Sensitivity Ellipsoids for Force Control of Magnetic Robots with Localization Uncertainty

The navigation of magnetic medical robots typically relies on localizing an actuated, intracorporeal, ferromagnetic body and back-computing a necessary field and gradient that would result in a desired wrench on the device. Uncertainty in this localization degrades the precision of force transmission. Reducing applied force uncertainty may enhance tasks such as in-vivo navigation of miniature robots, actuation of magnetically guided catheters, tissue palpation, as well as simply ensuring a bound on forces applied on sensitive tissue. In this paper, we analyzed the effects of localization noise on force uncertainty by using sensitivity ellipsoids of the magnetic force Jacobian and introduced an algorithm for uncertainty reduction. We validated the algorithm in both a simulation study and in a physical experiment. In simulation, we observed reductions in estimated force uncertainty by factors of up to 2.8 and 3.1 when using one and two actuating magnets, respectively. On a physical platform, we demonstrated a force uncertainty reduction by a factor of up to 2.5 as measured using an external sensor. Being the first consideration of force uncertainty resulting from noisy localization, this work provides a strategy for investigators to minimize uncertainty in magnetic force transmission.