Risk-Aware Path Planning

Safe navigation in dynamic environments requires robots to plan under obstacle predictions whose errors are uncertain, non-stationary, and can induce rare but safety-critical failures. Existing control-barrier-function safety filters can reject immediately unsafe controls, but they provide little guidance on when the current finite-horizon planning mode itself is becoming unsafe as prediction uncertainty evolves. We propose Conformal Event-Triggered Risk-Certified Replanning (CERT-Replan), a framework that uses calibrated barrier risk as an early-warning signal for replanning. CERT-Replan calibrates horizon-indexed obstacle-prediction residuals online and uses the resulting uncertainty radii to evaluate dynamic-obstacle safety margins. A one-step safety filter protects the next applied control, while a horizon-level risk monitor evaluates the upper-tail CVaR of predicted barrier-violation losses along the current MPC rollout. When this risk exceeds an allocated budget, CERT-Replan rejects the current planning mode and selects a lower-risk alternative, such as a different speed profile, corridor, or homotopy class, rather than repeatedly correcting the same nominal plan. In a non-stationary benchmark, CERT-Replan achieves an $83.3\%$ collision reduction relative to the safety-filter-only baseline \textcolor{black}{and a $77.8\%$ reduction relative to simple replanning triggers}, while reducing average safety-filter intervention by $32.4\%$. \textcolor{black}{With Trajectron++, CERT-Replan achieves $96\%$ collision-free operation. Hardware experiments and onboard runtime profiling demonstrate computational feasibility.}

Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.

Robot motion planning in everyday environments must satisfy hard geometric constraints while accounting for context-dependent semantic risk. We present a foundation-model-guided, topology-aware semantic risk field that extends manipulation safety beyond collision avoidance. For each manipulated-object/scene-object pair, a foundation model provides six directional risk weights and a pair-specific spatial decay scale. The method combines these priors with voxelized 3D scene geometry using topology-aware shielding and geodesic spatial decay. A GPU-parallel backend batches object-level distance and risk computations to construct a dense 3D field that serves as a modular cost for downstream motion planning. We evaluate the field's shielding behavior under full and partial barriers and compare its 3D workspace representation with a pixel-wise semantic-prior baseline. Across three household simulation scenarios, trajectories optimized with the proposed field have lower semantic exposure than collision-only trajectories under the same geometric constraints. We also evaluate the computational practicality and reliability of the supporting pipeline. Together, these results support the proposed field as a practical topology-aware semantic cost representation for manipulation planning beyond collision avoidance.

We consider robotic motion planning and control under unknown dynamics with hybrid state observations, where state measurements are available only in parts of the state space. Existing work combines system identification, predicted reachability, graph search and controller synthesis in a hierarchical framework using local affine approximated models over polytopic state space partitioning, but requires state observations for identification and feedback control. Based on this framework, we address blind regions by selecting nominal dynamics and precomputing open-loop control sequences before observation is lost. Since the true dynamics may differ from the selected nominal model, the robot may exit a blind polytope through an unintended facet. We quantify this transition risk and incorporate the possible outcomes into a stochastic transition system. The high-level planning problem is formulated as a stochastic shortest path problem, whose policy guides controller synthesis. A case study demonstrates that the method guides the robot from an initial state to a target while balancing route efficiency and the risks associated with traversing blind regions.

Autonomous mobile robots require timeefficient planning and safety-critical dynamic obstacle avoidance under constrained onboard computation. While Iterative Learning Planning (ILP) offers lightweight and efficient traversal planning, it lacks explicit mechanisms for dynamic obstacle perception and avoidance. This article extends ILP to safety-critical navigation in dynamic environments by integrating an anticipatory risk-blended control barrier function (ARB-CBF). The extended ILP learns traversal-speed and steering-bias profiles via a fractionalpower update based on local obstacle risk, generating nominal control commands that ARB-CBF modifies at runtime for real-time safety guarantees. Algorithmic analysis demonstrates that the ILP replanning stage scales at O(kN) for k iterations and N waypoints, while ARB-CBF executes with linear complexity. Comprehensive simulations and real-world experiments validate the framework, demonstrating superior temporal efficiency and safety with lower computational overhead compared to optimizationbased baselines, making it highly suitable for resourceconstrained platforms.

Hazardous robotic exploration requires robots to map spatial risks, such as unsafe terrain, radiation, fire, mines, or structural damage, while operating where collecting information can itself cause failure. A highly informative path may expose the robot to hazards, terminate execution, and prevent future observations. Hazardous exploration therefore requires deciding not only where uncertainty is largest, but when reducing it is worth the risk. This paper introduces a valuation-layer view of this problem. We keep the belief update, sensor model, physical risk model, and finite-horizon informative planner fixed, and change only the scalar objective used to rank feasible paths. Within this framework, we introduce a risk-augmented Behavioral Information objective based on Prelec probability weighting, yielding an interpretable family of conservative-to-aggressive information-risk valuations. Theoretically, we show that valuation parameters create switching boundaries between high-information/high-risk and lower-information/lower-risk paths, and induce a transformed Pareto-frontier structure over feasible exploration policies. Large-scale failure-truncated grid-world experiments show that valuation alone reshapes the information-risk frontier. Shannon information planning remains a strong raw-information baseline, while risk-aware objectives can reduce hazard exposure and robot losses by avoiding failures that truncate future sensing. Risk-augmented Behavioral valuation is Pareto-competitive with standard risk-aware baselines and provides interpretable conservative and intermediate regimes. These results support a framework in which robots reason not only about how much uncertainty an action reduces, but whether that reduction is worth the risk required to obtain it.

For autonomous space exploration, robotic agents need to perform motion planning in which environmental interactions may be unknown. Learning these interactions, such as terrain mechanics for wheeled robots, can introduce uncertainties that lead to risky motion plans and potentially hazardous operations or mission failures. Moreover, uncertainties induced by perception-based systems can exacerbate the problem of safe motion planning. In this letter, we address the problem of performing cost-optimal kinodynamic motion planning with risk awareness. We approach this in two steps. First, a sampling-based planner (AO-RRT) generates a dynamically feasible, risk-aware, and asymptotically cost-optimal trajectory. Second, we formulate motion planning as a nonlinear optimization problem and solve it using sequential convex programming (SCP), using the AO-RRT trajectory as an initial solution. By quantifying risk using conditional value-at-risk (CVaR), we demonstrate a reduction in risk by over $\sim$97% across trajectories in simulation and hardware experiments.

Safe robot navigation in crowded spaces requires planning that accounts for where people will be, not only where they are now. Model Predictive Path Integral (MPPI) control is an effective sampling-based planner, but many implementations encode humans as static point obstacles at their current positions, underestimating risk in dynamic scenes. We propose Predictive Gaussian Interaction Fields (PGIF), a spatiotemporal cost formulation that propagates pedestrian predictions forward over the full planning horizon and encodes them as anisotropic Gaussian repulsive fields aligned with each pedestrian's direction of motion. The forward spread of each field grows with the pedestrian's speed, creating a motion cone danger zone that penalises robot trajectories entering the pedestrian's path of travel more strongly than those approaching from behind. The formulation is closed-form and fully parallelisable across rollouts, adding no measurable computational overhead. Evaluated over 300 randomised crowd scenarios at three density levels, PGIF-MPPI achieves a 0% collision rate at every density level, compared with up to 82% for vanilla MPPI, while maintaining real-time planning performance.

This paper addresses multi-objective kinodynamic planning in environments with stochastic hybrid adversaries that probabilistically transition to adversarial modes based on the ego state. The goal is to construct the Pareto-front of paths that trade off execution cost and the probability of safety constraint violation (risk). Existing chance-constrained planners evaluate risk over open-loop trajectories, yielding overly conservative solutions that fail to account for ego-agent reactivity. To address this limitation, we shift the planning space to sequences of closed-loop policies, and integrate sample-based risk evaluation directly into tree construction via Monte-Carlo particle rollouts. We first introduce Stochastic Multi-Objective RRT (SMO-RRT), for which we prove probabilistic completeness, followed by Stochastic Multi-Objective Stable Sparse RRT (SMO-SST), which leverages selective pruning to improve numerical performance at the cost of completeness. For both algorithms, we derive a finite-sample bound on the probability of chance constraint violation for systems with non-Gaussian, state-dependent uncertainty, enabling probabilistically safe planning in a broad class of environments applicable to multi-agent systems, social navigation, and autonomous driving.

The problem of autonomous navigation for UAV inspection remains challenging as it requires effectively navigating in close proximity to obstacles, while accounting for dynamic risk factors such as weather conditions, communication reliability, and battery autonomy. This paper introduces the MOAR path planner which addresses the complexities of evolving risks during missions. It offers real-time trajectory adaptation while concurrently optimizing safety, time, and energy. The planner employs a risk-aware cost function that integrates pre-computed cost maps, the new concepts of damage and insertion costs, and an adaptive speed planning framework. With that, the optimal path is searched in a graph using a discrete representation of the state and action spaces. The method is evaluated through simulations and real-world flight tests. The results show the capability to generate real-time trajectories spanning a broad range of evaluation metrics: around 90% of the range occupied by popular algorithms. The proposed framework contributes by enabling UAVs to navigate more autonomously and reliably in critical missions.

Multi-agent Next-Best-View (NBV) selection for safe path planning in uncertain and unknown environments requires informative, safety-aware, and efficient coordination. Centralized approaches rely on sharing raw sensor data or significant communication overhead, resulting in limited scalability. We propose a distributed, risk-aware multi-agent NBV framework in which each robot maintains a private local 3D Gaussian Splatting map and the team jointly maximizes expected information gain (EIG) restricted to masked zones along planned trajectories. The resulting distributed objective is solved by Consensus ADMM (C-ADMM) over a communication graph, with each robot exchanging only candidate viewpoints, planned trajectory descriptors, and scalar EIG contributions. Collision risk along each trajectory is modeled via Average Value-at-Risk (AV@R) over the local 3DGS map and used both to shape the masking radius and to score planned paths. Experiments in Gibson environments at multiple team sizes show that the distributed formulation approaches the centralized baseline in mapping quality and trajectory safety while reducing communication by orders of magnitude.

Accurate and reliable vehicle trajectory prediction is essential for safe autonomous driving. Recent studies have incorporated safety risk into trajectory prediction to quantify dangers posed by surrounding agents. However, most risk-aware approaches use past risk information as a secondary signal to help guide decisions, overlooking its future evolution and uncertainty. In this paper, we propose a risk horizon profiling (RHP) module that incorporates a continuous, learnable potential field model for risk-aware trajectory prediction. The RHP module calculates the spatial-temporal proximity of surrounding objects to profile risk distributions across future horizons, which supports better trajectory prediction by adaptively identifying what human drivers perceive as critical moments. We evaluate our method on two datasets from different driving settings, highD for highway corridors and SHRP2 for urban streets, which cover diverse risk scenarios including safe, near-crash, and crash events. Compared to the baseline methods, our framework achieves a 25.0% reduction in 5s RMSE on the highD dataset and a 29.1% reduction in 5s minFDE on SHRP2. These results indicate strong performance for both short and long horizon prediction and robust generalization across highway and urban scenarios. The proposed method enables more realistic AV path planning and strategic selection, thereby supporting safer autonomous driving and more advanced driver-assistance systems. The source code for this work is available at: https://github.com/bilab-nyu/RHP

We present a provably safe sampling-based motion planning algorithm for robotic systems affected by random disturbances of unknown distribution. We consider systems with linear or linearizable dynamics evolving in workspace with arbitrary-shaped obstacles subject to state and control constraints. Safety requirements are formulated as chance-constraints. Our approach leverages data from trajectories of the system to learn a Wasserstein ambiguity tube, i.e., a sequence of ambiguity sets, which contains the trajectory of the system's state distribution with high confidence. This ambiguity tube is then used in a probabilistically complete algorithm to grow a sampling-based motion planning tree that respects the constraints of the problem. We show that learning several lower-dimensional ambiguity tubes instead of a single high-dimensional one effectively reduces the conservatism and boosts scalability. Additionally, we design an efficient bandit-based validity checker that remarkably increases the empirical performance of our approach without sacrificing probabilistic completeness. Case studies show our algorithm finds valid plans in cluttered environments under strict safety thresholds, outperforming state-of-the-art methods.

Mobile robots can fail before they collide: a velocity that is safe now may commit the robot to a passage that moving obstacles will soon close. We study this predictive near-miss commitment problem and propose Risk-Sensitive Conjectural Scenario Planning (RCSP), a planning layer that evaluates candidate commands against plausible short-horizon obstacle futures. RCSP maintains a lightweight belief over local motion conjectures, samples future interactions, penalizes high-risk tails, and executes through a local safety check. In controlled MuJoCo bottleneck tasks, the RCSP planner reaches the goal without collisions and yields higher secondary safety and path-quality point estimates than a non-adaptive predictor, with additional latency. In ROS2/Gazebo, adding the local safety layer to a standard Nav2 stack reduces dynamic near-miss failures. On official DynaBARN/Jackal transfer, tuned DWA and TEB remain stronger on strict benchmark success, revealing the boundary of the approach. These simulation results position RCSP as a predictive-risk module that complements existing navigation stacks in dynamic bottleneck regimes.

We present MC-Risk, a planner-aligned, multi-component risk field on a bird's-eye-view grid that yields early, calibrated, and class-aware risk localization. MC-Risk linearly composes three interpretable modules: (i) a motorized-agent field that fuses a black-box multimodal trajectory predictor with an analytic Gaussian-torus construction whose lateral width grows with speed/curvature and whose height attenuates with look-ahead; (ii) a VRU risk field that replaces isotropic pedestrian blobs with a forward-biased anisotropic kernel aligned to heading and speed; and (iii) a road penalty field that exploits full HD-map topology, imposing an off-road penalty and lane-aware risk exposure for same/opposite directions. We conduct, to our knowledge, the first standardized quantitative evaluation of a risk-field formulation on RiskBench's collision subset. MC-Risk attains the best overall risk localization and the earliest hazard indication. Finally, we demonstrate a plug-and-play planning interface by using the field as an MPC cost density, enabling risk-aware trajectory generation without additional training.

Risk-aware navigation should be selective: a policy should expose evasive degrees of freedom only when the local scene admits a lower-risk feasible maneuver, and suppress them when no safer alternative exists. We show that adding one context-energy term to a port-Hamiltonian navigation policy produces a learned force channel with exactly this falsifiable signature. When the local risk field contains a feasible lower-risk direction, the induced context force activates toward it; when the apparent escape is blocked or not yet available, a route-aware gate suppresses lateral force rather than hallucinating an unsafe maneuver. A CVaR tail-risk objective focuses gradient updates on rare but consequential risk transitions. We validate the selectivity signature across four settings. In the primary delayed-required-escape benchmark, route-aware CVaR reduces premature force activation from 0.950 to 0.180 versus DWA while raising success from 0.480 to 0.810 with zero replans. On real off-road terrain (RELLIS-3D), route-aware enrichment achieves correct activation rate 0.837 and false activation rate 0.114, compared to 0.378/0.752 for scalar risk gradients. On static semantic maps (DFC2018), enrichment reduces catastrophic failure from 0.60 to 0.10 and oscillation by 90.7% while preserving path efficiency. In highway traffic, collisions drop from 100% to 0% when a lane escape is feasible; when no escape exists, the policy suppresses the lateral maneuver. The selectivity property follows from the gradient structure of the context energy rather than from training-time tuning.

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.

Cooperative multi-robot missions require team of robots to traverse environments where adversaries or hazards with stochastic dynamics induce time-varying traversal risk. While support coordination--where robots assist teammates in traversing risky regions--can significantly reduce mission costs, its effectiveness depends on the team's ability to anticipate future risk. We formulate support-based multi-robot graph traversal problem with stochastically moving adversaries, where future risky regions become uncertain as adversaries move through the environment. When adversaries remain stationary, our formulation reduces to the static risky-edge setting. To address the stochastic case, we model individual adversaries as first-order Markov stay-move processes over graph edges and propagate their occupancy distributions over a finite planning horizon to obtain time-indexed edge-risk forecasts. These forecasts inform the support candidate selection and joint robot path planning. Experimental results show that forecast-informed support decisions consistently lower expected team cost relative to evaluated baselines in stochastic motion settings.

We present a risk-aware formalism for evaluating system trajectories in the presence of uncertain interactions between the system and its environment. The proposed formalism supports reasoning under uncertainty and systematically handles complex relationships among requirements and objectives, including hierarchical priorities and non-comparability. Rather than treating the environment as exogenous noise, we explicitly model how each system trajectory influences the environment and evaluate trajectories under the resulting distribution of environment responses. We prove that the formalism induces a preorder on the set of system trajectories, ensuring consistency and preventing cyclic preferences. Finally, we illustrate the approach with an autonomous driving example that demonstrates how the formalism enhances explainability by clarifying the rationale behind trajectory selection.

End-to-end autonomous driving models increasingly benefit from large vision-language models for semantic understanding, yet safe and reliable planning under long-tail conditions remains challenging, particularly in mixed-traffic environments involving heterogeneous road users and rare safety-critical interactions. This paper proposes HERMES, a holistic risk-aware end-to-end multimodal driving framework that explicitly incorporates long-tail semantic knowledge into trajectory planning. HERMES employs a foundation-model-assisted annotation pipeline to construct structured Long-Tail Scene Context and Long-Tail Planning Context, capturing hazard-centric scene information, maneuver intent, and risk-aware planning guidance. A Tri-Modal Driving Module then integrates multi-view visual observations, historical ego-motion, and long-tail semantic instructions through intent- and risk-aware conditioning for trajectory generation. Extensive experiments on a large-scale real-world long-tail driving benchmark demonstrate consistent improvements over representative recent baselines in overall planning performance and across diverse safety-critical scenarios. Ablation studies further validate the effectiveness and complementary roles of the major components within HERMES.