Trajectory Generation

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Trajectory generation studies how to produce or predict sequences of positions and motions that meet a goal while fitting the environment and the moving agent. Methods range from splines, graph search, model-predictive control, and numerical optimization to learned models such as diffusion, flow matching, transformers, and reinforcement learning. Work spans robot navigation and manipulation, autonomous driving, coordinated fleets, and synthetic human mobility, often conditioning plans on maps, language, dynamics, or other agents. A central challenge is balancing speed and diversity with physical feasibility and safety, while testing whether generated trajectories remain realistic and reliable in new settings.

Latest papers

182 papers31 papers in the last four weeks, up 55% on the four weeks before. 0.2% of all new papers.

Apr 5, 2026

InsTraj: Instructing Diffusion Models with Travel Intentions to Generate Real-world Trajectories

The generation of realistic and controllable GPS trajectories is a fundamental task for applications in urban planning, mobility simulation, and privacy-preserving data sharing. However, existing methods face a two-fold challenge: they lack the deep semantic understanding to interpret complex user travel intent, and struggle to handle complex constraints while maintaining the realistic diversity inherent in human behavior. To resolve this, we introduce InsTraj, a novel framework that instructs diffusion models to generate high-fidelity trajectories directly from natural language descriptions. Specifically, InsTraj first utilizes a powerful large language model to decipher unstructured travel intentions formed in natural language, thereby creating rich semantic blueprints and bridging the representation gap between intentions and trajectories. Subsequently, we proposed a multimodal trajectory diffusion transformer that can integrate semantic guidance to generate high-fidelity and instruction-faithful trajectories that adhere to fine-grained user intent. Comprehensive experiments on real-world datasets demonstrate that InsTraj significantly outperforms state-of-the-art methods in generating trajectories that are realistic, diverse, and semantically faithful to the input instructions.

Yuanshao Zhu, Yuxuan Liang, Xiangyu Zhao +5

Southern University of Science and Technology · City University of Hong Kong · The Hong Kong University of Science and Technology (Guangzhou) +2

Trajectory Generation Diffusion Models for Motion Generation

Apr 2, 2026

PlayGen-MoG: Framework for Diverse Multi-Agent Play Generation via Mixture-of-Gaussians Trajectory Prediction

Multi-agent trajectory generation in team sports requires models that capture both the diversity of possible plays and realistic spatial coordination between players on plays. Standard generative approaches such as Conditional Variational Autoencoders (CVAE) and diffusion models struggle with this task, exhibiting posterior collapse or convergence to the dataset mean. Moreover, most trajectory prediction methods operate in a forecasting regime that requires multiple frames of observed history, limiting their use for play design where only the initial formation is available. We present PlayGen-MoG, an extensible framework for formation-conditioned play generation that addresses these challenges through three design choices: 1/ a Mixture-of-Gaussians (MoG) output head with shared mixture weights across all agents, where a single set of weights selects a play scenario that couples all players' trajectories, 2/ relative spatial attention that encodes pairwise player positions and distances as learned attention biases, and 3/ non-autoregressive prediction of absolute displacements from the initial formation, eliminating cumulative error drift and removing the dependence on observed trajectory history, enabling realistic play generation from a single static formation alone. On American football tracking data, PlayGen-MoG achieves 1.68 yard ADE and 3.98 yard FDE while maintaining full utilization of all 8 mixture components with entropy of 2.06 out of 2.08, and qualitatively confirming diverse generation without mode collapse.

Kevin Song

Amazon Web Services, Seattle, Washington

Trajectory Generation Multi-Agent Trajectory Prediction

Mar 31, 2026

Self-Consistency for LLM-Based Motion Trajectory Generation and Verification

Self-consistency has proven to be an effective technique for improving LLM performance on natural language reasoning tasks in a lightweight, unsupervised manner. In this work, we study how to adapt self-consistency to visual domains. Specifically, we consider the generation and verification of LLM-produced motion graphics trajectories. Given a prompt (e.g., "Move the circle in a spiral path"), we first sample diverse motion trajectories from an LLM, and then identify groups of consistent trajectories via clustering. Our key insight is to model the family of shapes associated with a prompt as a prototype trajectory paired with a group of geometric transformations (e.g., rigid, similarity, and affine). Two trajectories can then be considered consistent if one can be transformed into the other under the warps allowable by the transformation group. We propose an algorithm that automatically recovers a shape family, using hierarchical relationships between a set of candidate transformation groups. Our approach improves the accuracy of LLM-based trajectory generation by 4-6%. We further extend our method to support verification, observing 11% precision gains over VLM baselines. Our code and dataset are available at https://majiaju.io/trajectory-self-consistency .

Jiaju Ma, R. Kenny Jones, Jiajun Wu +1

Stanford University

Trajectory Generation Self-Consistency Decoding

Mar 30, 2026

From Vessel Trajectories to Safety-Critical Encounter Scenarios: A Generative AI Framework for Autonomous Ship Digital Testing

Digital testing has emerged as a key paradigm for the development and verification of autonomous maritime navigation systems, yet the availability of realistic and diverse safety-critical encounter scenarios remains limited. Existing approaches either rely on handcrafted templates, which lack realism, or extract cases directly from historical data, which cannot systematically expand rare high-risk situations. This paper proposes a data-driven framework that converts large-scale Automatic Identification System (AIS) trajectories into structured safety-critical encounter scenarios. The framework combines generative trajectory modeling with automated encounter pairing and temporal parameterization to enable scalable scenario construction while preserving real traffic characteristics. To enhance trajectory realism and robustness under noisy AIS observations, a multi-scale temporal variational autoencoder is introduced to capture vessel motion dynamics across different temporal resolutions. Experiments on real-world maritime traffic flows demonstrate that the proposed method improves trajectory fidelity and smoothness, maintains statistical consistency with observed data, and enables the generation of diverse safety-critical encounter scenarios beyond those directly recorded. The resulting framework provides a practical pathway for building scenario libraries to support digital testing, benchmarking, and safety assessment of autonomous navigation and intelligent maritime traffic management systems. Code is available at https://anonymous.4open.science/r/traj-gen-anonymous-review.

Sijin Sun, Liangbin Zhao, Xiuju Fu

A*STAR IAIC Singapore

Trajectory Generation

Mar 27, 2026

Think over Trajectories: Leveraging Video Generation to Reconstruct GPS Trajectories from Cellular Signaling

Mobile devices continuously interact with cellular base stations, generating massive volumes of signaling records that provide broad coverage for understanding human mobility. However, such records offer only coarse location cues (e.g., serving-cell identifiers) and therefore limit their direct use in applications that require high-precision GPS trajectories. This paper studies the Sig2GPS problem: reconstructing GPS trajectories from cellular signaling. Inspired by domain experts often lay the signaling trace on the map and sketch the corresponding GPS route, unlike conventional solutions that rely on complex multi-stage engineering pipelines or regress coordinates, Sig2GPS is reframed as an image-to-video generation task that directly operates in the map-visual domain: signaling traces are rendered on a map, and a video generation model is trained to draw a continuous GPS path. To support this paradigm, a paired signaling-to-trajectory video dataset is constructed to fine-tune an open-source video model, and a trajectory-aware reinforcement learning-based optimization method is introduced to improve generation fidelity via rewards. Experiments on large-scale real-world datasets show substantial improvements over strong engineered and learning-based baselines, while additional results on next GPS prediction indicate scalability and cross-city transferability. Overall, these results suggest that map-visual video generation provides a practical interface for trajectory data mining by enabling direct generation and refinement of continuous paths under map constraints.

Ruixing Zhang, Hanzhang Jiang, Leilei Sun +3

The State Key Laboratory of Complex and Critical Software Environment, Beihang University China · H3I, Beihang University · China Mobile Information Technology Center China

Trajectory Inference Trajectory Generation

Mar 26, 2026

Integrated Multi-Drone Task Allocation, Sequencing, and Optimal Trajectory Generation in Obstacle-Rich 3D Environments

Coordinating teams of aerial robots in cluttered three-dimensional (3D) environments requires a principled integration of discrete mission planning-deciding which robot serves which goals and in what order -- with continuous-time trajectory synthesis that enforces collision avoidance and dynamic feasibility. This paper introduces IMD-TAPP (Integrated Multi-Drone Task Allocation and Path Planning), an end-to-end framework that jointly addresses multi-goal allocation, tour sequencing, and safe trajectory generation for quadrotor teams operating in obstacle-rich spaces. IMD--TAPP first discretizes the workspace into a 3D navigation graph and computes obstacle-aware robot-to-goal and goal-to-goal travel costs via graph-search-based pathfinding. These costs are then embedded within an Injected Particle Swarm Optimization (IPSO) scheme, guided by multiple linear assignment, to efficiently explore coupled assignment/ordering alternatives and to minimize mission makespan. Finally, the resulting waypoint tours are transformed into time-parameterized minimum-snap trajectories through a generation-and-optimization routine equipped with iterative validation of obstacle clearance and inter-robot separation, triggering re-planning when safety margins are violated. Extensive MATLAB simulations across cluttered 3D scenarios demonstrate that IMD--TAPP consistently produces dynamically feasible, collision-free trajectories while achieving competitive completion times. In a representative case study with two drones serving multiple goals, the proposed approach attains a minimum mission time of 136~s while maintaining the required safety constraints throughout execution.

Yunes Alqudsi, Murat Makaraci

Aerospace Engineering Department, Faculty of Aeronautics and Astronautics, Kocaeli University, Kocaeli, Turkiye · Interdisciplinary Research Center for Aviation and Space Exploration, KFUPM, Dhahran, Saudi Arabia · Mechanical Engineering Department, Faculty of Aeronautics and Astronautics, Kocaeli University, Kocaeli, Turkiye

Multi-Robot Motion Planning Aerial Robotics Multi-Robot Task Allocation Safe Motion Planning Trajectory Generation

Mar 25, 2026

Enhancing Drone Light Shows Performances: Optimal Allocation and Trajectories for Swarm Drone Formations

Drone light shows (DLShows) represent a rapidly growing application of swarm robotics, creating captivating aerial displays through the synchronized flight of hundreds or thousands of unmanned aerial vehicles (UAVs) as environmentally friendly and reusable alternatives to traditional pyrotechnics. This domain presents unique challenges in optimally assigning drones to visual waypoints and generating smooth, collision-free trajectories at a very large scale. This article introduces the Unified Assignment and Trajectory Generation (UATG) framework. The proposed approach concurrently solves two core problems: the optimal assignment of drones to designated goal locations and the generation of dynamically feasible, collision-free, time-parameterized trajectories. The UATG framework is specifically designed for DLShows, ensuring minimal transition times between formations and guaranteeing inter-drone collision avoidance. A key innovation is its exceptional computational efficiency, enabling the coordination of large-scale in real-time; for instance, it computes the optimal assignment and trajectories for 1008 drones in approximately one second on a standard laptop. Extensive simulations in realistic environments validate the framework's performance, demonstrating its capability to orchestrate complex formations, from alphanumeric characters to intricate 3D shapes, with precision and visual smoothness. This work provides a critical advancement for the DLShow industry, offering a practical and scalable solution for generating complex aerial choreography and establishing a valuable benchmark for ground control station software designed for the efficient coordination of multiple UAVs. A supplemental animated simulation of this work is available at https://youtu.be/-Fjrhw03594.

Yunes Alqudsi

Trajectory Generation Multi-Robot Motion Planning Aerial Robotics Multi-Robot Formation Control Multi-Robot Task Allocation

Mar 23, 2026

Trajectory Generation for Underactuated Soft Robot Manipulators using Discrete Elastic Rod Dynamics

Soft robots are well suited for contact-rich tasks due to their compliance, yet this property makes accurate and tractable modeling challenging. Planning motions with dynamically-feasible trajectories requires models that capture arbitrary deformations, remain computationally efficient, and are compatible with underactuation. However, existing approaches balance these properties unevenly: continuum rod models provide physical accuracy but are computationally demanding, while reduced-order approximations improve efficiency at the cost of modeling fidelity. To address this, our work introduces a control-oriented reformulation of Discrete Elastic Rod (DER) dynamics for soft robots, and a method to generate trajectories with these dynamics. The proposed formulation yields a control-affine representation while preserving certain first-principles force-deformation relationships. As a result, the generated trajectories are both dynamically feasible and consistent with the underlying actuation assumptions. We present our trajectory generation framework and validate it experimentally on a pneumatic soft robotic limb. Hardware results demonstrate consistently improved trajectory tracking performance over a constant-curvature-based baseline, particularly under complex actuation conditions.

Beibei Liu, Akua K. Dickson, Ran Jing +1

Division of Systems Engineering, Boston University, Boston MA, USA. · Department of Mechanical Engineering, Boston University, Boston MA, USA.

Robot Motion Generation Trajectory Generation Soft Robotics Continuum Robot Control

Mar 19, 2026

V-Dreamer: Automating Robotic Simulation and Trajectory Synthesis via Video Generation Priors

Training generalist robots demands large-scale, diverse manipulation data, yet real-world collection is prohibitively expensive, and existing simulators are often constrained by fixed asset libraries and manual heuristics. To bridge this gap, we present V-Dreamer, a fully automated framework that generates open-vocabulary, simulation-ready manipulation environments and executable expert trajectories directly from natural language instructions. V-Dreamer employs a novel generative pipeline that constructs physically grounded 3D scenes using large language models and 3D generative models, validated by geometric constraints to ensure stable, collision-free layouts. Crucially, for behavior synthesis, we leverage video generation models as rich motion priors. These visual predictions are then mapped into executable robot trajectories via a robust Sim-to-Gen visual-kinematic alignment module utilizing CoTracker3 and VGGT. This pipeline supports high visual diversity and physical fidelity without manual intervention. To evaluate the generated data, we train imitation learning policies on synthesized trajectories encompassing diverse object and environment variations. Extensive evaluations on tabletop manipulation tasks using the Piper robotic arm demonstrate that our policies robustly generalize to unseen objects in simulation and achieve effective sim-to-real transfer, successfully manipulating novel real-world objects.

Songjia He, Zixuan Chen, Hongyu Ding +5

Nanjing University. · Northwestern Polytechnical University.

Synthetic Data Generation for Robotics Robotic Manipulation Trajectory Generation Robotics Simulation Robot Motion Generation

Mar 18, 2026

GMT: Goal-Conditioned Multimodal Transformer for 6-DOF Object Trajectory Synthesis in 3D Scenes

Synthesizing controllable 6-DOF object manipulation trajectories in 3D environments is essential for enabling robots to interact with complex scenes, yet remains challenging due to the need for accurate spatial reasoning, physical feasibility, and multimodal scene understanding. Existing approaches often rely on 2D or partial 3D representations, limiting their ability to capture full scene geometry and constraining trajectory precision. We present GMT, a multimodal transformer framework that generates realistic and goal-directed object trajectories by jointly leveraging 3D bounding box geometry, point cloud context, semantic object categories, and target end poses. The model represents trajectories as continuous 6-DOF pose sequences and employs a tailored conditioning strategy that fuses geometric, semantic, contextual, and goaloriented information. Extensive experiments on synthetic and real-world benchmarks demonstrate that GMT outperforms state-of-the-art human motion and human-object interaction baselines, such as CHOIS and GIMO, achieving substantial gains in spatial accuracy and orientation control. Our method establishes a new benchmark for learningbased manipulation planning and shows strong generalization to diverse objects and cluttered 3D environments. Project page: https://huajian- zeng.github. io/projects/gmt/.

Huajian Zeng, Abhishek Saroha, Daniel Cremers +1

TU München · MBZUAI · MCML +1

Multimodal Transformer Trajectory Generation Robot Motion Generation Robotic Manipulation

Mar 17, 2026

Learning Lineage-guided Geodesics with Finsler Geometry

Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better understanding system dynamics. Previous work has focused on continuous geometric priors, utilizing data-dependent spatial features to define a Riemannian metric. In many applications, there exists discrete, directed prior knowledge over admissible transitions (e.g. lineage trees in developmental biology). We introduce a Finsler metric that combines geometry with classification and incorporate both types of priors in trajectory inference, yielding improved performance on interpolation tasks in synthetic and real-world data.

Aaron Zweig, Mingxuan Zhang, David A. Knowles +1

New York Genome Center · Irving Institute for Cancer Dynamics, Columbia University · Department of Systems Biology, Columbia University +3

Finsler Geometry Trajectory Inference Trajectory Generation

Mar 17, 2026

Enabling Dynamic Tracking in Vision-Language-Action Models via Time-Discrete and Time-Continuous Velocity Feedforward

While vision-language-action (VLA) models have shown great promise for robot manipulation, their deployment on rigid industrial robots remains challenging due to the inherent trade-off between compliance and responsiveness. Standard Behavior Cloning (BC) approaches predict discrete poses at low frequencies, omitting the velocity and acceleration feedforward terms typically used by low-level compliant controllers. This requires to rely on high stiffness for accurate tracking, thereby sacrificing safe contact dynamics. In this paper, we demonstrate the importance of integrating velocity feedforward terms into VLA policies to resolve this trade-off. We propose two methods for extracting velocity targets from VLAs: a time-discrete finite-difference approximation that serves as a highly effective bridge for existing models, and a continuous Cubic B-Spline action space that natively yields

C^2

continuous trajectories for high-frequency control. Crucially, both approaches are strictly model-agnostic and compatible with any standard action-chunking architecture, requiring modifications only to teleoperation, data processing, and the low-level controller. We fine-tune the

π_{0.5}

model and evaluate both of our approaches on a demanding, contact-rich cube-in-hole task. Our results indicate that incorporating the velocity feedforward term via finite differences significantly improves task execution speed, while the continuous B-Spline approach maintains high overall success rates and provides a foundation for smoother higher-order derivatives without compromising compliance.

Johannes Hechtl, Philipp Schmitt, Georg von Wichert +1

Siemens Foundational Technologies · Department of Computer Science & Artificial Intelligence, University of Technology Nuremberg, Germany.

Vision-Language-Action Models Robot Trajectory Tracking Trajectory Generation

Mar 16, 2026

TrajFlow: Nation-wide Pseudo GPS Trajectory Generation with Flow Matching Models

The importance of mobile phone GPS trajectory data is widely recognized across many fields, yet the use of real data is often hindered by privacy concerns, limited accessibility, and high acquisition costs. As a result, generating pseudo-GPS trajectory data has become an active area of research. Recent diffusion-based approaches have achieved strong fidelity but remain limited in spatial scale (small urban areas), transportation-mode diversity, and efficiency (requiring numerous sampling steps). To address these challenges, we introduce TrajFlow, which to the best of our knowledge is the first flow-matching-based generative model for GPS trajectory generation. TrajFlow leverages the flow-matching paradigm to improve robustness and efficiency across multiple geospatial scales, and incorporates a trajectory harmonization and reconstruction strategy to jointly address scalability, diversity, and efficiency. Using a nationwide mobile phone GPS dataset with millions of trajectories across Japan, we show that TrajFlow or its variants consistently outperform diffusion-based and deep generative baselines at urban, metropolitan, and nationwide levels. As the first nationwide, multi-scale GPS trajectory generation model, TrajFlow demonstrates strong potential to support inter-region urban planning, traffic management, and disaster response, thereby advancing the resilience and intelligence of future mobility systems.

Peiran Li, Jiawei Wang, Haoran Zhang +4

Hitotsubashi University · The University of Tokyo · LocationMind Inc. +1

Trajectory Generation Flow-Based Generative Modeling

Mar 14, 2026

Amortizing Trajectory Diffusion with Keyed Drift Fields

Diffusion-based trajectory planners can synthesize rich, multimodal action sequences for offline reinforcement learning, but their iterative denoising incurs substantial inference-time cost, making closed-loop planning slow under tight compute budgets. We study the problem of achieving diffusion-like trajectory planning behavior with one-step inference, while retaining the ability to sample diverse candidate plans and condition on the current state in a receding-horizon control loop. Our key observation is that conditional trajectory generation fails under naïve distribution-matching objectives when the similarity measure used to align generated trajectories with the dataset is dominated by unconstrained future dimensions. In practice, this causes attraction toward average trajectories, collapses action diversity, and yields near-static behavior. Our key insight is that conditional generative planning requires a conditioning-aware notion of neighborhood: trajectory updates should be computed using distances in a compact key space that reflects the condition, while still applying updates in the full trajectory space. Building on this, we introduce Keyed Drifting Policies (KDP), a one-step trajectory generator trained with a drift-field objective that attracts generated trajectories toward condition-matched dataset windows and repels them from nearby generated samples, using a stop-gradient drifted target to amortize iterative refinement into training. At inference, the resulting policy produces a full trajectory window in a single forward pass. Across standard RL benchmarks and real-time hardware deployments, KDP achieves strong performance with one-step inference and substantially lower planning latency than diffusion sampling. Project website, code and videos: https://keyed-drifting.github.io/

Gokul Puthumanaillam, Melkior Ornik

University of Illinois Urbana-Champaign

Trajectory Generation Diffusion-Based Planning Diffusion Model Inference Acceleration Generative Modeling Offline RL

Mar 12, 2026

Coupling Tensor Trains with Graph of Convex Sets: Effective Compression, Exploration, and Planning in the C-Space

We present TANGO (Tensor ANd Graph Optimization), a novel motion planning framework that integrates tensor-based compression with structured graph optimization to enable efficient and scalable trajectory generation. While optimization-based planners such as the Graph of Convex Sets (GCS) offer powerful tools for generating smooth, optimal trajectories, they typically rely on a predefined convex characterization of the high-dimensional configuration space-a requirement that is often intractable for general robotic tasks. TANGO builds further by using Tensor Train decomposition to approximate the feasible configuration space in a compressed form, enabling rapid discovery and estimation of task-relevant regions. These regions are then embedded into a GCS-like structure, allowing for geometry-aware motion planning that respects both system constraints and environmental complexity. By coupling tensor-based compression with structured graph reasoning, TANGO enables efficient, geometry-aware motion planning and lays the groundwork for more expressive and scalable representations of configuration space in future robotic systems. Rigorous simulation studies on planar and real robots reinforce our claims of effective compression and higher quality trajectories.

Gerhard Reinerth, Riddhiman Laha, Marcello Romano

Technical University of Munich, Germany · Northeastern University, Boston, USA

Motion Planning Robot Motion Planning Trajectory Generation

Mar 11, 2026

PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...

Eugene Ku, Yiwei Lyu

Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

Constrained Motion Planning Trajectory Generation Diffusion-Based Planning Control Barrier Functions Safety Filtering Safe Motion Planning+1

Mar 5, 2026

K-Gen: A Multimodal Language-Conditioned Approach for Interpretable Keypoint-Guided Trajectory Generation

Generating realistic and diverse trajectories is a critical challenge in autonomous driving simulation. While Large Language Models (LLMs) show promise, existing methods often rely on structured data like vectorized maps, which fail to capture the rich, unstructured visual context of a scene. To address this, we propose K-Gen, an interpretable keypoint-guided multimodal framework that leverages Multimodal Large Language Models (MLLMs) to unify rasterized BEV map inputs with textual scene descriptions. Instead of directly predicting full trajectories, K-Gen generates interpretable keypoints along with reasoning that reflects agent intentions, which are subsequently refined into accurate trajectories by a refinement module. To further enhance keypoint generation, we apply T-DAPO, a trajectory-aware reinforcement fine-tuning algorithm. Experiments on WOMD and nuPlan demonstrate that K-Gen outperforms existing baselines, highlighting the effectiveness of combining multimodal reasoning with keypoint-guided trajectory generation.

Mingxuan Mu, Guo Yang, Lei Chen +2

Harbin Institute of Technology Chongqing Research Inst. of HIT · Changan Automobile Co., Ltd Chongqing, China

Trajectory Generation Autonomous Driving Planning LLM Agent Trajectory Synthesis VLMs for Autonomous Driving

Mar 3, 2026

Learning Demographic-Conditioned Mobility Trajectories with Aggregate Supervision

Human mobility trajectories are widely studied in public health and social science, where different demographic groups exhibit significantly different mobility patterns. However, existing trajectory generation models rarely capture this heterogeneity because most trajectory datasets lack demographic labels. To address this gap in data, we propose ATLAS, a weakly supervised approach for demographic-conditioned trajectory generation using only (i) individual trajectories without demographic labels, (ii) region-level aggregated mobility features, and (iii) region-level demographic compositions from census data. ATLAS trains a trajectory generator and fine-tunes it so that simulated mobility matches observed regional aggregates while conditioning on demographics. Experiments on real trajectory data with demographic labels show that ATLAS substantially improves demographic realism over baselines (JSD

\downarrow

12%--69%) and closes much of the gap to strongly supervised training. We further develop theoretical analyses for when and why ATLAS works, identifying key factors including demographic diversity across regions and the informativeness of the aggregate feature, paired with experiments demonstrating the practical implications of our theory. We release our code at https://github.com/schang-lab/ATLAS.

Jessie Z. Li, Zhiqing Hong, Toru Shirakawa +1

University of California, Berkeley · Hong Kong University of Science and Technology (Guangzhou)

Trajectory Generation Conditional Generative Modeling Weakly Supervised Learning

Feb 28, 2026

Online Generation of Collision-Free Trajectories in Dynamic Environments

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.

Nermin Covic, Bakir Lacevic

Faculty of Electrical Engineering, University of Sarajevo, Bosnia and Herzegovina

Constrained Motion Planning Trajectory Optimization Trajectory Generation Robot Motion Generation Safe Motion Planning Dynamic Obstacle Avoidance+1

Feb 25, 2026

Trajectory Generation with Endpoint Regulation and Momentum-Aware Dynamics for Visually Impaired Scenarios

Trajectory generation for visually impaired scenarios requires smooth and temporally consistent state in structured, low-speed dynamic environments. However, traditional jerk-based heuristic trajectory sampling with independent segment generation and conventional smoothness penalties often lead to unstable terminal behavior and state discontinuities under frequent regenerating. This paper proposes a trajectory generation approach that integrates endpoint regulation to stabilize terminal states within each segment and momentum-aware dynamics to regularize the evolution of velocity and acceleration for segment consistency. Endpoint regulation is incorporated into trajectory sampling to stabilize terminal behavior, while a momentum-aware dynamics enforces consistent velocity and acceleration evolution across consecutive trajectory segments. Experimental results demonstrate reduced acceleration peaks and lower jerk levels with decreased dispersion, smoother velocity and acceleration profiles, more stable endpoint distributions, and fewer infeasible trajectory candidates compared with a baseline planner.

Yuting Zeng, Manping Fan, You Zhou +5

School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, P.R. China. · School of Medicine, University of Electronic Science and Technology of China, Chengdu, Sichuan, China. · Sichuan Provincial Key Laboratory for Human Disease Gene Study, Sichuan Academy of Medical Sciences & Sichuan Provincial People’s Hospital, University of Electronic Science and Technology of China, Chengdu, Sichuan, China.

Visually Impaired Navigation Assistance Trajectory Generation Motion Planning

Feb 24, 2026

TrajGPT-R: Generating Urban Mobility Trajectory with Reinforcement Learning-Enhanced Generative Pre-trained Transformer

Mobility trajectories are essential for understanding urban dynamics and enhancing urban planning, yet access to such data is frequently hindered by privacy concerns. This research introduces a transformative framework for generating large-scale urban mobility trajectories, employing a novel application of a transformer-based model pre-trained and fine-tuned through a two-phase process. Initially, trajectory generation is conceptualized as an offline reinforcement learning (RL) problem, with a significant reduction in vocabulary space achieved during tokenization. The integration of Inverse Reinforcement Learning (IRL) allows for the capture of trajectory-wise reward signals, leveraging historical data to infer individual mobility preferences. Subsequently, the pre-trained model is fine-tuned using the constructed reward model, effectively addressing the challenges inherent in traditional RL-based autoregressive methods, such as long-term credit assignment and handling of sparse reward environments. Comprehensive evaluations on multiple datasets illustrate that our framework markedly surpasses existing models in terms of reliability and diversity. Our findings not only advance the field of urban mobility modeling but also provide a robust methodology for simulating urban data, with significant implications for traffic management and urban development planning. The implementation is publicly available at https://github.com/Wangjw6/TrajGPT_R.

Jiawei Wang, Chuang Yang, Jiawei Yong +6

The University of Tokyo, Tokyo 113-0034, Japan · Toyota Motor Corporation, Tokyo 112-0004, Japan

Trajectory Generation RL for Generative Models Reinforcement Learning

Feb 18, 2026

Smooth trajectory generation and hybrid B-splines-Quaternions based tool path interpolation for a 3T1R parallel kinematic milling robot

This paper presents a smooth trajectory generation method for a four-degree-of-freedom parallel kinematic milling robot. The proposed approach integrates B-spline and Quaternion interpolation techniques to manage decoupled position and orientation data points. The synchronization of orientation and arc-length-parameterized position data is achieved through the fitting of smooth piece-wise Bezier curves, which describe the non-linear relationship between path length and tool orientation, solved via sequential quadratic programming. By leveraging the convex hull properties of Bezier curves, the method ensures spatial and temporal separation constraints for multi-agent trajectory generation. Unit quaternions are employed for orientation interpolation, providing a robust and efficient representation that avoids gimbal lock and facilitates smooth, continuous rotation. Modifier polynomials are used for position interpolation. Temporal trajectories are optimized using minimum jerk, time-optimal piece-wise Bezier curves in two stages: task space followed by joint space, implemented on a low-cost microcontroller. Experimental results demonstrate that the proposed method offers enhanced accuracy, reduced velocity fluctuations, and computational efficiency compared to conventional interpolation methods.

Sina Akhbari, Mehran Mahboubkhah

Intelligent Automation Centre, Wolfson School of Mechanical, Electrical & Manufacturing Engineering, Loughborough University, Loughborough, UK · Department of Mechanical Engineering, University of Tabriz, 51666-16471, Tabriz, Iran

Trajectory Generation Robotics Robot Motion Generation Industrial Robotics Trajectory Optimization

Feb 9, 2026

From Legible to Inscrutable Trajectories: (Il)legible Motion Planning Accounting for Multiple Observers

In cooperative environments, such as in factories or assistive scenarios, it is important for a robot to communicate its intentions to observers, who could be either other humans or robots. A legible trajectory allows an observer to quickly and accurately predict an agent's intention. In adversarial environments, such as in military operations or games, it is important for a robot to not communicate its intentions to observers. An illegible trajectory leads an observer to incorrectly predict the agent's intention or delays when an observer is able to make a correct prediction about the agent's intention. However, in some environments there are multiple observers, each of whom may be able to see only part of the environment, and each of whom may have different motives. In this work, we introduce the Mixed-Motive Limited-Observability Legible Motion Planning (MMLO-LMP) problem, which requires a motion planner to generate a trajectory that is legible to observers with positive motives and illegible to observers with negative motives while also considering the visibility limitations of each observer. We highlight multiple strategies an agent can take while still achieving the problem objective. We also present DUBIOUS, a trajectory optimizer that solves MMLO-LMP. Our results show that DUBIOUS can generate trajectories that balance legibility with the motives and limited visibility regions of the observers. Future work includes many variations of MMLO-LMP, including moving observers and observer teaming.

Ananya Yammanuru, Maria Lusardi, Nancy M. Amato +1

University of Illinois at Urbana-Champaign, Urbana IL 61801, USA

Trajectory Optimization Trajectory Generation Motion Planning Robot Motion Planning

Dec 3, 2025

LAMP: Language-Assisted Motion Planning for Controllable Video Generation

Video generation has achieved remarkable progress in visual fidelity and controllability, enabling conditioning on text, layout, or motion. Among these, motion control - specifying object dynamics and camera trajectories - is essential for composing complex, cinematic scenes, yet existing interfaces remain limited. We introduce LAMP that leverages large language models (LLMs) as motion planners to translate natural language descriptions into explicit 3D trajectories for dynamic objects and (relatively defined) cameras. LAMP defines a motion domain-specific language (DSL), inspired by cinematography conventions. By harnessing program synthesis capabilities of LLMs, LAMP generates structured motion programs from natural language, which are deterministically mapped to 3D trajectories. We construct a large-scale procedural dataset pairing natural text descriptions with corresponding motion programs and 3D trajectories. Experiments demonstrate LAMP's improved performance in motion controllability and alignment with user intent compared to state-of-the-art alternatives establishing the first framework for generating both object and camera motions directly from natural language specifications. Code, models and data are available on our project page.

Muhammed Burak Kizil, Enes Sanli, Niloy J. Mitra +3

Koç University · University College London · Adobe Research +1

Camera-Controlled Video Generation Trajectory Generation Language Model-Based Control Motion Planning Controllable Video Generation Language-Conditioned Robot Planning

Dec 2, 2025

EmbodiedDiffusion: End-to-End Traversability-Guided Visual Diffusion for Heterogeneous Robot Navigation

Visual traversability estimation is central to autonomous navigation, yet most approaches either rely on prompt-driven Vision-Language Model (VLM) or decouple traversability from trajectory planning, requiring separate planners with heavy mapping, manual tuning, and extended deployment time. We propose EmbodiedDiffusion, a diffusion-based framework that simultaneously predicts traversability maps and generates feasible trajectories from RGB images using planner-free synthetic supervision and embodiment conditioning for cross-platform transfer. The framework distills category-level traversability semantics from a VLM teacher into a lightweight student model during training, enabling prompt-free, real-time inference at deployment. A modular FiLM-based conditioning mechanism isolates embodiment-specific reasoning into a compact trainable subset of the network, allowing rapid adaptation to new robot platforms without retraining the visual backbone or the trajectory diffusion model. Across indoor environments with quadruped and aerial robots, EmbodiedDiffusion achieves 80-100% navigation success in the full-data regime with real-time inference (90 ms) and adapts to new platforms using only 10 min of visual data collection, demonstrating scalable, unified traversability reasoning and trajectory generation for heterogeneous robots.

Iana Zhura, Sausar Karaf, Faryal Batool +7

Intelligent Space Robotics Laboratory, Center for Digital Engineering, Skolkovo Institute of Science and Technology.

Robot Motion Generation Trajectory Generation Cross-Embodiment Robot Learning Visual Navigation Diffusion-Based Planning Robot Navigation+2

Oct 30, 2025

ART-TEB: Adaptive Trajectory Planning for Mobile Robots in Cluttered Environments

Trajectory planning for mobile robots remains a major challenge, particularly in cluttered environments, where existing planning algorithms often fail or produce suboptimal paths. To address this issue, we propose an adaptive trajectory refinement algorithm, ART-TEB, comprising two main stages. First, to ensure safety at the path-segment level, a segment-wise conservative collision test is applied, recursively subdividing risky path segments until the collision risk is eliminated. Second, to guarantee pose-level safety, pose correction based on separation direction and line search is applied, ensuring that each pose in the trajectory is collision-free and maximally clear from obstacles. Simulation results demonstrate that the ART-TEB achieves up to 3.12x higher success rates and up to 23.7x faster average planning times than state-of-the-art approaches. Furthermore, real-world experiments confirm that the robot can safely pass through highly constrained environments while maintaining rapid planning performance.

Hahjin Lee, Young J. Kim

Department of Computer Science and Engineering at Ewha Womans University in Korea

Trajectory Optimization Trajectory Generation Mobile Robotics Safe Motion Planning Robot Motion Planning

Oct 16, 2025

STITCHER: Constrained Trajectory Planning in Complex Environments with Real-Time Motion Primitive Search

Autonomous high-speed navigation through large, complex environments requires real-time generation of agile trajectories that are dynamically feasible, collision-free, and satisfy state or actuator constraints. Modern trajectory planning techniques primarily use numerical optimization, as they enable the systematic computation of high-quality, expressive trajectories that satisfy various constraints. However, stringent requirements on computation time and the risk of numerical instability can limit the use of optimization-based planners in safety-critical scenarios. This work presents an optimization-free planning framework called STITCHER that stitches short trajectory segments together with graph search to compute long-range, expressive, and near-optimal trajectories in real-time. STITCHER outperforms modern optimization-based planners through our innovative planning architecture and several algorithmic developments that make real-time planning possible. Extensive simulation testing is performed to analyze the algorithmic components that make up STITCHER, along with a thorough comparison with three state-of-the-art optimization planners. Simulation tests show that safe trajectories can be created within a few milliseconds for paths that span the entirety of two 50 m x 50 m environments. Hardware tests with a custom quadrotor verify that STITCHER can produce trackable paths in real-time while respecting nonconvex constraints, such as limits on tilt angle and motor forces, with flight speeds up to 63 km/h.

Helene J. Levy, Brett T. Lopez

VECTR Laboratory, University of California, Los Angeles, Los Angeles, CA, USA

Constrained Motion Planning Trajectory Generation UAV Navigation Graph-Based Planning Safe Motion Planning Motion Planning+1

Oct 10, 2025

Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization

Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often computationally intractable beyond a very small swarm size. In this paper, we propose Flow-Opt, a learning-based approach towards improving the computational tractability of centralized multi-robot trajectory optimization. Specifically, we reduce the problem to first learning a generative model to sample different candidate trajectories and then using a learned Safety-Filter(SF) to ensure fast inference-time constraint satisfaction. We propose a flow-matching model with a diffusion transformer (DiT) augmented with permutation invariant robot position and map encoders as the generative model. We develop a custom solver for our SF and equip it with a neural network that predicts context-specific initialization. The initialization network is trained in a self-supervised manner, taking advantage of the differentiability of the SF solver. We advance the state-of-the-art in the following respects. First, we show that we can generate trajectories of tens of robots in cluttered environments in a few tens of milliseconds. This is several times faster than existing centralized optimization approaches. Moreover, our approach also generates smoother trajectories orders of magnitude faster than competing baselines based on diffusion models. Second, each component of our approach can be batched, allowing us to solve a few tens of problem instances in a fraction of a second. We believe this is a first such result; no existing approach provides such capabilities. Finally, our approach can generate a diverse set of trajectories between a given set of start and goal locations, which can capture different collision-avoidance behaviors.

Simon Idoko, Prajyot Jadhav, Arun Kumar Singh

All authors are with the University of Tartu, Estonia.

Multi-Robot Motion Planning Constrained Motion Planning Multi-Agent System Optimization Trajectory Generation Safe Motion Planning Robotic Optimization

Sep 30, 2025

Learning from Hallucinating Critical Points for Navigation in Dynamic Environments

Generating large and diverse obstacle datasets to learn motion planning in environments with dynamic obstacles is challenging due to the vast space of possible obstacle trajectories. Inspired by hallucination-based data synthesis approaches, we propose Learning from Hallucinating Critical Points (LfH-CP), a self-supervised framework for creating rich dynamic obstacle datasets based on existing optimal motion plans without requiring expensive expert demonstrations or trial-and-error exploration. LfH-CP factorizes hallucination into two stages: first identifying when and where obstacles must appear in order to result in a near-optimal motion plan, i.e., the critical points, and then procedurally generating diverse trajectories that pass through these points while avoiding collisions. This factorization avoids generative failures such as mode collapse and ensures coverage of diverse dynamic behaviors. We further introduce a diversity metric to quantify dataset richness and show that LfH-CP produces substantially more varied training data than existing baseline. Experiments in simulation demonstrate that planners trained on a LfH-CP generated dataset achieves higher success rates compared to a prior hallucination method.

Saad Abdul Ghani, Kameron Lee, Xuesu Xiao

George Mason University · Thomas Jefferson High school intern affiliated with the RobotiXX Lab, George Mason University

Trajectory Generation Synthetic Data Generation for Robotics Motion Planning Dynamic Obstacle Avoidance

Jun 14, 2025

AntiGrounding: Executable Robot Trajectories as Visual Prompts for VLM-Guided Manipulation

Natural-language manipulation instructions specify the task goal but leave the underlying robot trajectory unspecified. We present AntiGrounding, a visual action-selection framework built around a dual geometric-visual trajectory interface. After feasibility filtering, each retained short trajectory is both an explicit motion plan for execution and a rendered prompt for instruction-conditioned vision-language model (VLM) evaluation. Structured multi-view visual question answering (VQA) scores safety, task alignment, efficiency, and physical plausibility; weighted view fusion aggregates the trajectory scores. These scores guide subsequent translational trajectory proposals; separate orientation and gripper controls coordinate interaction. An initialized digital twin provides the planning state and validates selected segments before the real robot executes the same waypoint sequences. Across eight real-world manipulation tasks, AntiGrounding with a single GPT-6 Astra evaluator achieves 71.25% overall success, compared with 50.00% for pi0.5 and 47.50% for a PIVOT-style visual proposal-selection baseline using the same evaluator under the reported deployment protocol. Component ablations and evaluator-sensitivity analyses examine trajectory evaluation, proposal search, orientation control, and evaluator choice. The interface connects general-purpose multimodal reasoning to executable trajectories, with performance bounded by digital-twin fidelity and physical interaction.

Wenbo Li, Yiteng Chen, Wenhao Li +1

School of Software Engineering, South China University of Technology

Trajectory Generation Language-Conditioned Robot Manipulation Visually Grounded Reasoning Robot Motion Planning VLMs for Robotics