To solve the problem of small objects with low gravitational force and large temperature difference, we propose to use ultrasonic drill as an anchoring tool and adopt a combination of fuzzy control and constant current control strategy to achieve ultrasonic drill drilling and anchoring under low drilling pressure and high and low temperature environment conditions. The piezoelectric-driven ultrasonic drill converts high-frequency electrical energy into high-frequency mechanical vibration to drive the drilling tool to break the rock at high frequency, which has the significant advantage of very low drilling pressure and is especially suitable for drilling and anchoring operations of small bodies with weak gravity. The resonant vibration control algorithm of ultrasonic drill is studied for the drive of ultrasonic drill. Firstly, the equivalent circuit model of the ultrasonic drill transducer is established, and the impedance characteristics, load characteristics, temperature characteristics and hysteresis characteristics of the transducer are studied on the basis of the equivalent model. Secondly, the resonant frequency identification algorithm, resonant frequency tracking algorithm and constant current control algorithm are developd according to the working characteristics of ultrasonic drill. The frequency tracking algorithm based on recursive least squares estimation and the frequency tracking algorithm based on fuzzy control are studied for the resonant frequency tracking algorithm. The actual control performance of these algorithms is compared and analyzed. Finally, drilling tests are conducted under normal temperature and pressure conditions, as well as high and low temperature environments. The test results show that the designed resonant control algorithm can achieve stable driving of the ultrasonic drill under different temperature environments and different drilling object conditions. The research results show that the fuzzy control and constant current control methods proposed in this paper can effectively achieve efficient drilling under low drilling pressure and different temperatures.