Trajectory Optimization

Trajectory planning strongly influences tracking accuracy, actuator demand, and overall execution behavior in robotic manipulators. Classical planners such as cubic, quintic, and trapezoidal profiles are widely used for their simplicity and smoothness, yet they remain purely kinematic and ignore system dynamics and control effort during trajectory generation. As a result, nominally smooth trajectories can lead to inefficient nonlinear execution and increased corrective control action. This paper presents a control-aware optimal trajectory planning framework that explicitly incorporates manipulator dynamics and actuator effort within a finite-horizon formulation. A midpoint linearization strategy is introduced to improve approximation accuracy for large point-to-point motions. In contrast to prior comparisons, the proposed approach enables fair, isolated evaluation of trajectory generation effects under identical closed-loop nonlinear execution conditions. To this end, a unified evaluation framework is developed in which all planners are executed under identical nonlinear dynamics, controller structure, and actuator constraints. Simulations on a nonlinear simplified UR5 manipulator show that the proposed approach consistently reduces tracking error, corrective torque, and closed-loop execution cost compared to classical methods, achieving substantial reductions in actuator effort and execution cost across all evaluated scenarios, demonstrating that kinematic smoothness alone does not ensure dynamically efficient execution.

This paper develops an Optimality-Informed Neural Network (OINN) approach for the energy-optimal, free-final-time powered descent of a lunar lander from any initial position, velocity, and mass within a bounded operating envelope to a fixed landing site with zero terminal velocity. Building on a recent framework that jointly embeds Pontryagin's minimum principle and the Hamilton-Jacobi-Bellman equation for general nonlinear optimal control, the proposed OINN approach specializes that idea to a lunar landing problem with free time of flight and fixed terminal state. Every boundary and transversality condition is hard-encoded into the network architecture by construction, the closed-form Pontryagin-optimal thrust magnitude and direction law is substituted directly rather than learned, and the remaining state, costate, and an auxiliary value-function output are trained against a physics-residual loss formed entirely from the necessary conditions of optimality, with no precomputed optimal trajectories required. A preliminary theoretical analysis is explored, establishing a stochastic-optimization stationarity guarantee for the offline training procedure, an explicit bound translating the achieved training residual into bounds on touchdown position, touchdown velocity, and flight-time error, and a fixed, input-independent onboard computational and memory cost suitable for real-time deployment. Numerical simulations evaluate the trained policy, with no retraining, against an independently solved indirect-method boundary-value problem at six representative initial states spanning the operating envelope and against eighty additional Monte Carlo simulation runs, demonstrating close agreement with the indirect-method solution and consistently small dynamics and transversality residuals throughout the envelope.

The high-angle-of-attack flip maneuver of reusable launch vehicles presents significant challenges for robust trajectory optimization due to the combined effects of highly nonlinear dynamics, aerodynamic uncertainties, and actuator saturation. This paper presents a differentiable physics framework for saturation-aware robust trajectory optimization. At its core, a Differentiable Particle Tube Control (DPTC) scheme is developed to optimize uncertainty evolution through an ensemble-based distribution shaping strategy. State uncertainty is represented by a Lagrangian particle ensemble, while hard actuator projection operators are embedded directly into the computational graph, enabling the joint optimization of the nominal feedforward trajectory and a time-varying feedback policy via end-to-end backpropagation. The proposed framework is evaluated against an automatic differentiation-based Successive Convexification (AD-SCvx) baseline combined with a conventional covariance steering feedback strategy. Six-degree-of-freedom Monte Carlo simulations demonstrate that, although the baseline achieves nominal fuel-optimal solutions, its unconstrained feedback formulation becomes susceptible to actuator saturation under aerodynamic disturbances, leading to degraded closed-loop robustness. In contrast, the proposed DPTC framework proactively performs a constraint-aware performance trade-off by relaxing spatial tracking to preserve critical control authority. These results demonstrate that integrating differentiable physics with ensemble-based optimization provides an effective and practical framework for robust guidance in highly constrained aerospace flight systems.

End-to-end autonomous driving models often encounter performance bottlenecks, as training-time scaling leads to high computational costs and diminishing marginal returns. Existing planners typically adopt a one-shot generation paradigm, lacking secondary validation and active correction mechanisms to detect and revise suboptimal or unsafe trajectories during inference. To address this issue, we propose DriveVer, a lightweight, plug-and-play Test-Time Verifier that leverages the test-time scaling paradigm to enable autonomous driving systems to validate and refine trajectories without costly and heavy training. We construct a dedicated trajectory dataset based on the NAVSIM benchmark through condition-driven clustering and balanced sampling according to ego-vehicle states and navigation commands. Employing a dual-head architecture, DriveVer efficiently fuses candidate trajectories with multi-view visual representations and ego-vehicle kinematic features to simultaneously predict a safety confidence score and an absolute geometric refinement vector. Extensive experiments on the NAVSIM benchmark show that DriveVer significantly improves the performance of base planning models. Notably, as an extremely compact model with only 34M parameters, DriveVer introduces minimal computational overhead, achieving competitive results while maintaining real-time inference efficiency.

Due to the limited endurance of embedded energy sources such as lithium-polymer (LiPo) batteries, the flight duration and operational range of unmanned aerial vehicles (UAVs) are severely constrained. Although energy-efficient trajectory planning and control have been widely studied, most existing approaches rely on accurate system models and computationally expensive optimization procedures. This paper proposes a model-free online iterative learning (IL) framework to minimize energy consumption. Without requiring explicit models of UAV dynamics or energy consumption, the proposed method improves energy efficiency while maintaining a low computational cost. The per-iteration computational complexity is O(n), where n denotes the number of path points. In the tested cases, the proposed method is approximately 50--60 times faster than the model-based IPOPT benchmark. Simulation results and real-world flight experiments across multiple UAV platforms validate the effectiveness, computational efficiency, and practical applicability of the proposed approach.

Redundant robotic multi-axis additive manufacturing (MAAM) enables support-free and conformal fabrication, but trajectory optimization for long-horizon paths remains challenging under strict deposition-position constraints and time-varying collision constraints. This work proposes a computational framework for collision-aware trajectory optimization in redundant robotic MAAM. We first formulate nozzle-workpiece relative kinematics using a relative Jacobian, and develop a differentiable SDF-based collision model that captures fabrication-induced geometry evolution and provides optimization gradients. The deposition position is then enforced as a hard waypoint-wise equality constraint through iterative projection onto the self-motion manifold, with the loss gradient restricted to the corresponding tangent space. Experiments on an 8-DOF robotic MAAM platform with diverse long-horizon support-free and conformal toolpaths show that our method maintains a mean nozzle-position error below 10μm, reduces maximum joint jerk by up to $77.6\%$, and eliminates all sampled collision and orientation violations. Compared with the SQP-based baseline, it achieves up to a 10.2x speedup and improved convergence. Physical fabrication experiments further verify that the resulting smooth, collision-free trajectories enable successful printing of complex geometries with fewer visible deposition artifacts.

Belief-space planning under motion uncertainty and state and control constraints remains a fundamental challenge, largely due to the difficulty of establishing reachability guarantees in constrained belief spaces. Existing constrained belief-space planners rely on sampling to construct multi-query belief roadmaps and explicitly find feasible trajectories between sampled nodes to establish reachability. These methods often struggle to cover the belief space or use robust control techniques that improve coverage at the cost of indirect, high-cost trajectories; they also lack finite-time or finite-memory completeness guarantees. We propose PRISM, a multi-query motion planning algorithm for belief spaces with state and control constraints that targets both high coverage and low cost. We present a new result on controllability of the state covariance under constraints, which is used by PRISM to decompose belief-space planning into deterministic mean planning and covariance shrinking. PRISM further includes an online local optimization method that reduces the cost of feasible belief-space trajectories. Under mild assumptions on the start and goal distributions, we prove that PRISM guarantees full coverage (i.e. completeness) despite actuator and obstacle constraints. In challenging simulated scenarios, PRISM achieves substantially higher roadmap coverage than state-of-the-art belief-space planning methods while producing trajectories with lower mean cost and cost variance. For example, PRISM achieves 100% coverage in easy and medium-difficulty scenarios, and, in the hardest scenario, which violates PRISM's coverage assumptions, it still achieves 97-100% coverage, while all other methods achieve less than 45%.

Many robotics problems, including trajectory optimization, inverse kinematics, and contact-rich motion planning, reduce to nonlinear programs (NLPs). Mature NLP solvers such as IPOPT can solve these problems, offering hard constraint satisfaction, optimality guarantees, and favorable scaling with problem dimension. These solvers underpin gradient-based methods in robotics, yet remain CPU-bound and solve only one problem at a time, preventing their integration into GPU-batched learning pipelines. On the other hand, sampling-based approaches such as reinforcement learning, model predictive path integral, and imitation learning have become the core of modern robotics research due to their ability to leverage GPU-batched simulators. These simulators can generate orders of magnitude more dynamics rollouts per second than was previously possible. If a GPU-batched NLP solver existed, it would unlock similar speedups in the number of constrained, locally optimal solutions generated per second. This regime of solving many problems concurrently versus solving a single problem at a time is a key requirement for integrating NLP solvers in modern GPU-batched robotics frameworks. To this end, we introduce jaxipm, the first GPU-batched NLP solver, based on IPOPT, and implemented in JAX. We accomplish this by redesigning IPOPT's algorithm to eliminate control flow with heterogeneous iteration fusion, and by minimizing GPU idle time with iteration level batching. We evaluate jaxipm on a variety of quadrotor nonlinear model predictive control benchmarks, including reference tracking in the presence of obstacles, multi-quadrotor navigation without collision, and navigation in a cluttered environment. We demonstrate up to a $32.85\times$ increase in throughput over IPOPT. Our complete open-source codebase is available at https://github.com/johnviljoen/jaxipm.

Unmanned aerial vehicle (UAV) can provide on-demand, high-capacity connectivity in disaster and normal situation. However, it faces a challenge of curse of dimensionality in trajectory optimization, where interference-limited environments and vast search spaces make real-time coordination computationally expensive. To overcome this challenge, we propose the Rate-Aware Quantum-Annealed Graph Condensation (RA-QAGC) scheme, which combines rate-aware graph abstraction with decentralized reinforcement learning to enable scalable, interference-aware UAV coordination. By identifying high throughput locations and guiding UAV trajectory adaptation toward throughput-optimal regions, RA-QAGC effectively balances network capacity by maintaining quality-of-service (QoS) requirements. Simulation results demonstrate the proposal outperformed over existing schemes by achieving 59.4 Mbps total throughput and 23.9 Mbps priority-user throughput, representing gains of approximately 15% and 34%, respectively, over the baseline schemes.

The development of trajectory planning strategies for autonomous ground vehicles (AGVs) represents a prevailing research interest within the domain of intelligent transportation systems. This paper introduces a trajectory planning framework tailored for multi-floor scenarios. The framework consists of two main modules: the task planning module and the trajectory planning module. The task planning module involves a strategic selection phase, where a task planning strategy based on generalized voronoi diagrams (GVD) and multi-objective algorithms is proposed to select the floor exits for each floor. The trajectory planning module utilizes optimization-based methods to generate high-quality trajectories, and a warm-started hierarchical planning framework is designed to ensure rapid convergence. Additionally, for handling complex obstacle constraints, a correlation constraint calculation method is designed for reducing obstacle constraints in trajectory planning. Finally, the feasibility and effectiveness of the proposed framework are verified through simulations.

Unmanned aerial vehicles (UAVs) are increasingly employed in urban inspection tasks, where reliable communication is critical but challenging due to the severe spatial channel heterogeneity. To address the issue, in this paper, we focus on the communication-aware path planning for multi-UAV tasks, and propose a channel knowledge map (CKM)-driven trajectory planning framework which integrates the channel modeling and trajectory decision-making. Specifically, we apply the diffusion model to construct a time-accumulated CKM and achieve the accurate perception with low flight overhead, which leverages the sparse observation data to reconstruct the high-fidelity global channel quality distribution. Based on the CKM, we propose a global-to-local graph attention network soft actor-critic algorithm. The graph attention network optimizes the complex combinatorial node ordering problem, generating an optimal and communication-aware sequence for the inspection targets. Subsequently, the soft actor-critic algorithm performs continuous action control to ensure the smoothness of the flight path and dynamically avoid communication attenuation areas. Simulation results demonstrate that the proposed method effectively guides UAVs through high-quality channel regions without dependence on real-time channel feedback, significantly improving both the trajectory efficiency and communication reliability.

The deployment of unmanned aerial vehicles (UAV) as open radio units (O-RUs) in 6G cellular systems presents a promising opportunity to achieve scalable and adaptive network coverage. However, optimizing UAV trajectories in dynamic and unfamiliar environments remains a critical challenge, particularly due to the need for extensive retraining in each new scenario. In this paper, we introduce a novel UAV trajectory optimization framework that integrates enhanced continual transfer learning within the O-RAN architecture. The proposed system maintains a library of pre-trained models and employs a model selection mechanism to identify and transfer knowledge from the most relevant environments, minimizing adaptation time and improving efficiency. When no sufficiently similar model is available, a fallback model empowered by continuous refinements ensures baseline performance. The framework leverages real-world city maps and ray tracing techniques to enhance learning reliability and improve trajectory planning. Simulation results demonstrate that the proposed model selection-based transfer learning approach reduces convergence time by 44% to 56% compared to retraining from scratch, and up to 40% compared to traditional transfer learning without model selection.

We study trajectory optimization in mobile sensing systems that must identify which member of a finite candidate set is the true target, while maintaining reachability to all potential candidate targets, under resource constraints. Deferred-Decision Trajectory Optimization (DDTO) addresses this setting by computing trajectories that reach individual targets but remain coincident for as long as possible before separating toward different targets. We propose Active-Sensing DDTO (AS-DDTO), which extends DDTO by adding a trajectory-dependent information-acquisition term to the planning objective. The resulting planner maintains reachability to candidate targets while biasing the coincident portion of the trajectories toward regions that enable earlier target identification. The framework supports Bayesian updates and conformal candidate-set updates for distance-dependent sensing. We derive a mixed-integer conic reformulation and provide guarantees on recursive feasibility, belief concentration, and fixed-time coverage for the raw conformal candidate set. Numerical simulations show improved target identification compared with standard DDTO under distance-dependent sensing uncertainty and limited sensing budget.

Distributed optimization is a highly scalable and structurally transparent technique to solve multi-agent robotics problems; however, such methods often suffer from the need for highly-specialized, problem-specific hyperparameter tunings. In this work, we propose Deep Coordinator, a deep-unfolding framework that learns to dynamically adjust the hyperparameters of ADMM-DDP, a popular distributed solver for robotics tasks, at solve-time in response to optimizer performance. Our architecture consists of unrolling a fixed number of ADMM-DDP iterations into a neural network with learnable functions between layers mapping the optimizer state to the next hyperparameters. To the best of our knowledge, Deep Coordinator is the first deep-unfolding framework to adapt the penalty parameters of a non-convex optimizer at solve-time; we show that the mainstream supervised approach can yield degenerate solutions when training such models, and propose an unsupervised learning scheme. On simulations with fleets of cars and quadrotors, Deep Coordinator produces trajectories of comparable quality 6.18-9.44x faster than conventional solvers. Furthermore, Deep Coordinator retains its performance benefits when deployed to systems up to 8x larger than trained on.

We present a unified framework that turns a set of 6-DoF inspection viewpoints into a time-optimal, collision-free route for a 9-DoF robotic system. Unlike modular pipelines that fix a single inverse-kinematics (IK) configuration per viewpoint, build an all-pairs travel-time map, and then route, our method jointly optimizes the visiting order and the per-viewpoint configuration in a single global search. The three-dimensional self-motion manifold of each viewpoint is parameterized in closed form so that the pose constraint holds by construction, the rest-to-rest travel time is approximated by a closed-form admissible double-integrator surrogate, and the tour is encoded by random keys. A derivative-free optimizer (CMA-ES) minimizes a cheap penalized objective over order and configuration, after which direct-collocation trajectory optimization is applied only to the edges of the selected route to certify dynamic feasibility and torque limits, and to return exact timings. This reduces the trajectory solves from quadratic to linear in the number of viewpoints and removes the decoupling that prevents modular pipelines from being globally time-optimal. Simulations and real-robot experiments on a KUKA LBR iiwa with a 2-DoF linear stage validate feasibility, smooth execution, and reduced end-to-end inspection time relative to modular and naive distance-based baselines.

Diffusion-based visuomotor policies deployed with asynchronous inference often exhibit inter-chunk discontinuities and lack explicit mechanisms for obstacle-aware execution, leading to jerky motions and collisions that hinder reliable manipulation in real-world scenes. To address these issues, we propose LAGO Policy, a unified asynchronous action-generation framework that integrates trajectory optimization with diffusion policy for smooth and safe execution. LAGO Policy improves inter-chunk consistency via latency-aware classifier-free guidance conditioning on future actions. It further enables goal-directed collision-free trajectory planning by predicting a task-relevant interaction goal from demonstrations. Finally, spatial-temporal trajectory optimization refines the actions to be executed for low-jerk and feasible motion. Extensive real-world experiments demonstrate that LAGO Policy achieves smooth collision-free execution with high task success across challenging manipulation tasks. Project Website: https://lago-policy.github.io/

Safe and efficient trajectory planning in unknown, cluttered 3D environments constitutes a critical bottleneck for deploying Unmanned Aerial Vehicles (UAVs) in real-world applications. This challenge is further exacerbated by the limited field-of-view (FOV) and sensing range of onboard sensors. Many existing methods either make simplistic assumptions about unexplored space or rely on conservative heuristics such as speed limits or fixed perception patterns, reducing efficiency and generalizing poorly across different sensor types. In this work, we propose a novel planning framework that directly integrates active perception into trajectory optimization, thereby improving safety while preserving efficiency. The perception constraints are derived from the UAV's dynamic model and formulated in the sensor coordinate frame, which enables precise handling of FOV geometry. The velocity-triggered activation mechanism enables the planner to balance perception and motion efficiency. We introduce an active perception sub-trajectory segment with parametric start-time optimization, mitigating collision risks from late obstacle detection. Our formulation enables active perception during arbitrary 3D maneuvers, extending beyond prior methods designed mainly for horizontal motion. All constraints and penalties are incorporated into a differentiable optimization problem, so the planner requires only a simple front-end global path for guidance, rather than a computationally expensive perception-aware path generator. Extensive simulations and real-world experiments demonstrate robust performance across diverse unknown environments with varying sensor configurations.

Real-time trajectory generation for on-orbit robotic servicing is challenging due to the nonlinear coupling between spacecraft bus motion, manipulator dynamics, visibility cone, and trajectory-level safety constraints. This paper studies learning-based warm-starting for sequential convex programming (SCP) in the terminal approach of a space manipulator toward a tumbling target. The proposed framework decomposes the problem into a system center-of-mass translational planning stage and a coupled attitude--manipulator torque-allocation stage, and applies a causal transformer warm-start to the latter, which constitutes the dominant computational bottleneck. Linear and flow matching action decoders are compared under different action-chunking and training dataset sizes, and the resulting warm-starts are evaluated under both cost-optimal and feasibility projection using SCP. Across 300 held-out scenarios, the learned warm-start reduces the second-stage SCP iteration count by up to 28% and the runtime by 23% while preserving the final control-cost distribution. When the learned warm-starts are used for nonconvex feasibility projection, they nearly halve the runtime relative to cost-optimal SCP, while avoiding the catastrophic high-cost tail behavior observed when initialized heuristically. These results indicate that sequence-model warm-starts can improve both the computational efficiency and trajectory robustness of optimization-based terminal guidance for space manipulation.

Robotic systems routinely encounter conflicting objectives, modeling errors, and degenerate contact conditions that render quadratic programs (QPs) infeasible. Yet most optimization solvers and differentiable QP layers assume feasibility, leading to numerical failures, unstable gradients, or solver breakdown when constraints cannot be simultaneously satisfied. We present Elastic ODYN, a primal-dual non-interior-point QP solver that handles infeasibility through smooth squared-$\ell_2$ elastic relaxations. The formulation remains well posed under ill-conditioning and degeneracy, supports warm starting, and converges to closest-to-feasible solutions, with lightweight refinement recovering physically meaningful dual variables. Building on this framework, we develop Elastic ODYNLayer, a differentiable QP layer with stable gradients under infeasibility, and Elastic OdynSQP, an SQP method that resolves inconsistent subproblems and intrinsically infeasible optimal control tasks through selective constraint elasticity. Across benchmark QPs, singular contact mechanics, differentiable parameter identification, and quadrupedal and humanoid trajectory optimization, Elastic ODYN outperforms state-of-the-art elastic QP solvers in robustness, warm-start performance, and convergence reliability, enabling optimization, simulation, control, and learning beyond standard feasibility assumptions.

We study semidefinite relaxations for collision-free motion planning. We focus on a point robot moving from start to goal through spherical obstacles in $\mathbb{R}^n$, subject to path continuity constraints and squared derivative costs; a setting that is conceptually simple yet captures the hardness of collision-free motion planning. We formulate this problem exactly as a nonconvex problem over polynomial curves, and present a natural semidefinite relaxation. We contribute two key theoretical insights; to our knowledge this is the first theoretical analysis of semidefinite relaxations for collision-free motion planning. First, we show that solving the convex relaxation is equivalent to solving, to global optimality, a related motion planning problem in a potentially higher-dimensional space. This geometric interpretation yields necessary and sufficient conditions for tightness, and a clear intuition for when the relaxation is loose. Second, we show that the relaxation admits a symmetry reduction that makes it significantly smaller than one might expect, with positive semidefinite cone sizes that scale linearly with the polynomial degree and are independent of the ambient dimension. The resulting relaxation is 10 to 100 times faster than direct nonlinear programming transcriptions solved with SNOPT and IPOPT, exhibits significantly lower variance in solve times, and reliably finds a locally optimal path for the original problem. We demonstrate its effectiveness as a convex steering function in an RRT planner for minimum-snap quadrotor planning with $C^4$ continuous trajectories.

This paper presents a distribution-agnostic robust trajectory-optimization framework based on chance-constrained reinforcement learning. The uncertainty is represented here through initial conditions and process noise, with the only requirement being that it can be sampled. A deterministic nominal trajectory is first computed offline, and reinforcement learning is then used only to robustify that baseline through a structured affine closed-loop correction law comprising a feedforward control adjustment and time-varying feedback gains. Probabilistic feasibility is enforced empirically through rollout-based upper-tail quantiles, while terminal dispersion is regulated through covariance-feasibility penalties. The framework is assessed on two materially different trajectory design problems. The flagship case study is a three-dimensional multi-impulse Earth-Mars transfer, where the learned policy is benchmarked against a recent robust trajectory-optimization reference under Gaussian uncertainty and then evaluated under bounded uniform uncertainty and under process disturbances not seen during training. The second case study is a stochastic atmospheric pinpoint rocket landing problem, used to assess portability to a short-horizon continuous-thrust setting with drag, mass depletion, and glide-slope constraints. The results show that the proposed framework can remain competitive in upper-tail fuel cost while preserving probabilistic feasibility, and that the same robustification scaffold can be carried across heterogeneous spacecraft trajectory planning problems without redesign of its core stochastic-control structure.

Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. While direct methods are widely used, the existing constrained optimizers typically operate in Euclidean space and ignore the manifold structure of rigid body motions. This mismatch may introduce singularities or lead to poorly conditioned optimization problems. To bridge this gap, we develop a structure-aware framework for constrained trajectory optimization directly on matrix Lie groups. Our approach is based on the second-order rigid body models utilizing Lie group structures, which enables efficient Newton-type updates while preserving the underlying geometry. Building on this model, we propose a line-search Lie Group Interior Point Method (LieIPM) to handle constraints on the manifolds. We instantiate the framework for rigid body motion planning using Lie group variational integrators and derive closed-form intrinsic derivatives that exploit group symmetries. The LieIPM preserves the topology of rotation motions by construction and avoids singularities. Numerical results demonstrate superior robustness and faster convergence compared to general-purpose solvers and structure-exploiting optimal control methods.

Bearing-only target localization is a fundamental problem in optical measurement and finds extensive applications in unmanned aerial vehicle (UAV) technology. Effective trajectory planning establishes favorable observation geometries, thereby enhancing the target localization accuracy of bearing-only UAV systems. This paper proposes an trajectory optimization method for unmanned aerial vehicles (UAVs) in bearing-only target localization scenarios. By leveraging the Fisher Information Matrix (FIM), the proposed approach dynamically integrates the geometric configuration and vehicle maneuverability into the optimization framework. Specifically, we introduce a spectrally-weighted FIM objective function that provides better gradient dynamics near degenerate configurations, enabling the planner to rapidly escape from poor observation conditions. For dual-UAV scenarios, an intersection angle sine term is introduced to optimize triangulation geometry by improving the sight-line intersection angle, thereby preventing trajectory aggregation. Furthermore, we propose an improved Particle Swarm Optimization (PSO) algorithm with motion model constraints and particle normalization to ensure the physical feasibility of the trajectory and enhance the compatibility with the objective functions. Simulation results demonstrate that the proposed method reduces the median localization error by 99.21% compared to conventional FIM-based approaches in single-UAV scenarios, and achieves a 69.70% improvement for dual-UAV configurations, exhibits superior performance in long-duration bearing-only target localization of maneuverability targets at extended ranges.

Offline reinforcement learning (RL) offers a path to policy improvement from logged data alone, using historical returns or other measurable outcomes as world feedback. A key difficulty is improving observed behavior without extrapolating beyond what the offline data supports. We propose counterfactual transport flows, a source-conditioned trajectory refinement framework for offline decision-making guided by world feedback. Given a low-feedback candidate trajectory, we construct local preference pairs from offline data by retrieving nearby trajectories in latent trajectory space with higher task-specific feedback, and use them as weak supervision for conservative refinement. The framework learns instance-specific refinement directions: at inference time, a refinement strength parameter controls how far the candidate trajectory is transported, enabling a trade-off between preserving the original behavior and applying stronger improvement. Experiments on D4RL benchmarks, including AntMaze and MuJoCo tasks, show that our method improves behavior from historical returns as world feedback, while providing interpretable trajectory-level refinement paths.

In teleoperation, the human operator typically controls only the end-effector pose, which often leads to self-collisions of the manipulator and collisions with environmental obstacles, since joints and links are not controlled individually. A common strategy to mitigate this issue is to enhance the operator's input using optimal-control-based trajectory planning. As derivative-based solvers require differentiable constraints, existing approaches either approximate robots and obstacles with spheres, reducing geometric accuracy, or approximate derivatives, degrading convergence and increasing computation times. We address these limitations by adapting a recent formulation of differentiable collision-avoidance constraints, based on duality in convex optimization, to the teleoperation setting. The robot is approximated with capsules and the environment with polytopes. We compare the resulting trajectory planning method against state-of-the-art techniques in simulation with varying numbers of obstacles and evaluate it on a UR5e manipulator in a real-world teleoperation test. Results show that our approach achieves lower computation times while enabling more accurate obstacle modeling, leading to smoother and collision-free end-effector teleoperation.

End-to-end planners for autonomous driving typically generate a set of candidate trajectories, score each one, and return the highest-scoring candidate. However, the scorer is applied only after the proposals are generated and cannot influence the set of trajectories: a weak set of candidates limits planning performance regardless of the scorer's quality. We instead treat the scorer as a learned trajectory-level reward function and search for trajectories that maximize it. Our method, TOAD, runs the Cross-Entropy Method at test time, warm-started from the planner's proposals. It requires no retraining and is plug-and-play for existing planners. Across seven base planners, TOAD improves results on NAVSIM-v1 (94.7 PDMS), NAVSIM-v2 (56.3 EPDMS), and the closed-loop HUGSIM benchmark. The code is made publicly available via the project page: https://valeoai.github.io/TOAD/.

Trajectory optimization is a critical component for enabling safe and reliable autonomous operations in space exploration. As space missions increase in frequency, complexity, and scope, there is a growing need to rapidly formulate mathematically sound trajectory optimization problems that accurately reflect mission objectives and operational constraints. However, translating mission intent into tractable analytical formulations for trajectory optimization requires substantial domain expertise. This paper presents a framework that leverages large language models (LLMs) to translate natural language descriptions of mission requirements and constraints into executable trajectory optimization code and corresponding mathematical formulations. Experiments in spacecraft rendezvous scenarios demonstrate a high success rate in reconditioning a convex trajectory optimization problem from semantic mission requirements. Ultimately, this work highlights the potential of LLMs to bridge high-level intent and formal optimization models, enabling more flexible and efficient trajectory design of spacecraft.

Spacecraft collision avoidance for low-thrust satellites often requires determining not only how to maneuver, but also how late a maneuver can begin while still ensuring safety. This paper presents a greedy time-optimal (GTO) backward-sweep method to find the latest maneuver initiation time. The method starts from the nominal time of closest approach and iteratively propagates the maneuver backward in time, selecting at each step the thrust direction that locally minimizes the chosen danger metric. Differential algebra is used to efficiently propagate state sensitivities and update the time of closest approach online. The method is tested on a large dataset of conjunctions, using both miss distance and probability of collision as safety metrics. The approach achieves accurate results and only a small loss of optimality relative to an optimal-control benchmark, while retaining runtimes suitable for on-board implementation.

This paper presents a fast, recursive neural solver for the J2-perturbed Lambert problem based on Tiny Recursive Models (TRM), termed the TRM-Perturbed Lambert (TRM-PL) model. TRM is a weight-shared architecture whose effective capacity emerges from iteration depth rather than parameter count: a compact reasoning module is applied repeatedly within a two-level latent hierarchy, refining a candidate departure velocity by simulating the J2 trajectory and correcting it from the resulting tracking error. This unifies initial-guess generation and iterative correction in a single, end-to-end differentiable architecture. The recursive refinement loop is a learned alternative to the homotopy and continuation schemes of classical perturbed-Lambert solvers: rather than following a hand-designed path from the Keplerian to the perturbed solution, the network learns its own sequence of corrections. We evaluate TRM-PL on three test cases of increasing difficulty: single-revolution low-Earth-orbit (LEO) transfers, multi-revolution LEO transfers, and multi-revolution Jovian transfers. Three training paradigms are compared: jointly learning the Lambert solution and the J2 correction; refining the Lambert initial velocity with target-position and J2-corrected velocity supervision; and refining it with target-position supervision alone. Across all cases, the refinement-only approaches are the most reliable. The position-supervised variant reduces the median terminal-position error from 21.7 km to 0.027 km on single-revolution LEO, from 340.9 km to 0.31 km on multi-revolution LEO, all with the same 2.3M-parameter architecture. A single Newton corrector iteration on the TRM-PL output tightens the Jovian median to 0.063 km, yielding compact models accurate enough for embedded deployment.

Autonomous robots in unknown indoor environments require both reliable collision avoidance and object-level understanding. Classical representations such as TSDF support safe planning but lack semantics, while photorealistic methods like Gaussian Splatting (GS) provide rich appearance yet suffer from soft geometry, limiting precise obstacle avoidance. We present LiftNav, a hybrid navigation framework built on GSFusion's TSDF+GS dual map, augmented with a real-time pipeline of YOLO-based detection, TSDF-based 3D lifting, and B-spline trajectory optimization. This design enables flexible semantic navigation without dense 3D embeddings. We further introduce a hinge-loss-based collision penalty that improves trajectory smoothness and safety. We evaluate our approach in a simulation using the Replica dataset. Compared against a state-of-the-art radiance field baseline we show a 100% feasibility rate and shorter trajectories.