Point It, Strike It: Direction-Conditioned Dynamic Manipulation of Deformable Linear Objects

Task and motivation

• The 4D striking task specifies a rope tip’s 3D position and arrival direction, across reachable workspace points and different ropes.The paper notes that many tasks depend on how the tip arrives, such as maintaining a spinning top’s rotation or knocking an obstruction aside.Source: §I · p. 2

Challenges

• Rope striking is difficult because dynamics and rope properties vary, demonstrations are unavailable, and distinct swings reaching one target differ in reliability.The sim-to-real mismatch also includes controller lag, mechanical vibration, and timing error.Source: §I · p. 2

Contributions

• DeformX 2.0 adds GPU acceleration, a stable Cosserat rod solver, and cross-flow aerodynamics, simulating ropes more than 20,000× faster than DeformX.The introduction also reports that TRACE covers 98.3% of the workspace, versus 49.5% for CEM with an example swing.Source: §I · p. 2
• TRACE warm-starts each target from the stored swing whose tip path passes closest and favors smooth, repeatable motion; its simulation-data-only flow-matching policy reaches 92.1% accuracy within 5 cm and 10°.Source: §I · p. 2
• RECAP fits rope and rig parameters from calibration swings and uses a simulation-trained correction policy to adapt nominal actions to real ropes.Across three ropes, the introduction reports hardware success within 5 cm rising from 72% to 87% for position goals and from 28% to 52% for position-and-direction goals.Source: §I · p. 2

A. Goal-conditioned dynamic rope manipulation

• Earlier methods target 2D or 3D rope-tip positions, whereas this work specifies both 3D position and arrival direction for a single zero-shot strike.The cited systems include planar targeting, repeated real attempts, and obstacle-related cable skills.Source: A. Goal-conditioned dynamic rope… · p. 2

B. Planner-generated training data

• TRACE starts from a hardware-verified swing and warm-starts each target from the stored swing whose tip path passes closest, favoring consistent, repeatable solutions.Its cost favors an extended rope and smooth tip motion; verified swings are labeled with their achieved outcomes.Source: B. Planner-generated training data · pp. 2–3, Figure 2 · p. 3

C. Generative policies for multimodal action distributions

• Distinct swings can reach the same goal, so a regressor may average them into an invalid swing; goal modulation in every residual block keeps flow-matching samples within a motion pattern.The passage contrasts this with generative samples that can spread between patterns when the goal enters only at the network input.Source: C. Generative policies for multimodal… · p. 3

D. Sim-to-real calibration

• Prior methods estimate rope parameters for simulation-based optimization or condition policies on estimates, while others correct actions from outcomes; RECAP fits rope and rig parameters and trains a parameter-conditioned delta policy.The cited examples include Wiggle&Go [6], GenDOM, TossingBot, and IRP.Source: D. Sim-to-real calibration · p. 3

III. PROBLEM FORMULATION

• The task is to generate a single-swing robot trajectory whose rope tip reaches a target position while moving in the desired arrival direction.The input goal comprises three position coordinates and one angular degree of freedom, with arrival angle measured after projecting tip velocity onto a tangent plane.Source: §III · p. 3
• The output is a parameter vector decoding to a joint trajectory through waypoints and duration, while distinct trajectories may reach the same goal and are represented by a conditional distribution.A clamped cubic spline reconstructs the trajectory, with duration adjusted to satisfy the joint-velocity limit; rope and setup properties are denoted by η.Source: §III · p. 3

A. Overview

• A nominal simulator generates feasible goal–trajectory pairs, from which conditional flow matching learns the general relationship between desired rope-tip outcomes and robot trajectories.The nominal rope properties are denoted by η̄.Source: A. Overview · pp. 3–4
• A few calibration swings characterize the real system, after which action adaptation corrects each nominal action and each goal is executed with an open-loop swing.Calibration is performed once per system.Source: A. Overview · p. 4

B. Learning robust motion patterns

• Conditional flow matching models a distribution of actions per goal, avoiding regression toward a conditional mean that can average incompatible swings.Similar swings form motion patterns with locally gradual trajectory changes, while transitions between patterns can produce unsuccessful swings.Source: B. Learning robust motion patterns · p. 4

1) Data generation:

• TRACE uses CEM to find accurate, robust strikes, warm-starting each target from the stored swing whose tip path passes closest and refining successful neighboring solutions.Its objective penalizes target, speed, and limit errors; curvature favors an extended rope and smooth tip motion.Source: 1) Data generation · p. 4

2) Flow matching model:

• The flow-matching policy learns normalized swing actions from noise and conditions each residual block on goal and flow time.At inference, 64 noise samples are integrated for 50 Euler steps, simulated, and ranked by J loss; Fig. 3 plots coverage and hit rate across arrival angles.Source: 2) Flow matching model · pp. 4–5, Figure 3 · p. 4

C. RECAP: residual calibration policy

• RECAP addresses the expected failure of nominal policy actions on hardware due to sim-to-real gaps.The method fits parameters for each new rope and applies a correction policy trained in simulation.Source: C. RECAP: residual calibration policy · p. 5
• RECAP fits rope and rig parameters to eight real calibration swings, using CEM to find parameters that reproduce their recorded tip trajectories in simulation.The identified parameter set contains 11 tunable parameters.Source: C. RECAP: residual calibration policy · p. 5
• A conditional flow-matching delta policy generates real actions from nominal actions, conditioned on the real goal and fitted system.It is trained on simulated ropes and rigs with perturbed parameters, using CEM-found corrections that improve the pass.Source: C. RECAP: residual calibration policy · p. 5
• At inference, RECAP simulates the nominal action and eight correction candidates, then executes the candidate with the lowest loss.Calibration costs eight real swings per rope; each later goal takes one strike without measurement during execution.Source: C. RECAP: residual calibration policy · p. 5

D. DeformX 2.0: the GPU co-simulation engine

• The GPU Cosserat-rod formulation separates position and rotation updates and solves orientation in closed form for stable, efficient batched integration.The simulator supports TRACE search, correction-policy training, and candidate verification.Source: D. DeformX 2.0: the GPU co-simulation… · p. 5
• Quadratic cross-flow drag damps each rope segment’s velocity normal to its local tangent at every substep.The simulation uses 100 solver substeps per 60 Hz control step and 16 constraint iterations.Source: D. DeformX 2.0: the GPU co-simulation… · p. 6
• More than 20,000× throughput over DeformX is achieved with 8192 parallel environments.DeformX 2.0 generates over 1 million trajectories per hour per GPU.Source: D. DeformX 2.0: the GPU co-simulation… · p. 6

V. EXPERIMENT

• One experiment measures simulation speed.All arms share the setup and protocol described for the experiments.Source: §V · p. 6
• A second evaluates policy accuracy for commanded position and arrival direction in simulation and on hardware.Source: §V · p. 6
• A third measures the contributions of data generation and rope calibration.Source: §V · p. 6

A. Experiment Setup

• The hardware setup uses a wall-mounted UR5e with a 0.65 m rigid stick and 1.0 m rope in a 30° workspace cone.The workspace radii are 1.6–2.3 m, with maximum height 2.5 m; joint velocities are limited to 2 rad/s.Source: A. Experiment Setup · p. 6
• Hardware evaluation covers 25 targets with three swings each, while simulation uses 5700 uniformly sampled workspace targets shared across policies.Source: A. Experiment Setup · p. 6

B. Hit Target Experiment

• Three ropes are tested on the same 25 targets with position-only 3D goals and 4D goals that add a randomly drawn arrival direction.Source: B. Hit Target Experiment · p. 6
• Base executes a candidate from the nominal simulator, Baseline uses learned simulator identification, and RECAP fits the simulator from eight calibration swings per rope.A swing succeeds within the chosen target radius; a 4D swing also requires arrival within 10° at at least 1 m/s along the commanded direction.Source: B. Hit Target Experiment · pp. 6–7
• RECAP raises mean SR@5 cm from 72% to 87% on 3D goals and from 28% to 52% on 4D goals, while halving mean 4D miss from 10.6 to 5.6 cm.On Rope C, RECAP brings 4D misses within 10 cm from 53% to 79%.Source: B. Hit Target Experiment · p. 7
• Across Rope A’s workspace, Base and Baseline success degrade toward the upper edge, while RECAP largely removes this degradation except at the top corner.The evaluation uses one-time eight-swing calibration to transfer a simulation-trained policy across three ropes.Source: B. Hit Target Experiment · p. 7

A. Learning distinct motion patterns

• The learning-method comparison includes the proposed model, naive flow matching, a matched-capacity regression head, and nearest-neighbor retrieval.Source: A. Learning distinct motion patterns · p. 7
• The proposed model keeps samples compact within each motion pattern and separates distinct patterns, unlike dispersed naive conditioning or regression predictions between incompatible swings.Averaging successful swings can produce a prediction that does not succeed.Source: A. Learning distinct motion patterns · p. 7

B. Data generation for policy learning

• The data-generation evaluation compares full TRACE with CEM initialized from an example swing and TRACE without an example, assessing coverage, strike accuracy, and trajectory quality.It also assesses policies trained on the resulting datasets.Source: B. Data generation for policy learning · p. 7
• TRACE provides broader workspace coverage and higher policy accuracy after candidate selection; its example contributes lower curvature loss and stronger post-selection performance.The example-free variant has slightly higher one-shot accuracy, showing that trajectory quality and an individual policy sample’s accuracy differ.Source: B. Data generation for policy learning · p. 7

• 92.1% success within 5 cm and 10° in simulation; on hardware, calibration raises success within 5 cm to 87% for position goals and 52% for position-and-direction goals.Hardware evaluation spans three ropes.Source: §VII · p. 7
• The data-generation ablation reports that the example seeds higher-quality motion patterns, while TRACE improves dataset coverage and accuracy.Table IV evaluates workspace coverage, policy accuracy on 5,700 random test goals, and mean curvature loss; the caption provides no cell values.Source: Table IV · p. 8
• Locally predictable regions of the action-to-outcome mapping can make inverse learning easier and may limit the effects of execution errors and physical-property variation.The authors distinguish gradual changes within motion patterns from potentially sensitive, chaotic transitions between patterns.Source: §VII · p. 8
• A sufficiently accurate simulator can generate effective motions and reliably rank candidates, complementing feedback control as a route to reliable manipulation.The authors state that better simulation can reduce reliance on online correction.Source: §VII · p. 8
• The framework is limited to single-swing rope-tip striking and remains open-loop after one-time calibration, so it cannot correct disturbances or system changes during a swing.Robustness may degrade when real-system dynamics substantially exceed the training range.Source: §VII · p. 8
• Future work should extend the framework toward closed-loop feedback and broader classes of dynamic DLO interactions.Source: §VII · p. 8