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Prior Evolution and Task Alignment for Aerial Grasping

Weiliang Deng, Zhengyang Dang, Yao Mu, Ximin Lyu

arXiv:2609.18153v1cs.ROcs.SYeess.SY

TL;DR

Aerial grasping planning must address initialization-sensitive nonconvex optimization and objectives that may not fully reflect physical success. The paper evolves a trajectory prior using feedback from the deployed optimizer and learns an Execution-Aware Critic from execution outcomes. Complete success rises from 83.04% with Heuristic Initialization to 99.06% with EAC, while requiring 1.13 optimizer calls on average.

  • Problem

    Nonconvex trajectory optimization is sensitive to initialization, while low numerical objective values may not indicate physical grasping success.

    Source: §I · p. 2, D. Emergent Avian-Like Motion and… · p. 5

  • Method

    The method evolves a learned trajectory prior using deployed-optimizer feedback and trains an Execution-Aware Critic on contact, lift, and completion outcomes to evaluate optimized trajectories.

    Source: §I · p. 3

  • Results

    Complete success rises from 83.04% with Heuristic Initialization to 96.26% after Online Evolution and 99.06% with EAC, with 1.13 optimizer calls on average.

    Source: §VI · p. 18

  • Takeaways & Limitations

    The frozen critic can also serve as a differentiable grasping cost, allowing execution outcomes to shape trajectory optimization.

    Source: §VI · p. 18

Abstract

from arXiv · show

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.

I. INTRODUCTION

Aerial grasping planning faces initialization-sensitive nonconvex optimization and a gap between numerical objectives and physical success. The paper combines optimizer-guided trajectory-prior evolution with execution-outcome learning, while retaining trajectory optimization as the planning backbone.

I. INTRODUCTION

  • Learning serves two distinct roles: optimizer experience informs favorable initializations, while physical execution reveals motion characteristics relevant to task completion.Source: §I · p. 2
  • The prescribed grasping penalties interact with planning constraints to create multiple local solution modes, and low analytical cost can still accompany physical failure.The paper identifies both initialization sensitivity and objective-task misalignment as distinct limitations.Source: §I · pp. 2–3
  • CEM-based sampling, optimizer refinement, selection, and replay evolve a trajectory prior toward initializations effective for the deployed optimizer.The prior first learns recurring motion structures from previously optimized trajectories.Source: §I · pp. 2–3
  • An Execution-Aware Critic learns from contact, lift, and completion outcomes to evaluate complete optimized trajectories without replacing the analytical planner.The frozen critic can also provide a differentiable grasping cost for trajectory optimization.Source: §I · p. 3

A. System Setup

  • The aerial manipulator combines a quadrotor with a three-DoF delta arm; its planning must coordinate platform and end-effector motion under geometric, temporal, kinematic, and dynamic constraints.The paper defines world, body, and delta frames, with the body and delta frames differing by a fixed translation.Source: §I · p. 1, A. System Setup · p. 3

B. Trajectory Optimization Formulation

The formulation represents the quadrotor and end-effector motion in different Cartesian frames and parameterizes the trajectory with intermediate waypoints and segment durations. Grasp requirements are encoded as penalties within a nonlinear optimization problem alongside other planning requirements.

B. Trajectory Optimization Formulation

  • The whole-body trajectory uses a hybrid Cartesian representation: quadrotor motion in the world frame and end-effector motion relative to the platform in the delta frame.Source: B. Trajectory Optimization Formulation · p. 3
  • The polynomial trajectory is parameterized by M −1 intermediate whole-body waypoints and M segment durations.Each segment duration is denoted T_i.Source: B. Trajectory Optimization Formulation · pp. 3–4
  • Aerial grasping is posed as nonlinear trajectory optimization with total trajectory duration, a control-effort/time trade-off, prescribed endpoint conditions, and geometric, kinematic, and dynamic constraints.Source: B. Trajectory Optimization Formulation · p. 4
  • Position and velocity penalties specify end-effector behavior at the grasp moment, with an additional thrust-direction orientation penalty for tasks requiring orientation.Continuously evaluated penalties are approximated using fixed numerical samples along each polynomial segment.Source: B. Trajectory Optimization Formulation · p. 4

C. Nonconvexity and Local Minima under Progressive Grasp Requirements

Adding grasp-specific requirements reshapes the optimization landscape and makes initialization increasingly consequential. Whole-body optimization can produce avian-like motion, yet low numerical cost does not ensure desirable physical execution.

C. Nonconvexity and Local Minima under Progressive Grasp Requirements

  • Adding position, velocity, and orientation penalties progressively reduces favorable local optima, making initialization increasingly important.The position penalty divides broad low-cost regions into distinct local solutions; velocity and orientation requirements make some previously favorable optima unsuitable.Source: C. Nonconvexity and Local Minima under… · p. 5

D. Emergent Avian-Like Motion and Objective-Task Misalignment

  • Temporal and velocity objectives can produce an outward approach followed by a backward end-effector sweep resembling avian prey capture.The sweep compensates for platform velocity through arm motion and platform rotation.Source: D. Emergent Avian-Like Motion and… · p. 5
  • Position and velocity penalties, collision costs, smoothness, and timing can yield a V-shaped approach and departure without explicitly prescribing that shape.The optimized motion approaches from above, reaches the grasp waypoint, and departs upward.Source: D. Emergent Avian-Like Motion and… · p. 5
  • Weighted requirements can trade off, allowing low-cost trajectories with residual errors, poor contact, oscillation, penetration, or object dragging.This objective-task misalignment differs from nonconvexity: low numerical cost may still accompany poor physical grasping performance, motivating execution feedback.Source: D. Emergent Avian-Like Motion and… · p. 5

III. PRIOR EVOLUTION AND TASK ALIGNMENT

The framework combines learned initialization, optimizer-guided prior evolution, and execution feedback with analytical trajectory optimization. A prior represents local whole-body motion using task conditions and a fixed waypoint-and-duration structure.

A. Framework Overview

  • Online Evolution samples around the offline prior prediction, evaluates candidates with the deployed optimizer, and uses selected optimizer inputs as new supervision.After the prior is frozen, the Execution-Aware Critic evaluates complete optimized trajectories using contact, lift, and task-completion outcomes during deployment.Source: A. Framework Overview · p. 6

B. Trajectory Prior Representation

  • The prior learns recurring whole-body motion from optimized solutions and maps local boundary conditions to trajectory initializations.The analytical optimizer still refines the prior's prediction; the framework retains analytical constraints while adding optimizer and execution feedback.Source: A. Framework Overview · p. 6, B. Trajectory Prior Representation · pp. 6–7
  • The fixed prior representation uses six trajectory segments and five intermediate waypoints, with 30 waypoint entries and six segment-duration entries.The input boundary conditions are initial and terminal platform positions expressed in a local frame centered at the grasp point.Source: B. Trajectory Prior Representation · p. 6
  • Five intermediate whole-body waypoints balance representation flexibility and optimization complexity across representative boundary configurations.Three provide insufficient flexibility, while seven add unnecessary variables and closely spaced segments.Source: B. Trajectory Prior Representation · p. 6

C. Offline Supervised Learning

Offline Supervised Learning reuses recurring trajectory structure from optimized motions to initialize new grasping tasks. It replaces coarse heuristic seeds while leaving subsequent trajectory optimization in place.

C. Offline Supervised Learning

  • Heuristic initialization supplies only a coarse seed that may not satisfy complete trajectory requirements, leaving the optimizer to correct its waypoint and duration assignments.The optimizer also reduces geometric, temporal, kinematic, dynamic, and grasp-specific penalties before obtaining a numerically acceptable trajectory.Source: C. Offline Supervised Learning · p. 7
  • The learned prior captures recurring whole-body coordination, waypoint arrangements, and segment durations to provide structured initializations across tasks.This reuses spatial and temporal patterns rather than reconstructing the motion from a heuristic seed for each task.Source: C. Offline Supervised Learning · p. 7
  • Because it is a deterministic regressor trained on a fixed dataset, the prior may predict a representative or averaged structure and still yield a suboptimal initialization.The optimizer then refines that initialization as before.Source: C. Offline Supervised Learning · p. 8

D. Online Evolution

Online Evolution adapts the offline prior using candidate initializations evaluated by the deployed optimizer. CEM-based sampling and elite selection provide new supervision that shifts the prior toward optimizer-favorable initializations.

D. Online Evolution

  • The learned prior sets the Gaussian proposal mean, while a prescribed covariance controls exploration and both candidate count and covariance shrink over rounds.This schedule broadens early exploration and concentrates later sampling around the evolved prediction.Source: D. Online Evolution · p. 8
  • Candidate objective values measure refined-trajectory quality, while optimizer iteration counts measure solver effort required from each initialization.The repeated refinements use the same cost function and are expected to have nonincreasing objective values.Source: D. Online Evolution · pp. 8–9
  • The selected elite is the candidate with the lowest numerical objective among those meeting the objective threshold, and its optimizer input becomes the supervision target.When needed, repeated optimizer restarts refine the candidate until it meets the objective and iteration targets or reaches the maximum number of calls.Source: D. Online Evolution · pp. 8–9
  • Online Evolution repeatedly samples around the current prior, evaluates candidates with the deployed optimizer, and updates the prior from selected optimizer inputs.The prior's current prediction is included as a nominal candidate, so each elite is selected against that initialization.Source: D. Online Evolution · p. 9

E. Execution-Aware Critic

Online Evolution improves initialization according to the numerical objective, but objective satisfaction does not ensure physical grasp success. The Execution-Aware Critic (EAC) evaluates optimized trajectories using execution outcomes while retaining the analytical planner’s constraints.

E. Execution-Aware Critic

  • A trajectory can satisfy the objective threshold yet fail during execution because the object falls from the end effector.The example shows that a low numerical objective does not guarantee successful task execution.Source: Figure 7 · p. 9, E. Execution-Aware Critic · p. 9
  • EAC evaluates complete optimized trajectories using physical execution outcomes while retaining the planner’s geometric, temporal, kinematic, and dynamic constraints.After Online Evolution, the trajectory prior is frozen and EAC learns an execution-aligned preference over its structured trajectories.Source: E. Execution-Aware Critic · p. 9

1) Trajectory Features:

EAC evaluates optimized trajectories through fixed motion features and execution labels. Its supervision combines separate execution checks with comparisons between successful and failed trajectories from the same scene.

1) Trajectory Features:

  • EAC uses fixed trajectory features, including 15-dimensional motion descriptors of platform position, velocity, acceleration, and relative end-effector motion.The descriptors are extracted at selected local times, with normalized grasp time and distance to the desired grasp point also included in the feature mapping.Source: 1) Trajectory Features · pp. 9–10

2) Execution Supervision:

  • Three binary execution checks label whether contact is established, the object is lifted, and the entire task is completed.The checks are obtained separately during execution and predicted as three corresponding logits.Source: 2) Execution Supervision · p. 10
  • Successful and failed trajectories from the same scene are paired to distinguish different task outcomes despite similar numerical objectives.Their completion logits are trained using a Bradley–Terry loss.Source: 2) Execution Supervision · p. 10
  • A soft monotonicity regularizer encodes the hierarchy that completion requires lifting and lifting requires contact.It penalizes a lift logit exceeding the contact logit and a completion logit exceeding the lift logit.Source: 2) Execution Supervision · p. 10

3) Conservative Execution Score:

The conservative EAC score penalizes trajectories predicted not to meet contact, lift, and completion margins, with uncertainty increasing assigned energy. At deployment, EAC decides whether to accept an optimized trajectory or try another initialization.

3) Conservative Execution Score:

  • Ensemble disagreement lowers the conservative execution logits, increasing energy assigned to an uncertain trajectory.The penalties combine the three execution checks; lower EEAC indicates a trajectory is more likely to satisfy them all.Source: 3) Conservative Execution Score · p. 10

F. Deployment

  • Deployment tests the nominal Online initialization first, then permits up to four optimization attempts, including the nominal one.Each optimized candidate is checked using both the objective and EAC criteria; the procedure stops when one is accepted or the attempt limit is reached.Source: F. Deployment · p. 10

IV. EXPERIMENTS

  • The experiments ask how learned components affect performance, whether EAC gains reflect candidate coverage or execution-aware selection, and where execution feedback should enter planning.They also examine the trajectory family, use of EAC for optimization, and transfer to real-world aerial grasping.Source: §IV · p. 10
  • Figure 8 depicts multiple planned trajectories being executed concurrently in vectorized Isaac Sim environments.The simulation is GPU-parallel and closed-loop.Source: Figure 8 · p. 11

A. Experimental Setup

The evaluation compares learned initialization and execution-aware selection while keeping the optimizer and controller unchanged. On 5,000 paired scenes, the learned stages improve complete success, and candidate-selection comparisons separate coverage gains from EAC selection gains.

1) Hardware Platform:

  • The real-world platform is a quadrotor equipped with a three-DoF delta arm, with state estimates fused from motion capture and the onboard IMU.The onboard computer is an Intel Processor N150 and the flight controller is NxtPX4v2.Source: 1) Hardware Platform · p. 11

2) Simulation Setup:

  • Closed-loop simulation models tracking, motor response, contact, and payload reaction; compared methods share the same controller, physical parameters, and execution criteria.Planned references are sampled at 100 Hz and tracked using a cascaded geometric controller.Source: 2) Simulation Setup · p. 11

3) Training:

  • Offline and Online priors share a 6-256-512-256-36 network; Online Evolution retains 12,000 selected optimizer inputs, while EAC trains on 227,626 labeled trajectories.EAC uses an ensemble of three independently trained models.Source: 3) Training · p. 11

B. Planning and Execution Performance

  • 99.06% complete success with EAC versus 96.26% with Online Evolution, recovering 149 failed scenes and losing 9 previously successful scenes.Failures fell from 187 to 47 (74.9%); p90 planning time rose from 235.9 to 255.9 ms, with 1.1258 optimizer calls on average.Source: Figure 9 · p. 12, B. Planning and Execution Performance · p. 12

C. Candidate Coverage and EAC Selection

D. Ablation of Execution Feedback

Execution feedback improved success when EAC assessed each optimized trajectory without changing the learned prior, while feedback-based prior updates produced little or negative overall gains. Online Evolution also made optimized trajectories less sensitive to initialization and nearby task-condition changes.

D. Ablation of Execution Feedback

  • GSD gained 0.14 percentage points, RIR left success unchanged, and EGJE reduced success by 1.84 percentage points across 5,000 fresh scenes.Prior finetuning corrected some failed conditions but also changed predictions for successful conditions; EGJE also reduced useful initialization supervision.Source: D. Ablation of Execution Feedback · p. 13
  • EAC recovered 126 analytical and 50 physical failures while harming four successful scenes, reaching 99.18% success with 1.13 optimizer calls on average.The paired recovery-and-harm comparison is shown in Figure 10.Source: D. Ablation of Execution Feedback · p. 13, Figure 10 · p. 13

1) Consistency under Initialization Perturbations:

  • Online Evolution produced the smallest trajectory deviations under waypoint and duration perturbations, followed by Offline Supervised Learning and Heuristic Initialization.Figure 11 compares three-dimensional Fréchet distances and maximum responses to those perturbations.Source: 1) Consistency under Initialization… · p. 14, Figure 11 · p. 14

2) Consistency under Nearby Conditions:

  • Under local changes to initial and terminal positions, Online Evolution reduced trajectory variation across nearby task conditions while maintaining a low numerical objective.Heuristic Initialization was also narrow but often retained the same searched path; Offline Supervised Learning varied more across nearby conditions.Source: 2) Consistency under Nearby Conditions · pp. 14–15

3) Consistency across Different Conditions:

Online Evolution produced spatial trajectories whose variation was more predictable from task conditions, while the frozen EAC energy improved physical success when used as the grasping cost. EAC’s score changes and feature contributions aligned with distinct stages of execution failure and recovery.

3) Consistency across Different Conditions:

  • On 48 fresh conditions, the median spatial reconstruction-error reduction from the constant to quadratic model was 0.358 m for Online Evolution, versus 0.237 m for Offline Supervised Learning and 0.0046 m for Heuristic Initialization.Under the quadratic model, Online Evolution’s median error was 0.064 m lower than Offline Supervised Learning and 0.471 m lower than Heuristic Initialization.Source: 3) Consistency across Different… · p. 15
  • Offline Supervised Learning and Online Evolution had substantially smaller timing errors than Heuristic Initialization, while the constant and quadratic models gave similar errors within each method.Online Evolution preserved temporal consistency while its spatial trajectory variation became more regularly related to task condition.Source: 3) Consistency across Different… · p. 15

F. From Execution Assessment to Grasping Cost

  • Replacing PVO with the frozen EAC grasping cost increased physical success from 96.86% to 98.96% and reduced failures from 157 to 52, or by 66.9%.Median optimization time fell from 49.79 to 36.42 ms, and median solver iterations fell from 137 to 113.Source: F. From Execution Assessment to… · p. 15, Figure 12 · p. 16
  • For no-contact recoveries, EAC scores improved most at all three execution stages; for lost-after-pickup recoveries, the largest gain was in Completion.In harm scenes, score changes remained small and optimized trajectories changed little.Source: F. From Execution Assessment to… · p. 16
  • No-contact recoveries drew most feature contribution from pre-grasp platform acceleration and velocity, while lost-after-pickup recoveries shifted contribution toward arm waypoints and end-effector motion.The paired examples connect improved pre-grasp alignment with contact and improved retention after pickup with Completion scores approaching zero.Source: F. From Execution Assessment to… · p. 16

G. Real-World Validation

The framework completed two continuous real-world manipulation runs, and its conclusion reports improved complete success after Online Evolution and EAC. Cross-task studies support a methodological extension of solver feedback and event-based execution feedback, with transfer requiring task-specific representations and training.

G. Real-World Validation

  • All four collection cycles and all six Cycle Grasp cycles completed without failure, covering ten object transfers in continuous real-world runs.The runs took 68.84 s and 72.48 s, respectively; horizontal offsets for all ten grasps remained below 4 cm.Source: G. Real-World Validation · p. 17, Figure 13 · p. 17

V. DISCUSSION

  • For Tilted Gate, Online Evolution reduced mean cost from 5.33 × 10^4 to 2.35 × 10^4; for Throw, EAC increased success from 77.2% to 81.4%.Tilted Gate uses solver feedback, whereas Throw uses release, full entry, and retention as execution supervision.Source: §V · p. 18, Figure 14 · p. 18
  • Transfer to new tasks generally requires task-specific condition and trajectory representations and new Offline and Online training; EAC additionally requires reliable observable execution events.The discussion frames the studies as methodological transfer rather than a fixed sequence of modules.Source: §V · p. 18

VI. CONCLUSION

  • Complete success rose from 83.04% with Heuristic Initialization to 96.26% after Online Evolution and 99.06% with EAC, requiring 1.13 optimizer calls on average.The conclusion also reports improved trajectory consistency and use of EAC’s frozen energy as a differentiable optimization cost.Source: §VI · p. 18

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