Highly-time-resolved and precise tracking of position, velocity, and acceleration is urgently required when highly dynamic legged robots are walking, trotting, and jumping. Frequency-modulated continuous-wave (FMCW) laser ranging is able to provide precise measurement in short distance. However, FMCW light detection and ranging (LiDAR) suffers from a low acquisition rate and poor linearity of laser frequency modulation in wide bandwidth. A sub-millisecond-scale acquisition rate and nonlinearity correction in the wide frequency modulation bandwidth have not been reported in previous studies. This study presents the synchronous nonlinearity correction for a highly-time-resolved FMCW LiDAR. The acquisition rate of 20 kHz is obtained by synchronizing the measurement signal and the modulation signal of laser injection current with a symmetrical triangular waveform. The linearization of laser frequency modulation is conducted by resampling of 1000 intervals interpolated in every up-sweep and down-sweep of 25 µs, while measurement signal is stretched or compressed in every period of 50 µs. The acquisition rate is demonstrated to be equal to the repetition frequency of laser injection current for the first time to the best of authors’ knowledge. This LiDAR is successfully used to track the foot trajectory of a jumping single-leg robot. The high velocity up to 7.15 m/s and high acceleration of 365 m/s2 are measured during the up-jumping phase, while heavy shock takes place with high acceleration of 302 m/s2 as the foot end strikes the ground. The measured foot acceleration of over 300 m/s2, which is more than 30 times gravity acceleration, is reported on a jumping single-leg robot for the first time.

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