Gradient-Based Trajectory Optimization

Aerial grasping is a remarkable capability exhibited by predatory birds, allowing them to capture prey through highly coordinated maneuvers in flight. Inspired by this capability, researchers have developed various formulations to reproduce such maneuvers through trajectory optimization. However, two limitations remain in practice. First, the resulting optimization problem is highly nonconvex and sensitive to initialization, making high-quality solutions difficult to obtain under a limited computational budget. Second, prescribed numerical objectives are human-designed abstractions that describe successful grasping through a limited set of mathematically tractable quantities and may not fully capture what determines task success. We investigate how learning can address these limitations within an analytical planner. Accordingly, a trajectory prior is first learned from optimized motions and then evolved through a CEM-based process that evaluates sampled initializations with the deployed optimizer and retains favorable ones as new supervision. An Execution-Aware Critic learns from contact, lift, and completion outcomes to assess whether the optimized trajectories are likely to succeed in physical execution. Its frozen energy can further serve as a differentiable grasping cost, allowing execution data to directly shape trajectory generation. Simulation and real-world experiments demonstrate improved optimization reliability, trajectory consistency, and grasping performance.

Deep Reinforcement Learning has demonstrated remarkable capability in quadrotor control, yet learned policies offer no guarantee of respecting safety constraints during training or deployment. We present CALOS (Control-Affine Lyapunov On-manifold Safety), a runtime safety layer that enforces attitude constraints on a quadrotor without modifying the underlying learning algorithm. CALOS formulates four tilt-angle inequalities and a Lyapunov descent condition as a single quadratic program whose solution is the minimum-norm correction to the nominal torque output of the policy. The quadratic program is solved exactly via active-set enumeration over the three-dimensional torque space, with a computational cost low enough to enforce constraints in real time across thousands of parallel simulation environments, as required by modern massively parallel Deep Reinforcement Learning training. Evaluated on trajectory-tracking tasks in NVIDIA Isaac Lab, CALOS reduces lateral tracking error by 55-60% relative to an unconstrained Proximal Policy Optimization baseline while achieving zero attitude-constraint violations on the training trajectory. By restricting exploration to safe regions of the state space, the safety layer also accelerates training convergence and improves data efficiency without producing suboptimal policies.

In this work, we propose a structured methodology for the system identification of underwater vehicles through the design of optimal excitation trajectories. To this end, the trajectories are parameterized using Bezier curves, which ensure smooth and differentiable motion profiles while facilitating the enforcement of constraints through appropriate manipulation of the control points. An optimization problem is formulated to determine a dynamically feasible excitation trajectory that respects safety limits and maximizes the quality of the collected data, thereby enabling reliable estimation of the vehicle's dynamic parameters using least squares. The proposed methodology is experimentally validated in a laboratory water tank, where the dynamic parameters, identified from the optimized trajectory, are evaluated by predicting the vehicle's velocity through forward simulation on previously unseen trajectories.

Dynamically feasible trajectory optimization for rigid-body systems is naturally formulated on the special Euclidean group SE(3) but is challenging when dynamics are available only as black-box computations without derivatives. This paper formulates the Trajectory Bundle Method (TBM) for motion planning implicitly on SE(3). Bundles are constructed in the Lie algebra and propagated through nonlinear rigid-body dynamics using exponential and logarithmic maps, enabling derivative-free planning of non-Euclidean trajectories. We show that Euclidean TBM interpolation error is bounded quadratically by bundle diameter and extend this result to SE(3), where the bound additionally depends on a local Lipschitz constant of the Log map. Numerical experiments corroborate these bounds. Finally, we demonstrate SE(3) TBM by optimizing an acrobatic, collision-free fixed-wing maneuver through a rotated aperture without explicit models or derivatives of the vehicle dynamics, aerodynamics, or collision model.

Multi-object tracking (MOT) is dominated by the tracking-by-detection paradigm, whose methods typically rely on a small set of hyperparameters that are conventionally chosen by hand. Tuning them requires repeated expert-guided experimentation, while the procedures used to select reported values are often not systematically evaluated or fully documented. Hyperparameter optimization (HPO) automates this process, yet it remains rarely used in MOT, and existing studies applying HPO to MOT predate modern deep-detector-based trackers and HOTA evaluation. We systematically apply HPO across two datasets and four tracking-by-detection methods. We also propose Multi-Fidelity Greedy Coordinate Search (MFGCS), which optimizes one hyperparameter at a time by first evaluating candidate values on a small subset of scenes and re-evaluating only promising candidates on the full dataset. Across all eight tracker-dataset combinations, the Tree-structured Parzen Estimator (TPE) and MFGCS outperform both our hand-tuned configurations and the corresponding published results, with improvements of up to 4.38 and 16.05 HOTA points, respectively. MFGCS also reaches a predefined HOTA target faster than TPE in seven of the eight combinations. Within each tracker-dataset pair, all optimizers share the same search space and evaluation pipeline, isolating the effect of the search strategy. We release the code and tuned configurations to enable future work to compare against systematically optimized rather than default or manually tuned baselines.

Planning trajectories for robot manipulators under kinematic equality constraints restricts feasible motions to a measure-zero submanifold of the configuration space, requiring special algorithmic treatment. A promising strategy is parametrizing the set of feasible configurations using analytic inverse kinematics (IK). Bespoke analytic IK functions can be written to be differentiable, a necessary property for gradient-based trajectory optimization. But the vast majority of IK functions are computed by automated meta-solvers like IKFast, and are difficult to modify for differentiability. We present a new approach for computing gradients of analytic IK parameterizations: we leverage the inverse function theorem to recover the desired gradients from the ordinary forward kinematic Jacobian. Furthermore, we present a least-squares domain extension and an optimization-amenable description of the reachability constraint, which preserves gradient signal outside the reachable workspace. We demonstrate the efficacy of our approach through numerical experiments and downstream tasks, including a hardware demonstration of an RB-Y1 picking up a box and placing it on a table. Project website: https://cohnt.github.io/inverse-function-theorem-parameterization/

Three properties determine whether a differentiable simulator can drive gradient-based optimization through contact: simulation accuracy, gradient reliability, and per-iteration cost. Tape-based engines such as MJX and Newton Semi-Implicit require timesteps small enough to keep contacts numerically tractable, and their backpropagation memory grows linearly with the number of timesteps T. Surrogate models bound memory by approximating contact away, but the resulting gradients lose the geometry the optimization depends on. We present Ostrich, a GPU-accelerated rigid-body simulator that resolves hard contacts and friction with non-smooth Newton iteration at large timesteps (h ~ 0.1 s), and differentiates the converged residual via the implicit function theorem, reusing the forward Schur complement to compute the adjoint at O(1) memory per timestep. On real-robot trajectories over a pallet obstacle, Ostrich holds MuJoCo's sim-to-real accuracy up to a 50x larger timestep. Its gradients converge from random initializations where MJX descends slowly and Newton Semi-Implicit stalls; a warm iteration runs 211x faster than MJX's and 4.7x faster than Semi-Implicit's. On the same scene Ostrich differentiates 8,192 parallel worlds on a single 24 GB GPU, sustaining 29x checkpointed MJX's optimization throughput; without checkpointing both baselines exhaust memory at far fewer worlds. We close with a gradient-based trajectory optimization demonstration over triangle-mesh terrain across a 10 s horizon, a setting where prior engines either restrict to primitive geometry or face the convergence and memory limits shown above.

Black-Box Optimization (BBO) has broad applications, while traditional algorithms such as evolutionary algorithms and Bayesian optimization face efficiency challenges as real-world BBO problems grow increasingly complex. Data-driven optimization has been the most popular paradigm to improve the efficiency of BBO, by learning from data. Offline data-driven optimization seeks high-quality solutions using only a fixed set of previous evaluations, attracting substantial attention because it requires no additional online evaluations. Many offline optimization methods have been proposed, but a fundamental question remains unanswered: what learnability is sufficient for offline optimization? Prior theoretical studies show that Probably Approximately Correct (PAC) learnability is insufficient, as the optimal region may remain poorly learned even when most regions are well learned. In this paper, we propose algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory. We prove that its value-query form is sufficient for representative discrete settings, including greedy and local search for submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization. Motivated by this notion, we formalize a trajectory-learning framework comprising trajectory construction, trajectory modeling, and candidate generation, and analyze existing trajectory-based methods under it. We further propose Uncertainty-aware Gradient-guided Trajectory Learning (UGTL), which constructs locally coherent improvement trajectories reflecting plausible search paths, models them with conditional diffusion, and selects a diverse candidate set. Our experiments show that UGTL achieves the best average rank, 3.1/25, among 25 methods on Design-Bench tasks, and confirm that our trajectory construction plays a significant role in the improvement.

Large-scale industrial robot fleets share constrained physical infrastructure, making vehicle travel times dependent on safety separation, intersection access, downstream blocking, and station contention. We study this problem in overhead hoist transport (OHT) systems, a representative ceiling-mounted material-handling system used in semiconductor fabs. Static shortest-path routing cannot account for these time-varying traffic costs, whereas tabular Q-routing adapts online but learns each destination--node--action value independently, limiting information sharing across sparsely visited routing contexts and making startup behavior sensitive to inaccurate value estimates. We propose Neural Double Q-routing, which replaces destination-indexed tables with a shared state--action value network. The network is warm-started through return-to-go regression on mixed simulator-generated routing trajectories and then refined online using Double-Q updates, local congestion correction, and event-stratified structured replay. Across nine matched fleet-size--arrival-rate settings with 100, 150, and 200 OHTs, the proposed framework reduces mean completion time relative to tabular Double Q-routing by $0.8\%$--$8.8\%$. It achieves the lowest mean completion time among all compared methods in the six 150- and 200-OHT settings, whereas Dijkstra remains best in the three 100-OHT settings. Completed-task counts remain within $1\%$ of tabular Double Q-routing in eight of nine settings, and 95th-percentile completion time decreases in eight settings. In two matched startup scenarios, offline initialization increases the number of completed tasks by up to $23\%$ and reduces tail completion time by up to $15\%$.

Contact-implicit trajectory optimization avoids prescribing contact sequences, but yields mathematical programs with complementarity constraints (MPCCs) whose degeneracy challenges conventional primal--dual solvers. Existing contact-specific methods improve robustness to this degeneracy but do not leverage a stagewise optimal-control factorization and primal--dual consistency, while structure-exploiting optimal-control solvers are not designed for complementarity constraints. We show that these capabilities can be combined in a single primal--dual method. ContactIPM identifies complementary inequality pairs, embeds them through a barrier-coupled elastic interior relaxation, eliminates slack and dual variables stagewise, and solves the reduced Newton system using a Riccati recursion. A fixed multi-phase MPCC recovery schedule provides four continuation and restart attempts from naive initializations, while termination is gated by the unrelaxed physical complementarity residual. We compare ContactIPM with two contact-specific MPCC solvers, CRISP and IMPACT, using matched benchmark conditions and common post-solve acceptance criteria. On four fixed CRISP benchmark cases, ContactIPM is $2.17$--$8.87\times$ faster over 20 paired timing repetitions per case and achieves higher success on the Push Box and Push-T robustness suites. Against IMPACT, ContactIPM is $2.96\times$ faster on Push T and $4.91\times$ faster on Cart Transport, but $4.46\times$ slower on Push Box. In 50 closed-loop Push Box rollouts spanning model mismatch, measurement noise, initial-pose errors, and state resets,

Autonomous mid-air docking of multi-rotor vehicles under disturbance-driven target motion poses a constrained non-linear trajectory optimization challenge. This work formulates the docking task as a finite-horizon optimal control problem based on a reduced-order nonlinear model augmented with disturbance states. The resulting problem is solved using sequential convex programming within a receding-horizon framework to generate dynamically feasible docking trajectories. State estimation with noisy measurements is incorporated to enable robust relative motion prediction, while trajectory execution is validated in a high-fidelity rigid-body MuJoCo simulation environment. The proposed framework is evaluated for stationary and constant-velocity target motions, demonstrating reliable convergence to the docking interface while satisfying geometric capture constraints. Quantitatively, the method maintains negligible docking-cone violations and terminal state errors within prescribed tolerances, and achieves consistent, safe docking performance for cone half-angles as low as 10 degrees. Robust operation is observed for wind disturbance levels up to a standard deviation of 0.5, while preserving bounded approach velocities and stable control effort. These results demonstrate the effectiveness of the SCP-based trajectory optimization framework for disturbance-robust aerial docking under estimation uncertainty.

Humanoid locomotion in highly confined environments requires navigating dense environmental obstacles and complex self-collision bounds while maintaining multi-contact dynamic feasibility. Traditional trajectory optimizers frequently struggle in these restricted spaces, as navigating the large collision space with splines on particle abstractions is insufficient and leads to poor local minima. To address this, we propose a three-stage whole-body planning framework that formulates kinematic path planning directly over kinematically reachable rigid-body volumes. By integrating differentiable collision avoidance into a reachability-constrained formulation, our framework synthesizes volume-informed guides that reliably guide a full-order trajectory optimizer over long horizons. We show that these optimized plans serve as high-quality references to train a residual reinforcement learning policy for robust online execution. We validate our approach on the Unitree G1 humanoid across three benchmark testbeds exceeding NIST emergency response standards, achieving restricted confinement ratios ($C_r < 1.5$). Our framework generates feasible trajectories across 12-to-18-second tasks with complex foot and hand contacts where standard baselines fail, while the learned policy successfully tracks these plans under extensive domain randomization in physics simulation.

Safe reinforcement learning maximizes reward subject to safety constraints. For Constrained Markov Decision Processes, the linear-programming view over occupancy measures implies that whenever the constraint is active at optimality, the optimal policy lies exactly on the constraint boundary, yet standard gradient-based methods do not exploit this structure and often settle in the feasible interior. We introduce Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side; the combined direction admits an algebraic Lagrangian form with an induced coefficient and no learned dual variable. Under exact gradients and stated regularity conditions, the constraint residual converges to zero from either side with a finite-horizon $O(1/\sqrt{T})$ bound, the tangential component is a reward-ascent direction on the boundary, and any convergent parameter sequence is stationary on the active constraint set, satisfying the KKT conditions when the limit is also a local maximizer over the feasible set. This complements existing analyses, which certify feasibility but do not characterize the constraint value at convergence. On a standard Safety-Gymnasium navigation task, BSPG attains higher reward while tracking the boundary more tightly than the compared baselines.

Collision avoidance systems are commonly used to avoid fragmentation events occurring in Low-Earth Orbit (LEO) and Geosynchronous Equatorial Orbit (GEO). However, these events have been growing in frequency as orbital congestion worsens with the launch of megaconstellations. Consequently, conjunction alerts and collision risks are becoming increasingly common. Current practices, which are commonly manual or rule-based, have difficulty scaling to these worsening dynamic environments. To address this intensifying situation, we propose a reinforcement-learning policy for autonomous collision avoidance, trained via Proximal Policy Optimization (PPO) along with an open-source, high-fidelity astrodynamics simulator for training and evaluation. In 1,000 deterministic GEO episodes, our agent achieves a 97.5% collision avoidance success rate, outperforming traditional controllers such as a rule-based baseline (20.7% success) and an impulsive delta-v planner baseline (27.5% success). To achieve these results, we designed a simulator to train and evaluate our agent, using real-world and simulated debris. We simulate Newtonian two-body dynamics using Sun/Moon third-body perturbations, fuel-dependent thrust, and configurable debris fields. The agent is trained with curriculum learning and shaped rewards oriented toward encouraging survival, adequate projected miss distance, and delta-v conservation. Finally, our evaluation consisted of a fully deterministic pipeline, including shared seeds, per-episode logs, and telemetry exports. Our work is a publicly available framework at https://purl.org/sat-trajectory-avoidance

Operational Design Domain (ODD) specifications describe where an automated driving system (ADS) is permitted to operate, but they do not prescribe what the ADS must demonstrably do once deployed within that domain. This gap between operating condition specification and behavioral validation represents a critical unresolved challenge in ADS safety assurance. This paper presents a structured, standards-grounded taxonomy of 21 behavioral competencies organized across three operational domains-Highway (HWY), Urban (URB), and Hub (HUB)-derived systematically from the PEGASUS six-layer model-based ODD. Each behavior is decomposed along longitudinal and lateral control axes and characterized against a four-property framework: Safety (gap maintenance, conflict avoidance, kinematic stability), Compliance (legal rules and behavioral norms), Comfort (rider dynamics and trust), and Efficiency (mission completion and product-level metrics). We further demonstrate that the crossing of ODD layer parameterizations with behavioral competency specifications yields concrete scenario families suitable for systematic behavioral testing and SOTIF coverage evidence. The taxonomy is grounded in AVSC00008202111, SAE J3237, and SAE J3016, and is validated as an operational specification layer through its deployment in a rule-enforced trajectory optimization system. The Hub domain is identified as a structurally distinct, underspecified domain warranting dedicated research attention.

This paper presents a scalable lateral control framework for robust path tracking of single-body and articulated autonomous vehicles at high speeds. A clothoid-based controller is extended with three key adaptations: 1) an integrated tangential check and Frechet distance method for optimized lookahead and oscillation mitigation; 2) real-time trajectory segment classification for dynamic adjustment of the lookahead search range; and 3) a dual-adaptive, rate-controlled lookahead mechanism responsive to cross-track error and upcoming path geometry. To support different vehicle configurations, the framework also incorporates flexible tracking point selection and curvature-to-steering lookup tables, enabling control of points such as the tractor rear axle, hitch point, or trailer-related locations without changing the core control architecture. The controller is evaluated using high-fidelity TruckSim and Simulink simulations for both standalone and articulated vehicles across dual lane changes and winding-road scenarios. Results demonstrate stable high-speed path tracking, reduced oscillations, effective lookahead adaptation, low cross-track errors, and acceptable lateral acceleration across different vehicle configurations. The results support the use of a unified lateral control architecture that can scale from single-body to articulated autonomous vehicles.

The growing deployment of delay-tolerant networks (DTNs) has made store-carry-forward (SCF) communication indispensable under sparse connectivity. However, intermittent contacts, finite buffers, and limited message time-to-live (TTL) often give rise to sparse delivery and congestion, leading to substantial end-to-end performance degradation. To address this challenge, this study explores the joint optimization of decentralized opportunistic routing and controllable unmanned aerial vehicle (UAV) flight, aiming to enlarge future contacts through discrete UAV headings while enabling per-node replication under contact-limited observations. Building upon this architecture, we study cooperative factored routing--UAV control under centralized training and decentralized execution (CTDE) and propose JUROR (Joint UAV flight and Opportunistic Routing, based on the proximal policy optimization (PPO) framework. In our design, we first cast the problem as a factored partially observable Markov decision process with sequential motion--routing coupling and a per-step team reward; subsequently, decentralized actors act on local observations while a training-time critic uses global statistics, and an optional multi-horizon hotspot predictor provides auxiliary supervision. Simulation results over four traffic modes demonstrate effective gains over PRoPHET and MaxProp, while retaining contact-limited decentralized execution.

Incentivized advertising allocates monetary or virtual rewards to drive user engagement, where a key challenge is optimizing continuous incentive magnitudes under strict global constraints. This problem is complicated by high-frequency interactions, delayed feedback, and non-Markovian user dynamics such as fatigue, which limit the effectiveness of existing uplift modeling and constrained reinforcement learning approaches. To address these challenges, we propose GOAL, a constraint-aware generative framework that formulates incentive allocation as a conditional sequence generation problem. GOAL directly generates incentive magnitudes conditioned on user histories and system-level global pressure, and integrates a hierarchical causal state encoder to capture both local behavioral dynamics and long-range dependencies. To enable flexible constraint control, we introduce \textbf{S}afe \textbf{C}onstrained \textbf{P}olicy \textbf{O}ptimization (SCPO), which learns a single generative policy that generalizes across a spectrum of ROI constraints without retraining. Experiments on large-scale real-world data and a synthetic fatigue-aware environment show that GOAL improves long-term revenue and user retention while substantially reducing ROI violation rates compared to strong baselines.

Stochastic single shooting trajectory optimization methods such as Model Predictive Path Integral control (MPPI) have been widely adopted in robotics due to their ability to reason about probabilistic dynamics and provide solutions where model gradients are noisy, costly to evaluate, or unavailable. However, satisfaction of terminal constraints when shooting over long action sequences is often sample inefficient, requiring a large number of iterations for convergence. In this paper, we present a stochastic multiple shooting method that optimizes short control action sequences connected via local feedback policies to improve sample efficiency and convergence to a terminal set. Additionally, we show that we are able to synthesize approximate system Jacobians purely from rollouts, making the method suitable for model-based reinforcement learning with black-box dynamics. We demonstrate the algorithm has improved sample efficiency and terminal set convergence for three nonlinear, underactuated optimization problems: a classic cartpole swingup task with analytical dynamics, a cartpole swingup task with learned neural network dynamics, and a VTOL quadplane performing a high angle-of-attack, precision post-stall landing maneuver.

Existing active reconstruction systems with Gaussian-splatting maps select observations greedily, optimizing a single next-best-view (NBV) at each step and connecting the chosen views by short-horizon path planning. This greedy decoupling disregards the global structure of scene information, producing inefficient trajectories that waste sensing capacity in transit between selected views. In this work, we study active reconstruction as an ergodic coverage problem: the time-averaged spatial statistics of the sensor trajectory should match a target information distribution induced by the current map. Our approach derives this target distribution online from uncertainty and visibility, and calculates ergodic trajectories via a kernel-ergodic horizon planner with gradient flow and footprint depletion, closing the loop between mapping and trajectory optimization. We thoroughly evaluate TRACE on the Replica dataset against the Next-Best-View (NBV) baselines, improving PSNR by 1.5 dB. Code: https://github.com/spikelab-jhu/trace-active-reconstruction.

Evaluating Multi-Agent Reinforcement Learning (MARL) policies in autonomous driving fundamentally relies on extrinsic statistical indicators (e.g., reward curves and success rates), which often mask intrinsic policy degradation and algorithmic blind spots. To break this black-box evaluation, this letter proposes a novel information-theoretic diagnostic framework. By leveraging a fully converged Monte Carlo Tree Search (MCTS) as an asymptotic oracle, we establish a theoretical ground-truth baseline distribution. We formulate a bounded policy optimality score ($\mathcal{M}_{opt}$) using the forward KL divergence to rigorously penalize fatal collaborative omissions. Crucially, we semantically decouple this metric into lateral and longitudinal dimensions, creating a granular "semantic microscope". Extensive spatial and temporal diagnostics on state-of-the-art MARL architectures and exploration mechanisms demonstrate that our framework conclusively exposes hidden directional biases, identifies temporal average-policy traps, and transforms heuristic hyperparameter tuning into a visually trackable trajectory optimization. This framework establishes a rigorous, model-agnostic standard for benchmarking intrinsic multi-agent policy quality.

A broad range of models face the mismatch where they are updated through trajectory losses but are evaluated by downstream task reward. Here, a trajectory is a training instance that induces a surrogate loss whose reduction might not track the model's decision utility update. Theoretically, we ask when one step of trajectory training reduces both population surrogate loss and decision risk, and how transfer accumulates along repeated updates. To formalize this, we first fix a checkpoint and a restricted update space, and define the reductions in population surrogate risk and decision risk induced by a trajectory as its learnability and decision utility, respectively. On this basis, our theory yields four main results. First, a one-step transfer bound separates their discrepancy into first-order gradient misalignment after nonnegative calibration and second-order curvature; and a pathwise extension accumulates the same terms over repeated updates. Second, when the accessible surrogate gradient is nonzero, universal first-order transfer over every accessible direction holds exactly when the accessible surrogate and decision gradients are positively collinear. Third, the calibration gap bounds the decision regret of learnability-based trajectory selection, while a candidate-difference refinement tightens this guarantee by retaining only directions that affect pairwise rankings. Finally, we establish an approximation--calibration trade-off across nested update spaces. Controlled gridworld and LLM post-training experiments yield results consistent with our predictions.

Mixed complementarity problems (MCPs) arise as the first-order optimality conditions of nonlinear programs and noncooperative games, and provide a natural formulation for multi-agent trajectory optimization problems that appear throughout robotics. The dominant solver for problems of this form is PATH, which offers strong performance on robotics problems but remains closed-source. We present MixedComplementarityProblems.jl, an open-source, pure Julia implementation of an interior point method for parametric MCPs that: (i) matches PATH's reliability on standard benchmarks, (ii) natively supports batched, parallel processing of many parameter instances, either across CPU threads or on an NVIDIA GPU, and (iii) supports efficient automatic differentiation of solutions with respect to problem parameters. On a multi-agent lane-change trajectory game representative of robotics planning problems, our CPU-multithreaded batched solver clears a batch of parametric instances ~100x faster than sequential calls to PATH. A GPU backend, running the same solver implementation unmodified, also clears these batches far faster than PATH, but does not outperform the multithreaded CPU on this problem; the GPU pulls ahead only once each per-instance KKT system grows large, and we characterize this regime dependence. We describe the solver's interior point formulation, the abstraction that lets a single solver implementation run unmodified across dense, batched-sparse, and single-large linear-algebra backends, and report benchmarks against PATH on both randomly generated quadratic programs and trajectory games.

Satellite constellations require orbital transfers that are both fuel efficient and collision avoidant. Yet, the computational cost of optimization methods traditionally used to plan their trajectories scales poorly with both the number of satellites as well as the number of obstacles to avoid, due to the pairwise safety constraints. In this work, we introduce a permutation-equivariant neural operator for trajectory planning of spacecraft swarms. This neural operator maps distributions of spacecraft initial states, target states, and obstacle initial states to trajectories which avoid collision and conserve fuel. This neural operator output is then paired with a batched Gauss-Newton finish to enforce exact orbital dynamics, and further reduce fuel use. The operator is self-supervised, trained without optimal trajectory labels. When trained on ten spacecraft, the proposed method generalized zero-shot to swarms of 1,000 spacecraft and 11,000 obstacles. The generated trajectories matched a per-agent optimal control solver's accuracy while retaining collision avoidance. Operator learning grounded in physics may offer a fast, scalable alternative to trajectory optimization in the increasingly crowded orbits of the future.

In Formula 1, drivers optimize racing lines within tire grip limits to minimize lap times; however, in rally racing, drivers intentionally break traction to drift on loose surfaces. This maneuver rapidly aligns the vehicle for corner exits, ultimately reducing lap time. Autonomously executing such maneuvers formulates a complex dual-objective control problem: stabilizing highly nonlinear drift dynamics while strictly minimizing lap time. Addressing this challenge motivates the development of advanced Minimum-Lap-Time (MLT) drift control architectures. This paper proposes a planning-control framework specifically designed for MLT drifting scenario. First, we formulate an optimal control problem to generate a MLT drift planning trajectory, which is used as prior data to train a deep reinforcement learning drift controller. Given that drifting involves extremely large sideslip angles and is therefore challenging to learn directly, a Track-guided Reinforcement Learning (TgRL) drift control method is proposed to enable progressive training in a step-by-step manner, from drift control policy, to drift corner policy, and finally to a comprehensive drift race policy. The reward function incorporates both an instant reward term and an end reward term derived from the Minimum-Lap-Time objective. Simulation results demonstrate that the proposed framework enables the agent to learn a drift racing policy that not only ensures vehicle motion control performance but also effectively reduces lap time.

Robust Optimization Over Time (ROOT) is a recent branch of evolutionary dynamic optimization that seeks solutions capable of remaining effective across multiple consecutive environments. Unlike the traditional track-the-moving-optimum (TMO) paradigm, which reoptimizes after every environmental change, ROOT explicitly values persistence. Although the field has grown considerably, most contributions remain algorithmic and empirical, leaving several fundamental properties poorly understood from a theoretical perspective. One such property is survival time, defined as the number of future environments in which a deployed solution continues to satisfy a prescribed quality threshold. While survival time is widely used as a measure of temporal robustness, little is known about how its expected value depends on environmental dynamics, deployment quality, or problem characteristics. This paper studies expected survival time for a fixed deployed solution under isotropic Gaussian environmental dynamics. Modeling survival as a discrete first-exit problem, we derive a rigorous lower bound and a computable multi-step upper bound. The analysis shows that expected survival scales as $Θ(σ^-{2})$ in slowly varying environments and approaches its minimum value of one future change in high dimensions. A comprehensive Monte Carlo study validates the theoretical predictions, examines sensitivity to modeling assumptions and parameter uncertainty, and illustrates how the bounds can support deployment decisions after optimization. The resulting framework provides an analytical characterization of deployment lifetime and identifies when a required deployment horizon can be guaranteed, ruled out, or remains analytically unresolved.

Differentiable simulation can accelerate contact-rich trajectory optimisation by exposing local sensitivities of task outcomes to controls. Existing approaches either use finite differences, which are expensive and step-size sensitive; differentiate iterative contact solvers by unrolling automatic differentiation (AD), which stores a growing computation trace; or require intricate, solver-specific KKT sensitivity derivations. We introduce an AD-assisted implicit derivative for regularised smooth contacts and apply it to Mujoco MJX, based on the Implicit Function Theorem (IFT). The method differentiates the stationarity residual at the tolerance-converged solution, avoiding both solver unrolling and hand-assembled KKT systems. IFT keeps compiled temporary memory nearly constant with solver effort, changing by less than 4$\%$ from one to ten iterations versus 10.6$\times$ growth for unrolled AD. IFT memory grows slower with active contacts and model dimension, using 20$\times$ less memory at 256 contacts and 6$\times$ less at 16 contacts and 96 DoF. We further introduce optimiser distillation for residual MPC, amortising batched full-horizon iLQR into a policy that guides short-horizon residual iLQR. Across Finger, Franka, and Unitree, this raises six-step success by 28-98 percentage points over standard iLQR.

Low-thrust trajectory optimization is a core technology in deep-space mission design. Indirect methods based on Pontryagin's Minimum Principle (PMP) offer rigorous optimality guarantees, yet their practical application faces three bottlenecks: (1) transversality conditions must be derived case by case for each constraint type; (2) different dynamics models require repeated code rewrites; and (3) shooting equations are highly sensitive to initial guesses. This paper presents HELIOS (Heuristic Engine for Low-thrust Interplanetary Optimization System), a trajectory optimization agent built around a large language model (LLM). Given a physical problem described in natural language, the system autonomously performs PMP symbolic derivation, SymPy verification, C++ shooting-code generation, and numerical solution without human intervention. Key innovations include: (1) a constraint-adaptive derivation framework that unifies arbitrary constraints into psi(x,p)=0 form and automatically generates stationarity conditions for free parameters (e.g., gravity-assist turning angle); (2) dynamics-adaptive four-module code generation supporting non-standard dynamics (solar sail, J2 perturbation) without modifying the underlying template; and (3) a general derivation rule set covering critical error-prone points in PMP derivation. Experiments on 11 progressive test scenarios show that HELIOS correctly derives and solves problems from simple rendezvous (8 variables) to multi-leg stay transfers (48 variables), gravity-assist trajectories (17 variables), and solar-sail minimum-time transfers (8 variables). The best compilation success rate reaches 100% (11/11). A multi-model comparison (8 open-source LLM backends, total scores 250-905) verifies the model-agnostic architecture and reveals a positive correlation between model scale and derivation capability.

Autonomous laboratories automate experimental execution, but a campaign must also decide which recovery pathway merits optimization. We formulate this as a sequential decision problem with a discrete pathway-identification stage and a continuous within-pathway optimization stage under heterogeneous experimental costs. Our implementation, Coactive learning, combines a cost-sensitive Bayesian hypothesis-discrimination policy motivated by EC2 (Golovin et al., 2010) with Gaussian-process Bayesian optimization (Srinivas et al., 2010). Under explicitly stated assumptions, the expected spend of one fixed-budget campaign attempt is bounded by the expected pathway-identification cost plus the capped within-pathway optimization budget. We evaluate the method on synthetic benchmarks constrained by selected results reported for PNNL's CICERO selective-precipitation study (Ritchhart et al., 2026). The method performs comparably to an oracle-pathway Bayesian-optimization reference and to a strong split-plate baseline that discriminates pathways with its first plate, without receiving an oracle label for the correct pathway. It is given a candidate hypothesis space and a diagnostic likelihood model. On an NdFeB-inspired instance, it avoids the simulated penalty of a commit-first baseline that initially selects a plausible but inferior hydroxide pathway. This hypothetical wrong-first-commitment scenario is motivated by the hydroxide-oxalate performance contrast reported by CICERO. We characterize the sensitivity of these conclusions to the assumed cost model. The code and benchmark are open source.

Expensive constrained optimization problems in real-world industry design often involve constraint thresholds that are difficult to determine in advance. Engineers may need to adjust constraint thresholds to explore different feasibility-performance trade-offs, requiring solutions under a wide range of threshold settings. However, existing constrained Bayesian optimization methods treat each threshold configuration independently, leading to repeated optimization and failing to exploit the shared relationship among continuously varying thresholds. To address this challenge, we propose constraint-bound agnostic Bayesian optimization (CBA-BO), a learning-based framework that learns a parametric constraint model mapping thresholds to optimal solutions. Once learned, CBA-BO directly predicts solutions for arbitrary unseen threshold configurations without additional optimization, with a one-step Bayesian optimization refinement further improving solution quality. Experiments on benchmark and engineering problems demonstrate that CBA-BO learns a transferable threshold-solution mapping, enabling efficient prediction and optimization for arbitrary threshold queries. An intent-guided constraint-bound recommendation mechanism is further developed to improve objective performance while satisfying user-specified constraint preferences.

LLM coding agents operate by constructing trajectories that accumulate reasoning, tool calls, and results to enable multi-step decision-making. However, the conventional append-only trajectory architecture found in practice tightly couples file-read actions with their observations, capturing snapshots that become permanently fixed in the chronological history. As files change through agent edits or concurrent human modifications, these snapshots become stale, causing reasoning errors and causing agents to redundantly re-read files, with each re-read appending yet another copy to the trajectory. To mitigate this, we propose CORVUS, a novel trajectory architecture that decouples file-read actions from their observations by maintaining a synchronized registry of relevant files and injecting only their current contents at each reasoning cycle. This structural change produces significantly lighter-weight trajectories that remain synchronized with the actual codebase state by construction, eliminating redundant file copies and stale snapshots that bloat conventional trajectories. We evaluated CORVUS on SWE- POLYBENCH_VERIFIED and SWE-BENCH PRO across four LLMs, achieving 9-50% reduction in average input tokens per task, 15-32% shorter final prompts, and up to 37% fewer reasoning cycles while maintaining comparable pass rates.

Coding agents are increasingly used to accelerate code generation in many downstream tasks, such as fixing bugs, building applications, and prototyping. However, despite their value as coding assistants, agent-generated code tends to be larger and more verbose than the corresponding human-written implementation. In this work, we show that the cause lies in the agent's own search process: while iterating toward a passing solution, an agent accumulates speculative edits, abandoned hypotheses, and temporary changes that persist into the final patch. This may seem harmless for a single patch, but the problem compounds as agents take responsibility for ever-larger portions of a codebase-a codebase that was once minimal and well-maintained slowly accumulates redundancy faster than it can be cleaned up, drifting to a state that is harder to maintain. Given the magnitude of this problem, we take a step towards alleviating this issue. First, we formally define this phenomenon as CodeSlop-the residual and functionally unnecessary edits commonly seen in AI-generated code. We then introduce our algorithm TRIM (Trajectory-guided Redundancy Identification and Minimization). Rather than minimizing CodeSlop directly, TRIM instead minimizes agent trajectories. As we show empirically, this indirect technique of minimizing CodeSlop is highly effective: TRIM cuts CodeSlop by 17.9%-32.9% across agentic scaffolds, with negligible performance regression. TRIM is also highly efficient, requiring roughly half the validation cost of algorithmic baselines such as Delta Debugging.

Efficient, collision-free, and time-optimal motion planning is a fundamental requirement for autonomous forestry cranes operating under hydraulic pump-flow constraints. The Via-Point-based Stochastic Trajectory Optimization (VP-STO) algorithm has demonstrated near-time-optimal hybrid motion planning in this domain, but requires a fixed terminal joint configuration specified prior to optimization. For kinematically redundant manipulators such as forestry cranes, this pre-commitment to a single inverse kinematics solution restricts the planner's ability to exploit redundancy, particularly under the nonlinear, globally coupled pump-flow constraint where admissible joint velocities depend on their combined hydraulic demand. This paper presents TSC-VP-STO, a task-space-constrained extension of VP-STO that replaces the strict terminal joint-space constraint with a task-space constraint, jointly optimizing the trajectory and the redundant degrees of freedom of the terminal configuration. This enables the planner to adapt end configurations to the environment-dependent motion and hydraulic flow allocation, yielding more balanced pump utilization and shorter trajectory durations. We formalize the approach through a configuration space decomposition and derive a concrete reachability constraint for the forestry crane kinematics. Experimental evaluations across multiple planning targets and via-point configurations demonstrates a reduction on trajectory durations by 12-15% on average and improved pump-flow utilization compared to the baseline VP-STO. The practical applicability of TSC-VP-STO is validated through real-world deployment on a forestry crane, including a full log-loading cycle.

This paper introduces the Dynamical Vehicle Orienteering Problem (DVOP), a generalization of the Orienteering Problem (OP). The OP maximizes the reward collected from spatial targets under a limited travel budget; the DVOP extends it by accounting for both external and vehicle-actuated forces. We study the DVOP in the context of multi-rotor Unmanned Aerial Vehicle (UAV) flight planning, using a three-dimensional Point-Mass Model (PMM) constrained by maximum velocity and acceleration magnitudes and subject to gravitational acceleration, with the travel budget expressed as a maximum flight time. Because the DVOP couples reward maximization with time-optimal trajectory planning, it cannot be formulated as a simple graph problem and solved exactly without relaxing or under-actuating the vehicle dynamics. We therefore propose two solution approaches: a Branch-and-Bound (BnB) procedure that combines Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP) to provide high-quality solutions, and a Large Neighborhood Search (LNS) metaheuristic that supplies an initial reward bound and scales to instances intractable for the BnB. The BnB relies on a novel MILP formulation of travel costs based on minimum-time trajectory primitives through target triplets, yielding a tight reward upper bound, while the LNS uses limited thrust decomposition to compute fast, high-quality PMM trajectories. Experiments on benchmark instances show improvements of up to 37 % over state-of-the-art solutions for the Kinematic Orienteering Problem, and a real-world deployment on a multi-rotor UAV verifies the proposed PMM solution trajectories.

Autonomous racing overtaking requires balancing competitive performance with safety under nonlinear vehicle dynamics and real-time constraints. Model Predictive Control (MPC) combined with Control Barrier Functions (CBFs) provides a principled mechanism for certifying forward invariance of a safe set. However, commonly used fixed-decay discrete-time CBF formulations can become overly conservative in interactive racing scenarios, limiting overtaking performance and requiring manual tuning across track conditions. This paper proposes a hierarchical overtaking framework that explicitly separates maneuver-level decision making from safety-certified trajectory control, reducing conservatism while preserving safety. A high-level Mixed-Integer Quadratic Program (MIQP) resolves the combinatorial passing-side selection problem by selecting a feasible overtaking topology, while a nonlinear Frenet-frame MPC enforces vehicle dynamics and safety through embedded discrete-time CBF constraints. This decomposition isolates the combinatorial complexity of maneuver selection from the continuous trajectory optimization. To further mitigate the sensitivity of fixed-decay barrier constraints, a reinforcement learning policy adapts the discrete-time CBF decay parameter online, enabling context-dependent modulation of safety margins without directly controlling vehicle inputs. Simulation and scaled-hardware experiments show that no single fixed decay parameter achieves uniformly strong performance across tracks, whereas the adaptive strategy attains the highest aggregate success rate and consistently strong safety--performance trade-offs without per-track tuning, improving robustness to environment variation while maintaining safety constraint satisfaction in nominal operation.

Modern robotic perception increasingly involves large-scale geometric optimization problems distributed across multiple robots or sessions. However, existing distributed solvers often depend on brittle hand tuning and primarily target rigid body pose graphs. To address this, we present DeepCORD, a learning-augmented framework for distributed factor graph optimization on general matrix Lie groups. By unfolding a parallel and accelerated Riemannian optimizer into differentiable iterations, DeepCORD learns a self-supervised feedback policy that dynamically adapts solver parameters according to the optimization phase and communication status. The resulting method enables adaptive distributed optimization over matrix Lie groups under both synchronous and asynchronous communication regimes. Extensive experiments on real-world $\mathrm{SE}$(3) pose graph optimization and $\mathrm{SL}$(4) projective submap alignment show that our method achieves lower objective values than existing distributed baselines on most benchmarks across realistic operating scenarios.

Engineering shape optimization faces challenges in both expert-dependent problem setup and surrogate-model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers, while surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape-optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization. We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty-estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment. Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of $1.16\%$ and a trend-prediction accuracy of $94.34\%$, outperforming the best baseline results of $1.52\%$ and $90.34\%$, respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately $4\%$ to $10\%$.

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.

Safe multi-arm motion planning is a challenging problem in robotics due to its high dimensionality, coupled configuration space, and complex collision constraints. Centralized planners are capable of coordinating all arms but often face scalability limitations, restricting applicability in real-time settings. On the other hand, decentralized methods are scalable and recent deep learning-based approaches have shown promising results. However, these depend on accurate behavior prediction or coordination protocols and may fail when other arms act unpredictably. To address these challenges, we introduce a neural Hamilton-Jacobi Reachability (HJR) learning-based approach to approximate a safety value function that captures worst-case inter-arm safety constraints. We further develop a decentralized trajectory optimization framework that uses the learned HJR representation for real-time planning. The proposed method is scalable and data-efficient, generalizes across multi-manipulator systems, and outperforms state-of-the-art baselines on challenging multi-arm motion planning tasks.

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.

Quadrotors offer the agility needed to rapidly transport suspended payloads during time-critical applications, including search-and-rescue and medical delivery. While suspended-payload transport and traversal for these missions are well studied, the highly dynamic targeted release of the payload remains comparatively underexplored. State-of-the-art approaches typically rely on model-based trajectory optimization and tracking; however, these methods often yield sub-optimal performance due to conservative feasibility constraints, tracking errors, and the inherent difficulty of analytically modeling flexible rope dynamics. To overcome these limitations, we propose a hybrid simulation framework that couples a high-fidelity analytical quadrotor model with a physics solver for complex rope and payload interactions. By exchanging forces between the two domains at every step, we obtain a physically accurate simulation of the suspended-payload system. Leveraging this environment, we train a deep reinforcement learning (RL) policy that executes agile, accurate payload throws to designated targets. Deployed zero-shot on hardware, our RL policy pushes the boundary of the agility-accuracy trade-off, outperforming the model-based baseline by reducing the landing error by up to 50% and the throw duration by up to 30%. Ablation studies confirm that the coupled simulation is the key enabler of these gains. We further show that the same pipeline trains a policy driven by visual observations rather than an explicit state estimate, achieving accuracy comparable to that of the state-based policy. To accelerate future research in dynamic aerial manipulation, we open-source the simulator to the community upon acceptance.

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 \texttt{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 \textit{heterogeneous iteration fusion}, and by minimizing GPU idle time with \textit{iteration level batching}. We evaluate \texttt{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.

We present a general answer set programming based hybrid quantitative-qualitative method for computing constrained branching trajectory modes for moving objects in real-world settings. The method performs constrained traversal of an environment graph, enumerating geometrically admissible motion behaviours as stable models, each constituting a distinct trajectory mode characterised by both domain-dependent and independent factors such as derived event sequence, map topology, and domain norms. The hybrid trajectory computation method is generally applicable across motion characteristics typically encountered in diverse dynamic domains with moving objects, e.g., autonomous driving. We demonstrate applicability and highlight how computed trajectories are traceable to their underlying stable model, thereby affording verifiable interpretability that purely learned approaches cannot provide. We also perform an empirical evaluation with Argoverse 2, a large-scale real-world autonomous driving benchmark representative of the class of dynamic domains within the scope of the proposed method.

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.

Time-series deployments often need delayed feasible decisions, not only accurate forecasts. UC-Search is a trace-only retained-search layer for delayed constrained control: a frozen backbone emits forecasts or action scores, a hard-feasibility automaton rolls paths forward, and bounded search returns the first action of a feasible trajectory. The main claim is conditional: retained lookahead can improve delayed constrained decisions only when delayed feasible-set coupling, retained-prefix premises, and fail-closed release certificates hold. The promoted public endpoint is Phase128 certified M4 expanded40: validation selects Certificate-Constrained Retained Pareto Beam with $λ=0.25$, the held-out test has certificate/risk-active rates $1.0000/0.9642$, and the weakest family remains above the unchanged $0.95$ gate at $0.9516$ on M4Weekly. The author-defined public $9$-family suite remains an uncertified stress-test boundary. The paper reports a trace-only mechanism, one certified public endpoint, failed-route certificates, and deployment boundaries rather than a universal risk-control theorem.

Behavioral Foundation Models (BFMs) offer a promising path toward universal physics-based character control by organizing a rich repertoire of physically plausible behaviors into a latent space, guided by a large-scale motion dataset. While these models excel at time-invariant tasks, such as goal-reaching and state-based reward optimization, their latent space does not directly support time-varying objectives, such as tracking a motion sequence. For tracking, existing heuristics rely on moving-window-averaging that fails to capture the nuances of highly dynamic motions. In this work, we propose a novel Latent Sequence Optimization (LSO) to address these shortcomings. Our approach combines simulation rollouts with a policy gradient update to optimize over a sequence of latents, extending the capabilities of BFMs toward precise motion tracking without requiring reward engineering and tuning. To guide the optimization toward smooth, coherent latent trajectories, we model the latent sequence using temporally correlated noise. We validate our approach across dense tracking, sparse keyframing, and direct deployment onto a real humanoid robot.

Reinforcement Learning with Verifiable Rewards (RLVR) for language-model reasoning can fail at both extremes of task difficulty: easy prompts often produce all-correct, low-diversity rollout groups with little gradient signal, while hard prompts can produce all-incorrect groups with no positive reward. We introduce ExTra (Exploratory Trajectory Optimization), a GRPO-compatible framework that extracts exploration signals from the model's own rollouts. ExTra combines two mechanisms: (i) a novelty reward that adds embedding-based diversity bonuses after GRPO normalization, rewarding diverse correct solutions; and (ii) entropy-guided prefix regeneration, which scores partial trajectories using entropy signals and continues exploration from promising intermediate steps. Across six mathematical reasoning benchmarks, ExTra improves Qwen3-1.7B over GRPO by about +5 points on pass@1 and +7 points on pass@16, showing that trajectory-level exploration signals can improve both single-sample accuracy and inference-time coverage.

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.

Spacecraft operations scheduling is a highly constrained, long-horizon combinatorial optimization problem that traditionally relies on heuristics, constraint programming, or manual planning. We present a scalable deep reinforcement learning framework developed and deployed for NASA's Carruthers Geocorona Observatory mission. Our framework introduces a macro-action abstraction known as activity blocks coupled with dynamic action-masking to navigate the intractably large search space and strictly enforce complex power, thermal, and instrument constraints. The resulting architecture generates globally feasible schedules with overwhelming probability, establishes operational trust, and executes a full training cycle in under six hours, circumventing the need for policy robustness by enabling rapid, on-demand retraining. Further, resulting schedules outperform baseline heuristics in scheduled science quality. The deep reinforcement learning framework was deployed as the default operational scheduler for the Carruthers Geocorona Observatory mission from the outset of the mission, demonstrating that deep reinforcement learning can be trusted for real spacecraft operations under complex, evolving constraints.

Lunar micro-rovers under 50 kg are a rapidly growing vehicle class, yet open, benchmarked tools for running optimization across design trades remain scarce. Rover sizing is a highly coupled problem with a feedback loop specific to surface vehicles: a heavier rover sinks deeper into loose regolith, deeper sinkage costs more power, more power requires a larger array, and the array adds mass. We present RoverDevKit, a tradespace exploration toolkit with an open evaluator that couples a closed-form wheel-soil model with bottom-up mass, solar-power, thermal-survival, and traverse models. It is fast enough to serve as the fitness function of a multi-objective genetic algorithm (NSGA-II): one search of 3000 mission evaluations takes under a minute on a single laptop core. We use it to map the trades among distance traveled, vehicle mass, and slope capability on mare, polar, highland, and crater-rim missions. Across those missions the limiting factor changes: energy storage at high latitude, slope traction on loose highland regolith, and traverse range on mare and crater-rim terrain. The wheel-soil model matches measured single-wheel drawbar pull on two independent datasets to within the 20-30% error typically reported for this class of model, and the mass model predicts published 5-50 kg rover masses to 10.5% median absolute error. A check against five published in-class designs places them near the designs the optimizer selects. Re-running the search after applying that wheel-soil comparison error leaves these conclusions unchanged.

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.

Autonomous robots operating in uncertain environments must satisfy complex temporal and safety specifications despite stochastic dynamics and sensing noise. While Signal Temporal Logic (STL) offers robustness measures for gradient-based optimization, existing extensions either lack differentiability or ignore belief-space uncertainty. We introduce pdSTL (probabilistic differentiable Signal Temporal Logic), a framework that unifies probabilistic semantics with differentiable robustness over belief trajectories. pdSTL employs interval-valued probabilistic semantics to compute conservative satisfaction bounds, propagated compositionally through the STL syntax tree. We formulate the temporal robustness evaluation as a recurrent, LSTM-style unfolding of STL operators, enabling linear-time, differentiable monitoring suitable for end-to-end trajectory optimization. We validate pdSTL on simulated obstacle avoidance, lane-change maneuvers, and real-world Crazyflie quadcopter flight experiments under aerodynamic disturbances. Results demonstrate that pdSTL achieves efficient optimization with formal probabilistic guarantees, significantly outperforming deterministic differentiable STL in maintaining safety margins under real-world uncertainty.

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/

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 resulting formulation remains well posed under ill-conditioning and degeneracy, supports warm starting, and converges to closest-to-feasible solutions when no feasible point exists. A lightweight refinement stage recovers physically meaningful dual variables from the elastic solution. Building on this framework, we develop Elastic OdynLayer, a differentiable QP layer with stable gradients under infeasibility, and Elastic OdynSQP, an infeasibility-aware SQP method that resolves inconsistent subproblems and intrinsically infeasible optimal control tasks through selective constraint relaxation. We evaluate the framework on benchmark QPs, singular contact mechanics, differentiable parameter identification, and quadrupedal and humanoid trajectory optimization. Across all settings, Elastic ODYN consistently outperforms state-of-the-art elastic QP solvers in robustness, warm-start performance, and convergence reliability, enabling optimization, simulation, control, and learning beyond the feasibility assumptions of existing methods.

We present SLS^2, a framework for safe feedback motion planning from pixels using robust model predictive control (MPC) in learned latent world models. Our approach trains an action-conditioned joint-embedding world model with compact Markovian latent states, enabling efficient gradient-based trajectory optimization through learned latent dynamics. To enforce safety for the true system despite imperfect latent predictions, we inform a GPU-accelerated system level synthesis (SLS) robust MPC scheme with conformal prediction to obtain calibrated latent error bounds and robust latent-space constraint sets. We further learn and conformalize a latent constraint checker, allowing the SLS planner to impose probabilistic safety constraints during closed-loop execution. We evaluate our method on vision-based control tasks, where it improves both goal-reaching performance and safety over latent world-model and safe-planning baselines.

ZIVARI-TLBO is a grouped Teaching-Learning-Based Optimization (TLBO) method that augments an existing population-state controller with a fixed inter-group evaluated-elite relay. At each scheduled event, every group offers its already evaluated elite to the next group in a fixed ring; the elite replaces the receiver's worst eligible learner only when its stored objective value is better. Because the exact relay copies an already evaluated solution and its stored fitness, it requires no additional objective-function calls. The frozen gts-v4-cm-fixed implementation is evaluated under equal 10,000-evaluation budgets on eight classical functions at dimensions 10, 30, 50, and 100, with 30 matched seeds, and on five constrained engineering problems. A direct ablation against the same grouped landscape-aware controller without relay records 728/11/221 wins/ties/losses and a rank-biserial effect size of 0.624 across dimensions. In an eight-method multidimensional comparison, WOA obtains the best average rank (2.914) and ZIVARI-TLBO ranks second (3.382); ZIVARI-TLBO significantly outperforms TLBO, MCTLBO, DE, PSO, and GWO, loses significantly to WOA, and is not significantly different from HHO after Holm adjustment. Feasibility-aware engineering results are mixed and sensitive to the current static-penalty formulation. The evidence supports a scoped relay contribution and budget-consistent information-sharing mechanism, but not universal state-of-the-art, global-convergence, engineering-dominance, or CEC superiority claims.

Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose Constraint-Sensitive Policy Optimization (CSPO), a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods