4. Experimental Section

4.1. Locomotion experiments

In each locomotion test, the robot was placed in a clear polycarbonate circular channel (inner diameter [ID]: 19 mm) with the robot center directly below a cylindrical actuator magnet (DY0X0-N52, K&J Magnetics) at a set vertical actuation offset distance (ya). Next, the actuator magnet, whose axis of rotation was perpendicular to the robot’s path and whose initial orientation was north pointing in the +x direction, was rotated at a fixed frequency (ω = 2 Hz), causing the robot to take steps at the same frequency and travel in the +x direction for 60 seconds. To demonstrate less-favorable locomotion and to maintain consistency with recent literature,(Steiner et al., 2022) the direction of robot locomotion was away from the actuator magnet (i.e., away from x = 0). Five trials were performed for each robot across ya offsets from 9 to 15 cm. Displacement was measured by tracking the center of the robot from a video recording of the test (Canon EOS 80D, frame rate: 29.97 fps). Displacement was calculated every 15 frames, or approximately one measurement per step. The initial speed was calculated by dividing the total displacement in the first ten steps by the number of steps. For variable-mass experiments, weight was added inside the rigid compartment of MR-LFs. Variability in locomotion test results could be due to several factors, including slight variations in robot starting position and magnet rotation frequency, and minor fabrication defects. To reduce potential data bias from possible imperfections in the robot’s feet, the channel and robot were rotated about the x-axis between trials so different portions of the foot were in contact with the floor.