cs.ROMar 10, 2026

Trajectory Optimization for Self-Wrap-Aware Cable-Towed Planar Object Manipulation under Implicit Tension Constraints

Authors: Yu Li, Amin Fakhari, Hamid Sadeghian

Organizations: Munich Institute of Robotics and Machine Intelligence, Technical University of Munich, Germany. · The author is with the Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794, USA.

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Abstract

Cable/rope elements are pervasive in deformable-object manipulation, often serving as a deformable force-transmission medium whose routing and contact determine how wrenches are delivered. In cable-towed manipulation, transmission is unilateral and hybrid: the tether can pull only when taut and becomes force-free when slack; in practice, the tether may also contact the object boundary and self-wrap around edges, which is not merely collision avoidance but a change of the wrench transmission channel by shifting the effective application point and moment arm, thereby coupling routing geometry with rigid-body motion and tensioning. We formulate self-wrap towing as a routing-aware, tensioning-implicit trajectory optimization (TITO) problem that couples (i) a tensioning-implicit taut/slack constraint and (ii) routing-conditioned transmission maps for effective length and wrench, and we build a relaxation hierarchy from a strict mode-conditioned reference to three tractable relaxations: Full-Mode Relaxation (FMR), Binary-Mode Relaxation (BMR), and Implicit-Mode Relaxation (IMR). Across planar towing tasks, we find that making routing an explicit decision often yields conservative solutions that stay near switching boundaries, whereas IMR induces self-wrap through state evolution and exploits the redirected torque channel whenever turning requires it.

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Fig. 1 : Illustration of cable-towed manipulation of a box by a mobile robot at three phases: (i) slack cable, (ii) taut cable without self-wrap contact, and (iii) taut cable with self-wrap contact with the object, where the application point of the wrench changes, as detailed in Fig. 2 for projected planar interpretation.
Fig. 2 : Illustration of cable-towed manipulation of a box in 2D (top view) at two modes: (a) direct routing mode, and (b) self-wrap routing mode.
Fig. 3 : Representative planar towing rollouts for three scenes (columns) and three formulations (rows: FMR, BMR, IMR). Dashed: reference box CoM path. Solid: actual box CoM path with wrap-active segments highlighted. Snapshots show box poses; the cable and the active redirection vertex are overlaid when applicable. The results are shown with the same initial condition (e.g. xk=0g,Tk=0x^{g}_{k=0},T_{k=0} , etc.) and model parameters.
Fig. 4 : Time histories for the rollouts in Fig. 3 (columns). From top: tracking error ∥e(x)∥\|e(x)\| , tension TT , taut/slack state (from gap gg ; cf. ( 4 ), ( 8f )), effective torque-channel difference Δτeff\Delta\tau_{\mathrm{eff}} , control action uu , and routing mode.
SceneFMRBMRIMR
 SR (%)Time (s)RMSE (m)Wrap (%)SR (%)Time (s)RMSE (m)Wrap (%)SR (%)Time (s)RMSE (m)Wrap (%)
Zigzag0.084.08±1.0184.08\pm 1.01––100.064.97±0.3564.97\pm 0.350.00370.00370.086.735.33±13.3435.33\pm 13.340.00170.00179.1
Arc Wrap0.092.36±5.0692.36\pm 5.06––100.083.36±4.0583.36\pm 4.050.03880.03880.773.380.12±8.0480.12\pm 8.040.02990.029916.0
Obstacle0.0107.67±5.90107.67\pm 5.90––100.081.29±4.7881.29\pm 4.780.05710.05710.380.0158.07±51.96158.07\pm 51.960.05700.05701.0
TABLE I : Randomized-Initialization Benchmark (N=15 per scene-method). Success policy: slalom towing uses strict task_success reported by solver; Arc-turn uses RMSE≤0.08, FinalErr≤0.10, WrapRatio≥0.05\mathrm{RMSE}\leq 0.08,\ \mathrm{FinalErr}\leq 0.10,\ \mathrm{WrapRatio}\geq 0.05 ; Constrained-obstacle towing uses RMSE≤0.10, FinalErr≤0.12\mathrm{RMSE}\leq 0.10,\ \mathrm{FinalErr}\leq 0.12 . Notations: SR (Success Rate), Time (solver time), RMSE (tracking error), Wrap (wrap ratio).
Fig. 5 : Parameter sweep on the slalom benchmark for BMR and IMR. Top: tracking RMSE (gray indicates failed runs). Bottom: planning of direct/redirected (wrap-active) mode.
Fig. 6 : Open loop trajectory validation on “real” numeric plant for BMR and IMR with mismatched plant parameters (0.85 and 1.15 fraction of the baseline parameters) and Mujoco simulation. Results focus on spatial trajectory and recorded wrap behavior.
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