Actuation and Control of Passive Tendon-Driven Soft Extensions Through Rigid Manipulator Motion

Ignacio Cuiral-Zueco, Gonzalo López-Nicolás, Youcef Mezouar

November 2026

Real UR10 with a free end effector: the soft tip is steered toward targets around a virtual obstacle (Exp. 1).

TL;DR An industrial arm bends a passive tendon-driven soft extension with its own joint motion, because tendons anchored on upstream links tighten or slacken as the arm moves, while the end effector holds a position or fulcrum constraint. In simulation the tip reached every feasible target within 4 mm; on a real UR10 with handmade extensions costing under US$10, it reached 6 of 16 targets and every safety barrier held.

What they do

A soft extension on an industrial arm combines the arm’s reach with compliant access to confined spaces, but usually needs its own tendon motors. Here the extension is passive: each tendon runs from an anchor on an upstream arm link to the base of the extension. As the arm moves, the exterior span between anchor and entry point changes, which tensions the tendon and bends the extension. The controller uses this to steer the soft tip while the end effector (EE) obeys a task constraint, such as holding a fixed position or pivoting through an aperture.

How it works

Differential model. Tip velocity is split into rigid transport with the EE and tendon-driven deformation. Arm and span kinematics are analytic; the span-to-deformation map is fitted from probing motions and refined online with Broyden’s rank-one update.
Null-space control. The EE constraint is the primary task, and a damped least-squares law regulates the tip and body points in its null space. They prove the weighted tip error does not increase, give conditions for exponential convergence, and bound how many deformation directions the tendons can transmit.
Safety. A QP with control barrier functions enforces obstacle clearance, the fulcrum’s aperture, cone and insertion limits, and keeps the spans inside the identified domain.

Results

Simulation (UR10 with a Cosserat-rod extension): every feasible target reached within 4 mm, with the EE constraint held to 0.2 mm. Without the obstacle barrier the extension penetrated a sphere by 18.8 mm; with it, clearance stayed above 10.7 mm.
Real UR10, six experiments with handmade foam extensions: spans changed by up to 35 mm, the position-constrained EE stayed within 0.5 mm, and all barrier values stayed nonnegative.
6 of the 16 targets predicted feasible were reached, all under the fulcrum. The rest stopped at active barriers or at stationary points of the controller, 14-42 mm from the target.

Limitations

The identified model is local to the probed span domain, which limited several real targets; marker predictions had 9-14 mm RMS error. Tendon count and anchor placement were not optimized, and the controller regulates shape only, not tension, contact force or stiffness.

Videos

Real UR10 through a laparoscopic-style fulcrum: arm motion bends the soft extension toward its targets (Exp. 4).

Simulation: UR10 joint motion changes the tendon spans and moves the soft tip under a fulcrum constraint.

Figures

From Figure 1: Three ways to extend a robot arm for confined access: a passive rigid extension, an active soft extens... — From Figure 1: Three ways to extend a robot arm for confined access: a passive rigid extension, an active soft extension that needs its own actuation, power and control hardware, and the passive soft extension proposed here, whose tendons are actuated by the manipulator's joint motion.

From Figure 2: Manipulator-driven actuation in a UR10 simulation under a laparoscopic fulcrum constraint. Two tendons... — From Figure 2: Manipulator-driven actuation in a UR10 simulation under a laparoscopic fulcrum constraint. Two tendons run from anchors on the forearm and wrist to the base of the soft extension. Bottom: joint angles, exterior tendon spans and tip position; the spans change by up to 18 mm and the tip moves by up to 170 mm.

From Figure 4: Method overview. Model: analytic arm and tendon kinematics plus a span-to-deformation map identified f... — From Figure 4: Method overview. Model: analytic arm and tendon kinematics plus a span-to-deformation map identified from probing motions and corrected online. Controller: the end-effector constraint is the primary task and the tip is regulated in its null space; a quadratic program with barrier functions can replace the nominal command. Plant: the robot reports joint angles and a camera measures the tip and body points.

From Figure 10: Real experiments with a free end effector (a) and a position-constrained end effector (b, c). Top: ca... — From Figure 10: Real experiments with a free end effector (a) and a position-constrained end effector (b, c). Top: camera snapshots. Middle: 3-D view of the targets, obstacles, tip path and soft extension. Bottom: tip error with the 10 mm threshold, joint rates and changes of the two exterior spans.

Abstract

Industrial manipulators offer reach and precision but can damage nearby structures in confined spaces. Soft robots provide compliant contact but typically have limited reach. Rigid-soft systems combine their advantages, although they often require dedicated actuation and control hardware. We propose actuating a passive tendon-driven soft extension through manipulator joint motion. As the robot moves, the exterior spans of tendons anchored to upstream links change, altering tendon tension and deforming the extension. Inspection through narrow apertures, for example, constrains the motion of the end effector (EE). We develop a controller that regulates the soft tip while preserving such EE constraints. A differential model separates rigid transport from soft deformation, combining analytic arm and tendon kinematics with a locally identified span-to-deformation map. We also derive a local upper bound on the number of independent deformation directions transmitted by the tendons under the EE constraint, and conditions for the exponential convergence of the tip error. A quadratic program with control barrier functions imposes obstacle clearance, fulcrum limits, and model-validity conditions. Simulations and real experiments show tip and shape regulation under free, position-constrained, and fulcrum-constrained EE motion.

Summaries are written automatically from each paper's text. Figures and videos come from the paper and its project page; all credit goes to the authors.

Matt Strong