Concentric Push/Pull Robot (CPPR)

• CPPR is a steerable robotic system composed of concentric, axially-translatable, and independently bendable segments that offer precise maneuvering in constrained environments.
• It integrates tendon-driven bending and push/pull translation with advanced kinematic models to achieve sub-millimeter to millimeter tip accuracy during navigation.
• Experimental evaluations with systems like TACTER and CPPR-dissector highlight enhanced dexterity and targeted performance for minimally invasive surgical applications.

A concentric push/pull robot (CPPR) is a steerable robotic system composed of concentric, axially-translatable, and independently bendable segments, typically incorporating hollow and thin-walled tubes or rod-and-segment architectures. Each segment can be actuated to enable controlled translation and bending, with push/pull and tendon-driven mechanisms providing multiple degrees of freedom (DoF). The CPPR paradigm supports dexterous navigation and manipulation in highly confined or tortuous anatomical environments and offers a platform for end-on and follow-the-leader insertion, as exemplified in endonasal or endovascular interventions. Kinematic, mechanical, and control modeling for CPPR systems has been developed to achieve sub-millimeter to millimeter-scale tip accuracy, with actuation and sensing strategies tuned to the specific structural configuration and clinical task (Yamamoto et al., 28 Apr 2025Zhu et al., 3 Feb 2026).

1. Mechanical Architecture and Design

State-of-the-art CPPR systems employ dual or nested, mechanically-coupled segments, often realized as tube pairs or composite tube-and-segment structures. Table 1 summarizes key geometrical and material parameters from recent representative designs.

Robot	Outer Diameter (mm)	Inner Channel (mm)	Actuation DoF	Segment Material
TACTER (Yamamoto et al., 28 Apr 2025)	4.0	1.5	2 bend + 1 translation	NiTi (outer), polymer-NiTi
CPPR-dissector (Zhu et al., 3 Feb 2026)	3.5	1.3–1.2 (channels)	2 bend + 2 trans + 2 rot	316L SS

TACTER consists of an outer unidirectionally asymmetric notched Nitinol tube (OD 1.97 mm; notch depth 2.93 mm) and an inner modular, 3 mm OD polymer-Nitinol hybrid segment with four circumferential holes. The inner segment supports two nitinol spine rods (0.23 mm OD) and two actuation tendons (0.127 mm), enabling independent bidirectional bending and up to 30 mm axial translation relative to the outer tube.

The CPPR-based surgical dissector is structured with two nested steerable segments, each built from a pair of 316L stainless steel tubes (proximal OD 3.5 mm/ID 3.3 mm, distal OD 2.9 mm/ID 2.7 mm), with tenon–mortise laser-cut slits for enhanced compliance in bending. The instrument integrates a three-lumen cross-section for endoscopic and tool access.

Material selections are based on required bending stiffness, superelasticity, and biocompatibility. NiTi enables highly elastic bending for outer sheaths and spines, while 316L SS provides frictional and load-bearing characteristics for inner segments (Yamamoto et al., 28 Apr 2025Zhu et al., 3 Feb 2026).

2. Actuation and Sensing Mechanisms

Both TACTER and the CPPR-dissector use a combination of tendon-driven bending and direct push/pull translational mechanisms. Inner and outer segment tendons are actuated via miniature gear motors (298:1 ratio for TACTER), with leadscrews providing fine position control. Linear travel of the TACTER inner-robot tendon is ≈4 mm over 15 steps (0.267 mm/step); the outer tendon travels ≈7 mm over 15 steps (0.467 mm/step), with real-time load feedback from three-pulley tension sensors (Honeywell FSS-SMT) (Yamamoto et al., 28 Apr 2025).

Inner-robot actuation enables axial translation (up to 30 mm, controlled by leadscrew/linear-bearing assemblies), facilitating independent segment motion essential for follow-the-leader deployment (Yamamoto et al., 28 Apr 2025).

For the CPPR-dissector, six DoF (two bends, two translations, two base rotations) are commanded by six DC motors. All actuation is open-loop, with joint states calculated from precomputed tip pose inverses and realized without tip-side feedback in the current implementation (Zhu et al., 3 Feb 2026).

3. Kinematic and Mechanical Modeling

TACTER implements a Cosserat-rod theoretical framework for predicting 3D centerline and tip pose, modeling each concentric tube as a discretized elastic continuum subject to tendon-generated forces and moments:

$$\dot{P}_i(s) = R_i(s)\,v_i(s), \quad \dot{R}_i(s) = R_i(s)\,[u_i(s)]$$

Tendon-induced distributed loads are included, enabling simulation of curved and follow-the-leader configurations under coupled tension and translation ($\lambda_1, \lambda_2, d$). This system is formulated as a first-order boundary-value problem and solved via shooting methods integrating arc-wise equilibrium to match boundary pose constraints (Yamamoto et al., 28 Apr 2025).

The CPPR-dissector employs a piecewise-constant-curvature model. For a single bent segment:

$$D = (d_o + d_i)\,\theta, \quad \theta = \frac{D}{d_o + d_i}$$

where $D$ is the tendon pull, $d_o, d_i$ are mid-wall offsets, and $\theta$ is the segment bend angle. The 6-DoF actuation vector ($Q$) parameterizes translations, bend pulls, and base rotations across segments; forward kinematics is derived via a product of homogeneous transformations (Zhu et al., 3 Feb 2026).

Optimization-based calibration (e.g., Newton–Raphson) inverts the forward kinematics for target tip pose realization under actuator constraints. Jacobians linearize the mapping, but full-closed loop correction has yet to be implemented (Zhu et al., 3 Feb 2026).

4. Control Strategies and Motion Planning

TACTER solves the inverse kinematics via numerical optimization embedding the Cosserat-rod forward model. The objective is to align the achieved tip position and orientation with a prescribed trajectory, minimizing

$$\|\mathbf{p}_{tip}(\lambda_1, \lambda_2, d) - \mathbf{p}_d\|^2 + \alpha \|\Delta R\|^2$$

Actuation commands are constrained by tendon tension and translation range. Sequential path parameterization allows for follow-the-leader deployment: as the inner tube advances ($d_k \rightarrow d_{k+1}$), tension profiles are computed to maintain tip curvature matching the next path segment (Yamamoto et al., 28 Apr 2025).

The CPPR-dissector control scheme is open-loop: the controller computes joint values ($\hat Q$) for a desired tip pose via constrained optimization and executes commands on DC motors. Control input can be provided through a 2-axis joystick with segment selection; typical computation time is 0.4–0.8 seconds per command. No feedback-based corrections are performed in the presented implementation (Zhu et al., 3 Feb 2026).

5. Performance and Experimental Evaluation

Bench and cadaveric tests of TACTER demonstrated mean tip-position RMSE ≤5 mm (2.5% of device length) across 13 configurations. The maximum error increased with inner-tube extension (up to ~11.9 mm at $d \approx 30$ mm), likely due to unmodeled compliance and alignment drift (Yamamoto et al., 28 Apr 2025). Cadaver studies validated endonasal pathway traversal, including navigation from the nasal entry to the sphenoid sinus.

The CPPR-dissector achieved tip placement accuracies of 1.2–2.0 mm (RMS/max) in both simulation and physical tests, and showed repeatable bending with tip force capability exceeding 1 N and sufficient stiffness for 300 g tip loads. Ex vivo pulmonary thromboendarterectomy (PTE) simulations on porcine lungs demonstrated access through consecutive arterial bifurcations (as small as 4 mm in diameter) and reduced plaque removal time from ~20 min (rigid tools) to ~5 min per pass. The instrument showed an ability to maintain distal reach, continuous visualization, and workspace coverage that rigid straight tools could not achieve (Zhu et al., 3 Feb 2026).

6. Application Contexts and Design Trade-Offs

CPPRs such as TACTER and the CPPR-dissector enable minimally invasive procedures in highly constrained anatomical spaces where distal dexterity, workspace coverage, and follow-the-leader capability are essential.

Key design trade-offs identified include:

• Bending stiffness vs. dexterity: Outer notched tubes provide greater load-bearing capacity but may restrict bending to a single plane; inner rod-and-segment elements increase dexterity but reduce distal stiffness, especially under significant extension (Yamamoto et al., 28 Apr 2025).
• Translation range vs. accuracy: Longer exposed inner segments are subject to accumulated modeling inaccuracies and increased compliance, as reflected in growing tip error metrics at maximal translation (Yamamoto et al., 28 Apr 2025).
• Open-loop vs. closed-loop control: Current hardware implementations can deliver sub-millimeter to millimeter-level tip accuracy in bench and ex vivo environments without continuous feedback. Integration of EM or fiber-Bragg-grating (FBG) shape sensing is suggested to close the loop for future accuracy improvement (Yamamoto et al., 28 Apr 2025).
• Segment scaling and lumen configuration: Maintaining ≤4 mm OD has been effective for endonasal and vascular access; CPPRs for larger anatomical tracts can scale proportionally (Yamamoto et al., 28 Apr 2025Zhu et al., 3 Feb 2026).

7. Recommendations for CPPR System Development

Robust CPPR design incorporates superelastic or stainless steels with tailored slot/notch or tenon–mortise geometries for bending, axial translation hardware for segment coordination, and miniaturized tendon actuation with tension feedback. For accurate workspace coverage and path following:

• Adopt Cosserat-rod or constant-curvature kinematic modeling (as appropriate) and implement multisegment shooting solvers.
• Use optimization-based inverse kinematics with actuator and structural constraints for real-time control, factoring translation and bending coordination for follow-the-leader operation.
• Integrate force sensing and, where achievable, shape/pose feedback to compensate for compliance and friction, particularly at large extensions.
• Prioritize geometry and materials matched to anatomical requirements and instrument channels, balancing dexterity, workspace, and load-bearing needs (Yamamoto et al., 28 Apr 2025Zhu et al., 3 Feb 2026).

The TACTER and CPPR-dissector architectures establish benchmark implementations for clinical CPPRs, achieving dexterous, slender, and robust navigation in demanding surgical environments, and providing validated mechanical blueprints and control methodologies for future system development.