Development of an untethered ultrasonic robot with fast and load-carriable movement imitating rotatory galloping gait

(i) At t = nTp [where n is an integer and Tp (= 1/f) is the period], the LF’s longitudinal vibration velocity and bending vibration displacement reach the peak values along the −x and +z axes, respectively. In the meantime, the RF’s longitudinal vibration velocity and bending vibration displacement are maximal in the +x and −z axes, respectively.(ii) At t = (n + 1/4)Tp, the longitudinal vibration velocities and the bending vibration displacements of the LF and RF are equal to zero. (iii) At t = (n + 1/2)Tp, the LF’s longitudinal vibration velocity and bending vibration displacement are maximal in the +x and −z axes, respectively; while the RF’s longitudinal vibration velocity and bending vibration displacement are maximal in the −x and +z axes, respectively.     (vi) At t = (n + 3/4)Tp, the state is inverse to that in step (ii).     When the transducer is used in the self-moving actuator, it is accelerated alternatively in the steps (i) and (iii) because the longitudinal vibration velocity exceeds the actuator’s speed, while it is decelerated in the other steps. Since the decelerating effect offsets the accelerating effect in a period, the actuator moves with almost constant speed. The operating sequences correspond to the quadruped’s rotatory galloping gait [see Fig. 4(b)]. At θ = −90°, the sequence becomes (i)→(vi)→(iii)→(ii) and the actuator moves in the opposite direction.