Fig. 2: Demonstration of contact-free object navigation.

a, Two typical medical scenarios. (i) A medical instrument traverses through avoidance tissues to reach the target area for treatment. (ii) A catheter navigates through blood vessels, unable to avoid contact. (iii) An abstract representation of bypassing the avoidance object in (i). b, Video snapshots illustrating the principles of three different operating modes (Supplementary Video 3). (i) Using the existing method, the position of the bend in the soft tube changes as it moves within a uniform magnetic field. (ii),(iii) The proposed operating modes, in which the soft tube forms one or two bends in a uniform magnetic field, with the position of the bends remaining anchored during the movement. c, Video snapshots showing the soft tube reaching and retracting from the target position without contact, corresponding to the scenario in a(iii) (Supplementary Video 4). d, Partial parameters corresponding to the operation process in c. (i) The magnetization profile of the soft tube quantified using s_A and s_B. (ii) Changes in the magnetization profile during the operation process. e, Video snapshots of the soft tube deforming with two bends to bypass avoidance objects (Supplementary Video 4). f, Video snapshots showing the soft tube navigating through blood vessel models without contact (Supplementary Video 5). g, Ultrasound imaging of a soft tube navigating through the vasculature of an ex vivo porcine heart (Supplementary Video 6). h, The 3D dual-obstacle traversal under a single magnetic field (Supplementary Video 17). Scale bars, 5 mm.