense of mission time and safety of UAVs. This study integrates Potential Based Reward Shaping (PBRS) with Control Lyapunov Functions (CLF) and Control Barrier Functions (CBF) to simultaneously optimize mission time and ensure formal safety guarantees. An RL model is trained in a generalized simple environment, then used in complex scenarios incorporating a CLF-CBF-QP filter without further training. Experimental results in simulated environments demonstrate a significant reduction in mission time and outstanding performance in complex environment.

Signal Temporal Logic (STL) offers verifiable task specifications and is crucial for safety-critical control. Yet STL planning remains challenging: exact optimization-based methods are often too slow, and learning-based methods struggle to generalize across varying environments. We propose a zero-shot STL planning solver for variable-map environments that generates feasible trajectories without retraining. By integrating a map-conditioned Transformer architecture with a lightweight heuristic, our approach effectively handles complex disjunctive (OR) subformulas. Furthermore, we leverage Transitive Reinforcement Learning (TRL) to ensure consistent temporal grounding and logical coherence across decomposed sub-tasks. Experiments on dynamic semantic maps with diverse obstacle layouts demonstrate consistent gains, highlighting the framework's superior zero-shot generalization to changing environments and broad STL coverage.

Safety critical control of robotic manipulation tasks involving deformable media such as fluids, cloth, and soft objects remains challenging because existing learning based approaches encode safety indirectly through reward shaping, which provides no guarantee of constraint satisfaction at deployment. We present a constraint driven online safety filter for deformable object manipulation that enforces explicit task level safety constraints in real time by minimally modifying any nominal control policy. Our approach combines two key components: a horizon agnostic neural operator that learns the boundary input output mapping of the underlying PDE dynamics and generalizes across variable rollout lengths without retraining, and a boundary control barrier function that certifies safety at the task relevant output level via a lightweight quadratic program. The resulting safety constraint is affine in the boundary input rate, enabling real time online filtering. We evaluate the proposed method on fluid manipulation tasks in FluidLab, where the filter improves safe trajectory rates by up to 22% over unfiltered base policies while also reducing the number of steps required to reach the safe set, demonstrating that constraint driven safety enforcement is both more reliable and more efficient than reward shaping approaches.

While Bellman equations for basic reach, avoid, and reach-avoid problems are well studied, the relationship between value optimality and policy optimality becomes subtle in the undiscounted infinite-horizon setting, particularly for more complicated tasks. Greedily maximizing the Q-function can produce policies that indefinitely defer task completion for reach-avoid problems, or equivalently, Until specifications, even when the value function is optimal. Building upon recent results decomposing the value function for temporal logic (TL) into a graph of constituent value functions, we construct non-Markovian policies based on state history that avoid this pathology and prove their optimality with respect to the quantitative robustness score for nested Until, Globally, and Globally-Until specifications. We further show how the Q function can serve as a safety filter for complex TL specifications, extending prior results beyond simple avoid or reach-avoid tasks.

Dense, dynamic crowds pose a persistent challenge for autonomous mobile robots. Purely reactive planning methods, such as Model Predictive Path Integral (MPPI) control, often fail to escape local minima in complex scenarios due to their limited prediction horizon. To bridge this gap, we propose Ray-based Task-Oriented Latent Dynamics (RAY-TOLD), a hybrid control architecture that integrates obstacle information into latent dynamics and utilizes the robustness of physics-based MPPI with the long-horizon foresight of reinforcement learning. RAY-TOLD leverages a LiDAR-centric latent dynamics model to encode high-dimensional sensor data into a compact state representation, enabling the learning of a terminal value function and a policy prior. We introduce a policy mixture sampling strategy that augments the MPPI candidate population with trajectories derived from the learned policy, effectively guiding the planner towards the goal while maintaining kinematic feasibility. Extensive tests in a stochastic environment with high-density dynamic obstacles demonstrate that our method outperforms the MPPI baseline, reducing the collision rate. The results confirm that blending short-horizon physics-based rollouts with learned long-horizon intent significantly enhances navigation reliability and safety.

Navigating quadruped robots in unstructured 3D environments poses significant challenges, requiring goal-directed motion, effective exploration to escape from local minima, and posture adaptation to traverse narrow, height-constrained spaces. Conventional approaches employ a sequential mapping-planning pipeline but suffer from accumulated perception errors and high computational overhead, restricting their applicability on resource-constrained platforms. To address these challenges, we propose Hierarchical Posture-Adaptive Navigation (HiPAN), a framework that operates directly on onboard depth images at deployment. HiPAN adopts a hierarchical design: a high-level policy generates strategic navigation commands (planar velocity and body posture), which are executed by a low-level, posture-adaptive locomotion controller. To mitigate myopic behaviors and facilitate long-horizon navigation, we introduce Path-Guided Curriculum Learning, which progressively extends the navigation horizon from reactive obstacle avoidance to strategic navigation. In simulation, HiPAN achieves higher navigation success rates and greater path efficiency than classical reactive planners and end-to-end baselines, while real-world experiments further validate its applicability across diverse, unstructured 3D environments.

This paper presents a unified control framework for robust trajectory tracking and moving obstacle avoidance applicable to a broad class of mobile robots. By formulating a generalized kinematic transformation, we convert diverse vehicle dynamics into a strict feedback form, facilitating the design of a Sliding Mode Control (SMC) strategy for precise and robust reference tracking. To ensure operational safety in dynamic environments, the tracking controller is integrated with a Collision Cone Control Barrier Function (C3BF) based safety filter. The proposed architecture guarantees asymptotic tracking in the presence of external disturbances while strictly enforcing collision avoidance constraints. The novelty of this work lies in designing a sliding mode controller for ground robots like the Ackermann drive, which has not been done before. The efficacy and versatility of the approach are validated through numerical simulations and extensive real-world experiments on three distinct platforms: an Ackermann-steered vehicle, a differential drive robot, and a quadrotor drone. Video of the experiments are available at https://youtu.be/dWcxwum96vk

While Vision-Language-Action (VLA) models have been demonstrated possessing strong zero-shot generalization for robot control, their massive parameter sizes typically necessitate cloud-based deployment. However, cloud deployment introduces network jitter and inference latency, which can induce severe spatiotemporal misalignment in mobile navigation under continuous displacement, so that the stale intents expressed in past ego frames may become spatially incorrect in the current frame and lead to collisions. To address this issue, we propose AsyncShield, a plug-and-play asynchronous control framework. AsyncShield discards traditional black-box time-series prediction in favor of a deterministic physical white-box spatial mapping. By maintaining a temporal pose buffer and utilizing kinematic transformations, the system accurately converts temporal lag into spatial pose offsets to restore the VLA's original geometric intent. To balance intent restoration fidelity and physical safety, the edge adaptation is formulated as a constrained Markov decision process (CMDP). Solved via the PPO-Lagrangian algorithm, a reinforcement learning adapter dynamically trades off between tracking the VLA intent and responding to high-frequency LiDAR obstacle avoidance hard constraints. Furthermore, benefiting from a standardized universal sub-goal interface, domain randomization, and perception-level adaptation via Collision Radius Inflation, AsyncShield operates as a lightweight, plug-and-play module. Simulation and real-world experiments demonstrate that, without fine-tuning any cloud-based foundation models, the framework exhibits zero-shot and robust generalization capabilities, effectively improving the success rate and physical safety of asynchronous navigation.

Wheeled-legged robots combine the efficiency of rolling with the adaptability of legged locomotion, offering unique agility for dynamic environments. However, enabling rapid reflexive evasion remains challenging due to the coexistence of heterogeneous wheel-leg dynamics, hybrid locomotion modes, and non-holonomic constraints. In this work, we investigate how wheeled-legged robots can exploit their hybrid morphology for high-dynamic obstacle avoidance. We propose AWARE, a hierarchical reinforcement learning framework that decomposes avoidance into navigation-avoidance and reflexive-evasion regimes coordinated by a threat-conditioned high-level policy. By learning specialized low-level experts, AWARE autonomously discovers distinct rolling-, stepping-, and hybrid-dominated evasive behaviors, including forward lunges and lateral dodges. Simulation experiments across different reaction times and approach directions, together with real-robot evaluations on the M20 platform, demonstrate improved evasion capability and effective online transition between locomotion regimes. These results highlight the potential of exploiting hybrid wheel-leg actuation for agile and reactive mobility in dynamic environments. Paper homepage: https://aware-ral-2026.github.io/.

Multi-robot control in cluttered environments is a challenging problem that involves complex physical constraints, including robot-robot collisions, robot-obstacle collisions, and unreachable motions. Successful planning in such settings requires joint optimization over high-level task planning and low-level motion planning, as violations of physical constraints may arise from failures at either level. However, jointly optimizing task and motion planning is difficult due to the complex parameterization of low-level motion trajectories and the ambiguity of credit assignment across the two planning levels. In this paper, we propose a hybrid multi-robot control framework that jointly optimizes task and motion planning. To enable effective parameterization of low-level planning, we introduce waypoints, a simple yet expressive representation for motion trajectories. To address the credit assignment challenge, we adopt a curriculum-based training strategy with a modified RLVR algorithm that propagates motion feasibility feedback from the motion planner to the task planner. Experiments on BoxNet3D-OBS, a challenging multi-robot benchmark with dense obstacles and up to nine robots, show that our approach consistently improves task success over motion-agnostic and VLA-based baselines. Our code is available at https://github.com/UCSB-NLP-Chang/navigate-cluster

Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time, continuous-space systems subject to uncertainty, which provide certified lower bounds on the probability of remaining within a safe set over a finite horizon. These certificates explicitly account for time-varying unsafe regions induced by obstacle dynamics. By leveraging Bellman's optimality perspective, the time-varying formulation directly captures temporal structure and yields less conservative bounds than state-of-the-art approaches. By restricting certificates to polynomial functions, we show that time-varying barrier synthesis can be formulated as a convex sum-of-squares program, enabling tractable optimization. Empirical evaluations on nonlinear systems with dynamic obstacles show that time-varying certificates consistently achieve tight guarantees, demonstrating improved accuracy and scalability over state-of-the-art methods.

Vision-Language-Action (VLA) models map multimodal inputs directly to robot actions and are typically trained through large-scale imitation learning. While this paradigm has shown strong performance, prevailing VLA training procedures do not explicitly supervise hard physical constraints such as obstacle avoidance or kinematic feasibility. As a result, the geometric structure underlying physically feasible behavior must be inferred only implicitly from demonstrations. In this paper, we study whether introducing explicit feasibility supervision can provide effective structured guidance for VLA policies. We formulate a simple geometry-grounded feasibility objective and integrate it into the training stage of a diffusion-based VLA policy. To evaluate this idea systematically, we use obstacle-aware manipulation as a controlled probe of geometry-dependent physical feasibility. Empirical results show that augmenting VLA training with feasibility supervision improves both physical reliability and overall task performance, while also enhancing learning efficiency in the low-data regime. These findings indicate that explicit feasibility signals can effectively complement imitation-based VLA learning, highlighting their potential for developing more reliable VLA policies.

This paper presents a framework for safe navigation of a unicycle point robot to a goal position in an environment populated with obstacles from almost any admissible state, considering input limits. We introduce a novel QP formulation to create a Cinfinity-smooth vector field with reduced total bending and total turning. Then we design an analytic, non-linear feedback controller that inherently satisfies the conditions of Nagumo's theorem, ensuring forward invariance of the safe set without requiring any online optimization. We have demonstrated that our controller, even under hard input limits, safely converges to the goal position. Simulations confirm the effectiveness of the proposed framework, resulting in a twice faster arrival time with over 50% lower angular control effort compared to the baseline.

Obstacle detection in railway environments is crucial for ensuring safety. However, very few studies address the problem using a complete, modular, and flexible system that can both detect objects in the scene and estimate their distance from the vehicle. Most works focus solely on detection, others attempt to identify the track, and only a few estimate obstacle distances. Additionally, evaluating these systems is challenging due to the lack of ground truth data. In this paper, we propose a modular and flexible framework that identifies the rail track, detects potential obstacles, and estimates their distance by integrating three neural networks for object detection, track segmentation, and monocular depth estimation with LiDAR point clouds. To enable a reliable and quantitative evaluation, the proposed framework is assessed using a synthetic dataset (SynDRA), which provides accurate ground truth annotations, allowing for direct performance comparison with existing methods. The proposed system achieves a mean absolute error (MAE) as low as 0.63 meters by integrating monocular depth maps with LiDAR, enabling not only accurate distance estimates but also spatial perception of the scene.

Specular glare on reflective floors, glass boundaries, and glossy indoor surfaces can corrupt active-stereo RGB-D measurements, producing holes and spikes that persist as phantom obstacles in navigation costmaps. This article presents a glare-resilient RGB-D sensor-fusion method based on explicit per-pixel depth reliability. A lightweight Depth Reliability Map network (DRM-Net) predicts sensor trustworthiness, and reliability-guided fusion (RGF) combines continuous weighting with a minimum gate before occupancy integration. Rejected measurements generate neither obstacle insertion nor free-space clearing; affected cells remain unknown or retain prior evidence. Training targets are built from a five-frame, pose-aligned multiview buffer using independent LiDAR/AMCL poses, occlusion-aware aggregation, and a calibrated range-dependent depth-uncertainty model. The evaluation includes tuned nvblox TSDF, Intel RealSense SDK postprocessing, high-threshold stereoconfidence filtering, TDCNet, and HDCNet baselines, together with statistical, safety, generalization, and embedded-runtime analyses. Under severe glare, Depth Reliability Map (DRM)+RGF achieves false obstacle rate (FOR) 0.056 +/- 0.012, free-space recall (FSR) 0.897 +/- 0.045, FNOR 0.018, 1.00 +/- 0.00 degraded-mode safety interventions per 10 m, and 91.4% task success while operating at 16.5 ms per frame. Across the retained reflective-scene trials (Baseline N = 98; DRM+RGF N = 105), collisions decrease from 14 to 1. These results support RGF as a favorable safety-utility tradeoff relative to aggressive filtering and dense completion for glare-affected indoor navigation.

This paper studies obstacle avoidance under translation invariant dynamics using an avoid-side travel cost Hamilton Jacobi formulation. For running costs that are zero outside an obstacle and strictly negative inside it, we prove that the value function is non-positive everywhere, equals zero exactly outside the avoid set, and is strictly negative exactly on it. Under translation invariance, this yields a reuse principle: the value of any translated obstacle is obtained by translating a single template value function. We show that the pointwise minimum of translated template values exactly characterizes the union of the translated single-obstacle avoid sets and provides a conservative inner certificate of unavoidable collision in clutter. To reduce conservatism, we introduce a blockwise composition framework in which subsets of obstacles are merged and solved jointly. This yields a hierarchy of conservative certificates from singleton reuse to the exact clutter value, together with monotonicity under block merging and an exactness criterion based on the existence of a common clutter avoiding control. The framework is illustrated on a Dubins car example in a repeated clutter field.

This paper proposes SoftGM, an octopus-inspired distributed control architecture for segmented soft robotic arms that learn to reach targets in contact-rich environments using online obstacle discovery without assuming full obstacle geometry at the start of each episode. SoftGM formulates each arm section as a cooperative agent and represents the arm-environment interaction as a graph. SoftGM uses a two-stage graph attention message passing scheme following a Centralised Training Decentralised Execution (CTDE) paradigm with a centralised critic and decentralised actor. We evaluate SoftGM in a Cosserat-rod simulator (PyElastica) across three tasks that increase the complexity of the environment: obstacle-free, structured obstacles, and a wall-with-hole scenario. Compared with six widely used MARL baselines (IDDPG, IPPO, ISAC, MADDPG, MAPPO, MASAC) under identical information content and training conditions, SoftGM matches strong CTDE methods in simpler settings and achieves the best performance in the wall-with-hole task. Robustness tests with observation noise, single-section actuation failure, and transient disturbances show that SoftGM maintains comparable performance under non-ideal simulated conditions while keeping control effort bounded, suggesting that selective contact-relevant information routing improves resilience in the tested settings.

In this paper, we present an online method for converting an arbitrary geometric path, represented by a sequence of states, and generated by any planner (e.g., sampling-based planners such as RRT or PRM, search-based planners such as ARA*, etc.), into a kinematically feasible, jerk-limited trajectory. The method generates a sequence of quintic/quartic splines that can be discretized at a user-specified control rate and streamed to a low-level robot controller. Our approach enables real-time adaptation to environmental changes and can be re-invoked at any instant to generate a new trajectory from the robot's current state to a desired target state or sequence of states. Under a bounded-obstacle-velocity assumption, the method provides conditional stopping-safety guarantees over a finite time interval in dynamic environments, while allowing bounded geometric deviation from the original path. Kinematic constraints, including jerk limits, are explicitly considered. We validate the approach in a comparative simulation study against a competing method, demonstrating favorable behavior w.r.t. smoothness, computational time, and real-time performance, particularly with frequent target-state changes (up to 1 [kHz]). Real-robot experiments demonstrate applicability in real-world scenarios, including scenarios with a human as an obstacle.

Visual navigation models often struggle in real-world dynamic environments due to limited robustness to the sim-to-real gap and the difficulty of training policies tailored to target deployment environments (e.g., households, restaurants, and factories). Although real-to-sim navigation simulation using 3D Gaussian Splatting (GS) can mitigate these challenges, prior GS-based works have considered only static scenes or non-photorealistic human obstacles built from simulator assets, despite the importance of safe navigation in dynamic environments. To address these issues, we propose ReaDy-Go, a novel real-to-sim simulation pipeline that synthesizes photorealistic dynamic scenarios in target environments by augmenting a reconstructed static GS scene with dynamic human GS obstacles, and trains navigation policies using the generated datasets. The pipeline provides three key contributions: (1) a dynamic GS simulator that integrates static scene GS with a human animation module, enabling the insertion of animatable human GS avatars and the synthesis of plausible human motions from 2D trajectories, (2) a navigation dataset generation framework that leverages the simulator along with a robot expert planner designed for dynamic GS representations and a human planner, and (3) robust navigation policies to both the sim-to-real gap and moving obstacles. The proposed simulator generates thousands of photorealistic navigation scenarios with animatable human GS avatars from arbitrary viewpoints. ReaDy-Go outperforms baselines across target environments in both simulation and real-world experiments, demonstrating improved navigation performance even after sim-to-real transfer and in the presence of moving obstacles. Moreover, zero-shot sim-to-real deployment in an unseen environment indicates its generalization potential. Project page: https://syeon-yoo.github.io/ready-go-site/.

Quadrotor unmanned aerial vehicles (UAVs) are increasingly deployed in complex missions that demand reliable autonomous navigation and robust obstacle avoidance. However, traditional modular pipelines often incur cumulative latency, whereas purely reinforcement learning (RL) approaches typically provide limited formal safety guarantees. To bridge this gap, we propose an end-to-end RL framework augmented with model-based safety mechanisms. We incorporate physical priors in both training and deployment. During training, we design a physics-informed reward structure that provides global navigational guidance. During deployment, we integrate a real-time safety filter that projects the policy outputs onto a provably safe set to enforce strict collision-avoidance constraints. This hybrid architecture reconciles high-speed flight with robust safety assurances. Benchmark evaluations demonstrate that our method outperforms both traditional planners and recent end-to-end obstacle avoidance approaches based on differentiable physics. Extensive experiments demonstrate strong generalization, enabling reliable high-speed navigation in dense clutter and challenging outdoor forest environments at velocities up to 7.5 m/s}.

Insect neuroethology provides a compelling biological template for efficient autonomous navigation. We draw an analogy between the formal embodied AI visual point-goal navigation task and the ability of insects to discover, learn, and refine visually guided paths around obstacles between a discovered food location and their nest. We develop a novel integrative model of mushroom body and central complex, two insect brain structures, that have been implicated, respectively, in associative learning and path integration. We demonstrate the mushroom body learning triggered by collisions results in adaptive obstacle avoidance and consequently optimised paths to the goal, corroborating the hypothesis of recent behavioural work that an insect can learn continuously as they travel. The embodied insect-inspired model achieves success rates comparable to recent state-of-the-art models at many orders of magnitude less computational cost in the standardised Habitat point-goal navigation benchmark. Testing in a more realistic simulated environment validates its robustness to perturbations.

Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this demand, optimization problems are often simplified via linearization, narrowing the horizon window, or reduced temporal nodes, each compromising accuracy or reliability. This work presents the first general convex obstacle avoidance formulation, enabled by a novel approach to integrating logic. This facilitates the incorporation of an obstacle avoidance formulation into convex MPC schemes, enabling a convex optimization framework with substantially improved computational efficiency relative to conventional nonconvex methods. A key property of the formulation is that obstacle avoidance remains effective even when obstacles lie outside the prediction horizon, allowing shorter horizons for real-time deployment. In scenarios where nonconvex formulations are unavoidable, the proposed method meets or exceeds the performance of representative nonconvex alternatives. The method is evaluated in autonomous vehicle applications, where system dynamics are highly nonlinear.

Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons. Low-fidelity planners scale but cannot directly control the system, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible. We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second-tail horizon of a single multi-phase MPC, rather than being solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

Reactive control can gracefully coordinate the motion of the base and the arm of a mobile manipulator. However, incorporating an accurate representation of the environment to avoid obstacles without involving costly planning remains a challenge. In this work, we present ReMoSPLAT, a reactive controller based on a quadratic program formulation for mobile manipulation that leverages a Gaussian Splat representation for collision avoidance. By integrating additional constraints and costs into the optimisation formulation, a mobile manipulator platform can reach its intended end effector pose while avoiding obstacles, even in cluttered scenes. We investigate the trade-offs of two methods for efficiently calculating robot-obstacle distances, comparing a purely geometric approach with a rasterisation-based approach. Our simulation experiments on both synthetic and real-world scans demonstrate the feasibility of the proposed method, achieving performance comparable to controllers that rely on perfect ground-truth information. We further validate the approach on a real robot platform more details: https://remosplat.github.io

Vision-Language-Action (VLA) models have demonstrated remarkable capabilities in generalizing across diverse robotic manipulation tasks. However, deploying these models in unstructured environments remains challenging due to the critical need for simultaneous task compliance and safety assurance, particularly in preventing potential collisions during physical interactions. In this work, we introduce a Vision-Language-Safe Action (VLSA) architecture, named AEGIS, which contains a plug-and-play safety constraint (SC) layer formulated via control barrier functions. AEGIS integrates directly with existing VLA models to improve safety with theoretical guarantees, while maintaining their original instruction-following performance. To evaluate the efficacy of our architecture, we construct a comprehensive safety-critical benchmark SafeLIBERO, spanning distinct manipulation scenarios characterized by varying degrees of spatial complexity and obstacle intervention. Extensive experiments demonstrate the superiority of our method over state-of-the-art baselines. Notably, AEGIS achieves over 50% improvement in obstacle avoidance rate while substantially increasing the task success rate by nearly 10%. All benchmark datasets, code, and supplementary materials are publicly available at https://vlsa-aegis.github.io/.

Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.

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.

Reactive obstacle avoidance methods often cause agents to become trapped in local minima, because they can often only reason one step ahead (i.e., the next action based on the current state). In this paper, we use model checking to achieve reactive multi-step planning and obstacle avoidance on an autonomous robot. Our small, purpose-built model checking algorithm generates plans in situ (within the robot's code) based on ``core'' knowledge and attention as found in biological agents. This is achieved in real-time using no pre-computed data on a low-powered device. Our approach is based on chaining temporary control systems that are spawned to counteract disturbances in the local environment which disrupt an autonomous agent from its preferred action (or resting state). We mitigate state-space explosion by relying on temporary snapshots of the immediate environment, restricting the number of states. Multi-step planning using counter-examples generated by depth-first search and a negated LTL path property is applied to scenarios involving a cul-de-sac and a free-standing obstacle. Empirical results and informal proofs of two fundamental properties demonstrate the effectiveness of our approach for the creation of efficient multi-step plans for local obstacle avoidance. We significantly improve performance compared to a purely reactive agent that can only plan one step ahead. Our approach is an instructional case study for the development of safe and reliable navigation in the context of autonomous vehicles. We believe it also has general application in navigation for mission-critical mobile robots.

Robot learning has produced remarkably effective ``black-box'' controllers for complex tasks such as dynamic locomotion on humanoids. Yet ensuring dynamic safety, i.e., constraint satisfaction, remains challenging for such policies. Reinforcement learning (RL) embeds constraints heuristically through reward engineering, and adding or modifying constraints requires retraining. Model-based approaches, like control barrier functions (CBFs), enable runtime constraint specification with formal guarantees but require accurate dynamics models. This paper presents SHIELD, a layered safety framework that bridges this gap by: (1) training a generative, stochastic dynamics residual model using real-world data from hardware rollouts of the nominal controller, capturing system behavior and uncertainties; and (2) adding a safety layer on top of the nominal (learned locomotion) controller that leverages this model via a stochastic discrete-time CBF formulation enforcing safety constraints in probability. The result is a minimally-invasive safety layer that can be added to the existing autonomy stack to give probabilistic guarantees of safety that balance risk and performance. In hardware experiments on an Unitree G1 humanoid, SHIELD enables safe navigation (obstacle avoidance) through varied indoor and outdoor environments using a nominal (unknown) RL controller and onboard perception.

Machine Learning (ML) has become central to Autonomous Vehicles (AVs), supporting perception, prediction, planning, control, and decision-making in dynamic environments. However, achieving full autonomy in cluttered and complex scenarios, such as intricate intersections, diverse scenes, varied trajectories, and complex missions, remains challenging; moreover, data labeling is still a major bottleneck. These limitations motivate Human-in-the-Loop Machine Learning (HITL-ML), in which human input is incorporated through validation, annotation, task organization, reward design, action correction, preference feedback, and supervisory intervention. To advance safe and ethical autonomy, this paper presents a tutorial survey of HITL-ML for AVs, focusing on Curriculum Learning (CL), Human-in-the-Loop Reinforcement Learning (HITL-RL), Human-in-the-Loop Large Language Models (HITL-LLMs), Active Learning (AL), and ethical principles. We first review CL methods that structure training from simple to complex tasks, covering navigation, path planning, obstacle avoidance, data collection, landing, intersection handling, motion planning, and UAV swarm coordination. We then examine HITL-RL through reward shaping, action injection, demonstrations, preference-based feedback, and interactive learning, emphasizing improved learning efficiency, safer policy exploration, and real-time intervention. Next, we review HITL-LLM through collaboration and oversight and specify key challenges. After that, we discuss AL for perception, anomaly detection, semantic mapping, object detection, vehicle recognition, and security-related classification. Ethical principles are reviewed as technical requirements for transparency, accountability, human oversight, safety, security, regulatory compliance, and reliability of human input.

Safe control in unknown environments is a key challenge in mobile robotics. Control Barrier Functions (CBFs) provide a principled framework for guaranteeing safety constraint satisfaction. State-of-the-art CBF approaches assume either known environments with predefined obstacles, or rely only on obstacles currently within the robot's Field of View (FoV). However, practical robots in a priori unknown environments can observe their surroundings only partially, and therefore can violate safety due to limited FoV, sensor range, or occlusion. This paper incorporates the memory of previously observed obstacles of arbitrary shape that have left the robot's FoV into CBF-based safe control. In particular, we couple the Signed Distance Function (SDF)-based CBF formulation to an occupancy grid map built online during the system's operation. Furthermore, the lack of steering authority induced by the SDF gradient degeneracy when facing obstacles head-on is addressed by constructing a Gaussian pyramid of the SDF, yielding a multi-level CBF. The efficacy of the proposed approach is evaluated against memory unaware baselines in the CARLA simulator. Moreover, we demonstrate the generalizability of the proposed approach in real deployments on a small warehouse robot and a large, articulated frame steering autonomous wheel loader.

This paper addresses the autonomous robot navigation problem in a priori unknown n-dimensional environments containing disjoint convex obstacles of arbitrary shapes and sizes, with pairwise distances strictly greater than the robot's diameter. We propose a hybrid feedback control scheme that guarantees safe and global asymptotic convergence of the robot to a predefined target location. The proposed control strategy relies on a switching mechanism allowing the robot to operate either in the move-to-target mode or the obstacle-avoidance mode, based on its proximity to the obstacles and the availability of a clear straight path between the robot and the target. In the obstacle-avoidance mode, the robot is constrained to move within a two-dimensional plane that intersects the obstacle being avoided and the target, preventing it from retracing its path. The effectiveness of the proposed hybrid feedback controller is demonstrated through simulations in two-dimensional and three-dimensional environments.

This work presents an algorithm for changing from latitudinal to longitudinal formation of autonomous aircraft squadrons. The maneuvers are defined dynamically by using a predefined set of 3D basic maneuvers. This formation change is necessary when the squadron has to perform tasks which demand both formations, such as lift off, georeferencing, obstacle avoidance and landing. Simulations show that the formation change is done without collision. The time complexity analysis of the transformation algorithm reveals that its efficiency is optimal, and the proof of correctness ensures its longitudinal formation features.

The Moving Target Vehicle Routing Problem with Obstacles (MT-VRP-O) seeks trajectories for several agents that collectively intercept a set of moving targets. Each target has one or more time windows where it can be visited, and the agents must avoid static obstacles and satisfy speed and capacity constraints. Previously studied VRPs are often addressed using a framework called branch-and-price. This framework requires computing the cost for a single agent to visit a given sequence of target-time window pairings, for several candidate sequences. These sequences are called tours. Computing tour costs is more expensive in the MT-VRP-O than in previously studied VRPs due to the presence of both moving targets and static obstacles. Thus, we introduce a new exact algorithm, Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), for the MT-VRP-O. The key idea in Lazy BPRC is to use cheap-to-compute lower bounds on tour costs where costs are traditionally used, and lazily update lower bounds to true costs. When computing a tour's true cost is needed, we do so by searching for a shortest path on a graph of convex sets, and we introduce a new heuristic to accelerate the search. We demonstrate that Lazy BPRC runs up to an order of magnitude faster than two ablations.

Long-duration outdoor coverage with autonomous platforms remains challenging beyond classical planning: deployments face localization drift in open spaces, obstacles in cluttered sites, controller feasibility in turn-heavy maneuvers, and persistent autonomy with energy management. We propose a unified ROS 2 architecture for single-robot outdoor coverage: a dual-antenna RTK-GNSS fused in an EKF keeps both position and heading accurate across long missions; three controller-aware refinements extend a mature coverage planner; a Nav2-based behavior-tree mission executive coordinates multi-goal execution, layered recovery, cost-aware goal management, and autonomous docking for return-to-charge. In real-world trials across five outdoor areas with varying geometries and obstacle densities, the robot completed every coverage route, sweeping 93.1% to 96.1% of the planned coverage area.