ABSTRACT We develop a Markov decision process (MDP) framework to autonomously make guidance decisions for satellite collision avoidance maneuver (CAM) and a reinforcement learning policy gradient (RL-PG) algorithm to enable direct optimization of guidance policy using historic CAM data. In addition to maintaining acceptable collision risks, this approach seeks to minimize the average propellant consumption of CAMs by making early maneuver decisions. We model CAM as a continuous state, discrete action and finite horizon MDP, where the critical decision is determining when to initiate the maneuver. By deciding to maneuver earlier than conventional methods, the Markov policy effectively favors CAMs that achieve comparable rates of collision risk reduction while consuming less propellant. Using historical data of tracked conjunction events, we verify this framework and conduct an extensive parameter-sensitivity study. When evaluated on synthetic conjunction events, the trained policy consumes significantly less propellant overall and per maneuver in comparison to a conventional cut-off policy that initiates maneuvers 24 hours before the time of closest approach (TCA). On historical conjunction events, the trained policy consumes more propellant overall but consumes less propellant per maneuver. For both historical and synthetic conjunction events, the trained policy is slightly more conservative in identifying conjunctions events that warrant CAMs in comparison to cutoff policies.

Abstract--This paper presents a novel trajectory planning pipeline for complex driving scenarios like autonomous lane changing, by integrating risk-aware planning with guaranteed collision avoidance into a unified optimization framework. We first construct a dynamic risk fields (DRF) that captures both the static and dynamic collision risks from surrounding vehicles. Then, we develop a rigorous strategy for generating time-varying convex feasible spaces that ensure kinematic feasibility and safety requirements. The trajectory planning problem is formulated as a finite-horizon optimal control problem and solved using a constrained iterative Linear Quadratic Regulator (iLQR) algorithm that jointly optimizes trajectory smoothness, control effort, and risk exposure while maintaining strict feasibility. Extensive simulations demonstrate that our method outperforms traditional approaches in terms of safety and efficiency, achieving collision-free trajectories with shorter lane-changing distances (28.59 m) and times (2.84 s) while maintaining smooth and comfortable acceleration patterns. In dense roundabout environments the planner further demonstrates robust adaptability, producing larger safety margins, lower jerk, and superior curvature smoothness compared with APF, MPC, and RRT based baselines. These results confirm that the integrated DRF with convex feasible space and constrained iLQR solver provides a balanced solution for safe, efficient, and comfortable trajectory generation in dynamic and interactive traffic scenarios.

This paper proposes a new strategy for collision avoidance system leveraging Time-to-Collision (TTC) metrics for handling cut-in scenarios, which are particularly challenging for autonomous vehicles (AVs). By integrating a deep learning with TTC calculations, the system predicts potential collisions and determines appropriate evasive actions compared to traditional TTC -based approaches.

UAVs equipped with a single depth camera encounter significant challenges in dynamic obstacle avoidance due to limited field of view and inevitable blind spots. While active vision strategies that steer onboard cameras have been proposed to expand sensing coverage, most existing methods separate motion planning from sensing considerations, resulting in less effective and delayed obstacle response. To address this limitation, we introduce SPOT (Sensing-augmented Planning via Obstacle Threat modeling), a unified planning framework for observation-aware trajectory planning that explicitly incorporates sensing objectives into motion optimization. At the core of our method is a Gaussian Process-based obstacle belief map, which establishes a unified probabilistic representation of both recognized (previously observed) and potential obstacles. This belief is further processed through a collision-aware inference mechanism that transforms spatial uncertainty and trajectory proximity into a time-varying observation urgency map. By integrating urgency values within the current field of view, we define differentiable objectives that enable real-time, observation-aware trajectory planning with computation times under 10 ms. Simulation and real-world experiments in dynamic, cluttered, and occluded environments show that our method detects potential dynamic obstacles 2.8 seconds earlier than baseline approaches, increasing dynamic obstacle visibility by over 500\%, and enabling safe navigation through cluttered, occluded environments.

This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic collision checks of planned trajectories are often inaccurate or overly conservative, as noisy perception, localization errors, and uncertain predictions of other traffic participants introduce significant uncertainty into the planning process. This paper presents two semi-analytic methods to compute the collision probability of planned trajectories with arbitrary convex obstacles. The first approach evaluates the probability of spatial overlap between an autonomous vehicle and surrounding obstacles, while the second estimates the collision probability based on stochastic boundary crossings. Both formulations incorporate full state uncertainties, including position, orientation, and velocity, and achieve high accuracy at computational costs suitable for real-time planning. Simulation studies verify that the proposed methods closely match Monte Carlo results while providing significant runtime advantages, enabling their use in risk-aware trajectory planning. The collision estimation methods are available as open-source software: https://github.com/TUM-AVS/Collision-Probability-Estimation

Overtaking in high-speed autonomous racing demands precise, real-time estimation of collision risk; particularly in wheel-to-wheel scenarios where safety margins are minimal. Existing methods for collision risk estimation either rely on simplified geometric approximations, like bounding circles, or perform Monte Carlo sampling which leads to overly conservative motion planning behavior at racing speeds. We introduce the Gauss-Legendre Rectangle (GLR) algorithm, a principled two-stage integration method that estimates collision risk by combining Gauss-Legendre with a non-homogeneous Poisson process over time. GLR produces accurate risk estimates that account for vehicle geometry and trajectory uncertainty. In experiments across 446 overtaking scenarios in a high-fidelity Formula One racing simulation, GLR outperforms five state-of-the-art baselines achieving an average error reduction of 77% and surpassing the next-best method by 52%, all while running at 1000 Hz. The framework is general and applicable to broader motion planning contexts beyond autonomous racing.

--Accurate vessel trajectory prediction is essential for enhancing situational awareness and preventing collisions. Still, existing data-driven models are constrained mainly to single-vessel forecasting, overlooking vessel interactions, navigation rules, and explicit collision risk assessment. We present a transformer-based framework for multi-vessel trajectory prediction with integrated collision risk analysis. For a given target vessel, the framework identifies nearby vessels. It jointly predicts their future trajectories through parallel streams encoding kinematic and derived physical features, causal convolutions for temporal locality, spatial transformations for positional encoding, and hybrid positional embeddings that capture both local motion patterns and long-range dependencies. Evaluated on large-scale real-world AIS data using joint multi-vessel metrics, the model demonstrates superior forecasting capabilities beyond traditional single-vessel displacement errors. By simulating interactions among predicted trajectories, the framework further quantifies potential collision risks, offering actionable insights to strengthen maritime safety and decision support. Maritime shipping is critical not only for global trade and economy but also for various socio-economic activities, including fishing, passenger transportation, and recreational sailing [1]. To enhance navigational safety, the International Maritime Organization (IMO) mandated the use of the Automatic Identification System (AIS) in 2003, with satellite AIS integration in 2008, further expanding monitoring coverage [2], [3]. Consequently, the widespread adoption of AIS generates a vast volume of vessel movement data, which has spurred research to address maritime challenges.

This article proposes a collision risk anticipation method based on short-term prediction of the agents position. A Long Short-Term Memory (LSTM) model, trained on past trajectories, is used to estimate the next position of each robot. This prediction allows us to define an anticipated collision risk by dynamically modulating the reward of a Deep Q-Learning Network (DQN) agent. The approach is tested in a constrained environment, where two robots move without communication or identifiers. Despite a limited sampling frequency (1 Hz), the results show a significant decrease of the collisions number and a stability improvement. The proposed method, which is computationally inexpensive, appears particularly attractive for implementation on embedded systems.

The growing number of ADAS-equipped vehicles has led to a dramatic increase in driving data, yet most of them capture routine driving behavior. Identifying and understanding safety-critical corner cases within this vast dataset remains a significant challenge. Braking events are particularly indicative of potentially hazardous situations, motivating the central question of our research: Why does a vehicle brake? Existing approaches primarily rely on rule-based heuristics to retrieve target scenarios using predefined condition filters. While effective in simple environments such as highways, these methods lack generalization in complex urban settings. In this paper, we propose a novel framework that leverages Large Language Model (LLM) for scenario understanding and reasoning. Our method bridges the gap between low-level numerical signals and natural language descriptions, enabling LLM to interpret and classify driving scenarios. We propose a dual-path scenario retrieval that supports both category-based search for known scenarios and embedding-based retrieval for unknown Out-of-Distribution (OOD) scenarios. To facilitate evaluation, we curate scenario annotations on the Argoverse 2 Sensor Dataset. Experimental results show that our method outperforms rule-based baselines and generalizes well to OOD scenarios.

We present a methodology for estimating collision risk from counterfactual simulated scenarios built on sensor data from automated driving systems (ADS) or naturalistic driving databases. Two-agent conflicts are assessed by detecting and classifying conflict type, identifying the agents' roles (initiator or responder), identifying the point of reaction of the responder, and modeling their human behavioral expectations as probabilistic counterfactual trajectories. The states are used to compute velocity differentials at collision, which when combined with crash models, estimates severity of loss in terms of probabilistic injury or property damage, henceforth called fractional collisions. The probabilistic models may also be extended to include other uncertainties associated with the simulation, features, and agents. We verify the effectiveness of the methodology in a synthetic simulation environment using reconstructed trajectories from 300+ collision and near-collision scenes sourced from VTTI's SHRP2 database and Nexar dashboard camera data. Our methodology predicted fractional collisions within 1% of ground truth collisions. We then evaluate agent-initiated collision risk of an arbitrary ADS software release by replacing the naturalistic responder in these synthetic reconstructions with an ADS simulator and comparing the outcome to human-response outcomes. Our ADS reduced naturalistic collisions by 4x and fractional collision risk by ~62%. The framework's utility is also demonstrated on 250k miles of proprietary, open-loop sensor data collected on ADS test vehicles, re-simulated with an arbitrary ADS software release. The ADS initiated conflicts that caused 0.4 injury-causing and 1.7 property-damaging fractional collisions, and the ADS improved collision risk in 96% of the agent-initiated conflicts.