The forward kinematics of the Stewart–Gough platform is vital for high-precision positioning and sensing in six degrees of freedom. In this paper, the solving of forward kinematics is converted to searching for the best posture corresponding to the input outrigger length vectors by inverse kinematic calculation. The simulated annealing (SA) process is embedded into particle swarm optimization (PSO) to improve the convergence speed and overcome the local convergence. The proposed SA–PSO algorithm not only accelerates the convergence speed but also improves the reliability and success rate. After the optimization of algorithm parameters, the success rate of the SA–PSO for random outrigger length vector input is steadily above 99.9% while the results of PSO is between 93% and 100%. In the workspace simulation, the average iteration number of the proposed algorithm is reduced from 146.6 to 122.7, meanwhile, the success rate of SA–PSO is 99.992%, much higher than the 93.805% of PSO. Compared with the traditional Newton–Raphson method, the SA–PSO method has a higher success rate and is less time consuming. Finally, a physical experiment is conducted on a six-degree-of-freedom platform, revealing that the given algorithm is reliable and accurate.

As the loading space in rockets and mirror fabrication technology is limited, optical systems in space cannot have large optical apertures. However, the successful launch and excellent performance of the James Webb Telescope indicate that segmented mirrors can help realize large-aperture optical systems in space, owing to the fold–unfold mechanism in the telescope. However, all segments in the segmented mirror should be co-phased so that it is equivalent to a monolithic mirror. The co-phasing problem is significant in optical systems in space because of their low error tolerance. Owing to some accident factors, the piston error can be more than 1 mm after the unfolding process. Here, we introduced a multiwavelength interference method and dynamic adjusting strategy, aiming to solve the two problems of co-phasing: large detection range (~2 mm) and high detection precision (<1/20λ). Numerical simulations were performed, and a 400 mm aperture-segmented spherical mirror system was used to verify this method. The original piston error was set to 1 mm, after the coarse co-phasing, and the residual piston error to less than half the wavelength of the monochromatic light; for fine co-phasing, the achieved detection precision was approximately 1.2 nm.

An active optical system with three segmented mirrors was proposed to verify the co-focus and co-phase progress. In this system, a kind of large-stroke and high-precision parallel positioning platform was specially developed to help support the mirrors and reduce the error between them, which can move in three degrees of freedom out of plane. The positioning platform was composed of three flexible legs and three capacitive displacement sensors. For the flexible leg, a kind of forward-type amplification mechanism was specially designed to amplify the displacement of the piezoelectric actuator. The output stroke of the flexible leg was no less than 220 μm and the step resolution was up to 10 nm. Further, a linear model was established to identify the amplification ratio between the actuator and the flexible leg, which can increase the precision of the positioning platform. Moreover, three capacitive displacement sensors with a resolution of 2.5 nm were symmetrically installed in the platform to accurately measure the position and attitude of the platform. To improve the stability and precision of the platform, particle swarm optimization algorithm was applied to identify the control matrix, which can help the platform achieve ultra-high precision positioning. The results showed that the theoretical matrix parameters had a maximum deviation of 5.67% from the experimental ones. Finally, abundant experiments verified the excellent and stable performance of the platform. The results proved that while bearing the heavy mirror, which is no more than 5 kg, the platform can realize a 220 μm translation stroke and 2.0 mrad deflection stroke, with a high step resolution of 20 nm and 0.19 μrad. These indicators can perfectly cater to the requirements of the proposed segmented mirror system’s co-focus and co-phase adjustment progress.

Presently, the segmented mirror is the mainstream development direction of large-aperture telescopes. The key problem affecting the performance of segmented mirror telescopes concerns the co-phase of the segments. The segments’ co-phase includes the fine phasing stage with high detection accuracy requirements and a small measurable range, and the coarse phasing stage with relatively high detection accuracy requirements and a large measurable range. For interferometry, the required accuracy of the transition from the coarse phasing stage to the fine phasing stage is half of the measured wavelength (~300 nm). In this study, a piston measure method based on the wavefront data of the interference measurement results of multiple different wavelengths is proposed. The simulation results show that the method can achieve a measurement accuracy of more than 300 nm in a large range of 1 mm. The experimental results show that the method can achieve a more-than-300-μm measurable range and approximately 1.5 μm detection accuracy under laboratory conditions; this method has advantages in terms of the measured range and speed and is suitable for the coarse phasing stage.