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Directional dithering of a laser beam potentially limits the detection accuracy of a laser triangulation displacement probe. A theoretical analysis indicates that the measurement accuracy will linearly decrease as the laser dithering angle increases. To suppress laser dithering, a scheme for reduction of the influence of laser beam directional dithering in a laser triangulation displacement probe, which consists of a collimated red laser, a laser beam pointing control setup, a receiver lens, and a charge-coupled device, is proposed in this paper. The laser beam pointing control setup is inserted into the source laser beam and the measured object and can separate the source laser beam into two symmetrical laser beams. Hence, at the angle at which the source laser beam dithers, the positional averages of the two laser spots are equal and opposite. Moreover, a virtual linear function method is used to maintain a stable average of the positions of the two spots on the imaging side. Experimental results indicate that with laser beam pointing control, the estimated standard deviation of the fitting error decreases from 0.3531 mm to 0.0100 mm, the repeatability accuracy can be lowered from ±7 mm to ±5 sans-serifμnormalm, and the nonlinear error can be reduced from ±6 % FS (full scale) to ±0.16 % FS.

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The fuel-optimal control problem of soft landing becomes a significant challenge due to the highly irregular gravitational field of an asteroid. An indirect method is used to deal with this fuel-optimal control problem. The difficult bang-bang control problem caused by the indirect method is solved through an improved fast homotopic approach. To validate the advanced homotopic method, the landing site is selected in a region where the gravitational field is especially irregular. The results show that this method is effective for the fuel-optimal control problem in an irregular gravitational field. Moreover, the trajectory designed with the fuel-optimal control is taken as a nominal descent trajectory for a sliding mode control. Monte Carlo simulations show that the desired soft landing can be achieved by tracking the fuel-optimal trajectory.