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

2026-03-10

AI Summary

This work addresses the abrupt force transmission and motion coupling in cable-driven planar object manipulation caused by self-wrapping and implicit tension constraints. The authors propose a routing-aware, tension-implicit trajectory optimization framework that, for the first time, treats self-wrapping not as a disturbance but as a beneficial torque redirection mechanism. A hierarchical optimization strategy is introduced, featuring three levels of relaxation—Full-Mode, Binary-Mode, and Implicit-Mode—that effectively couple routing-dependent effective cable lengths, torque transmission mappings, and implicit tension constraints. Experimental results demonstrate that the Implicit-Mode spontaneously induces advantageous self-wrapping configurations, enabling efficient exploitation of redirected torque pathways during turning tasks and outperforming conventional explicit-routing approaches.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Manipulation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• trajectory optimization
• cable-towed manipulation
• self-wrap
• tension constraints
• deformable-object manipulation

Innovation

• trajectory optimization
• cable-towed manipulation
• self-wrap
• implicit tension constraints
• routing-aware control