Hybrid trajectory planning of two permanent magnets for medical robotic applications

Independent robotic manipulation of two large permanent magnets, in the form of the dual External Permanent Magnet (dEPM) system has demonstrated the possibility for enhanced magnetic control by allowing for actuation up to eight magnetic degrees of freedom (DOFs) at clinically relevant scales. This precise off-board control has facilitated the use of magnetic agents as medical devices, including catheter-like soft continuum robots (SCRs). The use of multiple robotically actuated permanent magnets poses the risk of collision between the robotic arms, the environment, and the patient. Furthermore, unconstrained transitions between actuation inputs can lead to undesired spikes in magnetic fields potentially resulting in unsafe manipulator deformation. This paper presents a hybrid approach to trajectory planning for the dEPM platform. This is performed by splitting the planning problem in two: first finding a collision-free physical path for the two robotically actuated permanent magnets before combining this with a path in magnetic space, which permits for a smooth change in magnetic fields and gradients. This algorithm was characterized by actuating each of the eight magnetic DOFs sequentially, eliminating any potential collisions and reducing the maximum undesired actuation value by 203.7 mT for fields and by 418.7 mT/m for gradients. The effect of this planned magnetic field actuation on a SCR was then examined through two case studies. First, a tip-driven SCR was moved to set points within a confined area. Actuation using the proposed planner reduced movement outside the restricted area by an average of 41.3%. Lastly, the use of the proposed magnetic planner was shown to be essential in navigating a multi-segment magnetic SCR to the site of an aneurysm within a silicone brain phantom.