Multi-Section Magnetic Soft Robot with Multirobot Navigation System for Vasculature Intervention

Abstract

Magnetic soft robots have recently become a promising technology that has been applied to minimally invasive cardiovascular surgery. This paper presents the analytical modeling of a novel multi-section magnetic soft robot (MS-MSR) with multi-curvature bending, which is maneuvered by an associated collaborative multirobot navigation system (CMNS) with magnetic actuation and ultrasound guidance targeted for intravascular intervention. The kinematic and dynamic analysis of the MS-MSR's telescopic motion is performed using the optimized Cosserat rod model by considering the effect of an external heterogeneous magnetic field, which is generated by a mobile magnetic actuation manipulator to adapt to complex steering scenarios. Meanwhile, an extracorporeal mobile ultrasound navigation manipulator is exploited to track the magnetic soft robot's distal tip motion to realize a closed-loop control. We also conduct a quadratic programming-based optimization scheme to synchronize the multi-objective task-space motion of CMNS with null-space projection. It allows the formulation of a comprehensive controller with motion priority for multirobot collaboration. Experimental results demonstrate that the proposed magnetic soft robot can be successfully navigated within the multi-bifurcation intravascular environment with a shape modeling error $3.62\pm {1.28}^{\circ }$ and a tip error of $1.08\pm 0.45\mathrm{mm}$ under the actuation of a CMNS through in vitro ultrasound-guided vasculature interventional tests.

Fig. 1.

(A) Schematic illustration of MS-MSR in US-guided cardiovascular intervention, which is constituted of 2 cannulas with integrated tip magnets. (B) Design details of CMNS. MS-MSR is steered into the patient’s body through the main artery of the thigh by the corresponding actuation and tracking system. (a) The mobile US navigation manipulator (MUNM) with US probe contacts the body of the patient to enable real-time tracking of the MS-MSR’s tip. (b) The mobile magnetic actuation manipulator (MMAM) utilizes a UR5e robotic manipulator to mount an external mobile magnet (EMM). (c) The mobile linear advancement manipulator (MLAM) is advancing MS-MSR inside the artery. (C) The surgeon could remotely control the entire surgical system through the US monitor.

Fig. 2.

Modeling of the kinematics and dynamics of MS-MSR under different telescoping states based on the Cosserat rod theory. (A) Design details (including cross-section) of the deformation of 2 PDMS tubes under the external magnetic field B_m. (B) Deflection kinematics of MS-MSR w.r.t. the arc length s considering the external loads and boundary conditions. The forces and moments acting on an infinitesimal segment of MS-MSR: 2 tubes (right top) and single tube (left bottom). (C) Actual photo of MS-MSR under the effect of the external magnetic field. (D) Comparisons of FEM results and numerical computation results of MS-MSR under different magnetic field strengths in 2 states: single tube (left) and 2 tubes (right).

Fig. 3.

Modeling of the interaction between MMAM and MS-MSR considering the dynamic motion. (A) Pose of MMAM w.r.t. the preplanned trajectory of MS-MSR. (B) Effective phase for actuating the MS-MSR’s steering motion considering the optimized pose planning of MMAM, which is classified into 4 scenarios: Scenario I, MS-MSR is targeted for steering into a smaller bifurcation; Scenario II, MMAM rotates in a velocity of ${\stackrel{·}{\varphi }}_m$, while Tube-I is steered forward; Scenario III, MS-MSR is targeted for steering into a larger bifurcation; Scenario IV, MMAM rotates in a velocity of $-{\stackrel{·}{\varphi }}_m$, while Tube-I is steered forward.

Fig. 4.

The collaborative scheme of CMNS. (A) Kinematic representation of the dual-manipulator MMAM and MUNM. (B) Whole system of CMNS with the EE of each manipulator tracked using the external tracking system via the marker to calibrate them with the global frame $\left\{\mathcal{G}\right\}$. (C) Four kinematic collaborative scenarios of MMAM and MUNM during the interventional procedure. (D) US tracking imaging plane updating through the endovascular intervention of MS-MSR along with the movement of MUNM.

Fig. 5.

The control block diagram of CMNS and MS-MSR using the optimization method. This controller addresses the collaboration motions of the multirobot system with constraints.

Fig. 6.

Testing of kinematic and dynamic responses of MS-MSR with free-bending configuration. (A) Experimental setup with NDI Aurora tracking system to perform the dynamic tip following test with the Tube-II base fixed at ${\mathbf{p}}_2\left(s_2=0\right)={\left[0,0,0\right]}^T$. (B) Dynamic performance of MS-MSR following preset tip-space trajectories of a circle w/ (right) and w/o (left) optimization scenario. (C) Dynamic performance of MS-MSR following preset tip-space trajectories of letter “W” under w/ (right) and w/o (left) optimization scenario. (D to F) Single-curvature bending (SCB): Quasi-static SCB scenario with different bending angle of MS-MSR by the magnetic field ${\mathbf{B}}_m$ provided by MMAM with different tube length, i.e., $\left[\mathrm{\Delta }{l}_1=0,\mathrm{\Delta }{l}_2=100\mathrm{mm}\right]$ and $\left[\mathrm{\Delta }{l}_1=60\mathrm{mm},\mathrm{\Delta }{l}_2=60\mathrm{mm}\right]$. (G to I) Multi-curvature bending (MCB): Quasi-static multiple curvature bending scenario of MS-MSR with different tube length, i.e., $\left[\mathrm{\Delta }{l}_1=80\mathrm{mm},\mathrm{\Delta }{l}_2=60\mathrm{mm}\right]$ and $\left[\mathrm{\Delta }{l}_1=80\mathrm{mm},\mathrm{\Delta }{l}_2=70\mathrm{mm}\right]$.

Fig. 7.

Demonstration of autonomous intervention and navigation capabilities of MS-MSR through a 3D tortuous path (13 rings with the shape of the letter “M”). (A) Experimental setup with MMAM and MS-MSR with a large orientation difference between adjacent rings. (B) Specifications of tests and results. (C) Snapshots of the ring-steering tests: The motion of MS-MSR’s tip ${\mathbf{p}}_i\in {\mathrm{ℝ}}^3$ is the superposition of bending and steering, actuated by the magnetic field ${\mathbf{B}}_m$ provided by MMAM and insertion motion by MLAM. The magnetic robotic soft robot is required to pass through the center of the ring set ${\mathbf{p}}_i^{\mathit{ref}}$ with different central positions, heights, and orientations. (D) Final steering results of MS-MSR.

Fig. 8.

In vitro intravascular testing under magnetic actuation and US tracking of MS-MSR with soft anthropomorphic phantom. (A) Experimental setup for multirobot actuation and tracking system. (B) Real-time tip tracking (yellow rectangle) of US probe (16HL7) with different tracking frames with the selected US parameters: thermal index score (TIS) < 0.4, mechanical index (MI) of 0.4, gain settings (Gn) of 50, frequency of 7 to 16 MHz, and depth of 5.0 cm. (C) The trajectory following scenario of 2 bifurcation-selection of MS-MSR. (D) Intraoperative shape estimation using the proposed optimal Cosserat rod modeling compared with other beam theories. (E) The error color map comparisons of the proposed method with the optimization.

Fig. 9.

The performance of the QP-based task-space multi-objective controller for CMNS to navigate MS-MSR. (A) Motion snapshots of CMNS with MMAM (left) and MUNM (right). (B) QP-based control method under the reference trajectory of EE task-space position tracking of MMAM (top) and MUNM (middle). The reference force tracking of MUNM (bottom). Unstable tracking would occur during the scanning.