Traditional vehicle-mounted supporting platforms have large shaking amounts and are difficult to meet the requirements of high and non-landing measurement accuracy of the vehicle-mounted optoelectronic theodolite. We design a novel supporting platform with the truss skinned structure based on a discrete topology optimization method with considering the demand for high stability, light weight, and easy manufacturing. The vehicle-mounted theodolite characterized by stronger mobility, faster, and more convenient deployment processes, has been the major trend in test ranges. The supporting platform provides a new measurement reference for vehicle-mounted theodolite. Therefore, the stability of the supporting platform is an important factor enabling theodolite to achieve high-accuracy measurement. Due to the limited size, weight conditions, and dynamic characteristics of theodolite, the platform stability is consistently low. Generally, the shaking amount is over 40″, even up to hundreds of arc seconds. Some appropriate correction methods can be employed to improve the pointing accuracy of the theodolite, but the timeliness is limited. As a result, it is necessary to design a kind of supporting platform featuring high stiffness, good dynamic characteristics, and light weight.

A truss discrete topology optimization method is adopted to design the supporting platform. The platform frame is established according to its basic shape, and the design domain and non-design domain of the structure are also determined according to the finite element grids. The solid isotropic material with penalization (SIMP) interpolation model is adopted in the topology optimization. The minimum flexibility is set as an objective function and the volume fraction as a constraint. The topology optimization layout is then obtained (Fig. 3). Based on the above topology optimization results, a detailed model of the optimized platform system, which consists of theodolite, platform, and lifting legs, is developed for simulation (Fig. 5). The platform truss structure is discretized by the truss element. The theodolite has a mass of 30000 N, and the maximum angular accelerations of 20 (°)/s², which are set as the static load and dynamic load in the analysis respectively. The static and model properties of the supporting platform are simulated successfully, and the supporting platform is also manufactured. The stability experiment is then carried out.

Simulations are conducted to determine the stability of the optimized platform. The mass of the optimized platform is reduced by 411.1 kg to ensure the support stiffness and dynamic characteristics (Table 1). The deformations of the optimized platform under gravity loading are obtained (Fig. 6). The maximum deformation is 0.142 mm, which occurs on the position fixed by the theodolite. The surface tilt of the position is 3.9″. The static deformations under the torques in the direction of the length, width, and height of the platform are also acquired (Fig. 7). The maximum amount of platform shaking is 4.3″, with the sound performance of the platform to resist torque load. The first four vibration mode shapes for the platform system are obtained (Fig. 8). The first order frequency is 19.2 Hz. Square steel tubes are welded to the trusses. The upper and lower platform surfaces are fitted with metal skins for protection and as mounting bases for theodolite and legs. The platform weighs 2000 kg, with the length of 3150 mm, width of 1830 mm, and height of 300 mm. We also set up the experimental apparatus, which consists of the theodolite, the platform, four lifting legs, a dual-axis collimator, and a collimator target (Fig. 9). The theodolite works on the platform and each lifting leg is mounted separately on all four corners of the platform. The legs utilize servo motors and CAN communication technology to achieve automatic leveling with the help of a program-controlled computer. The theodolite does sinusoidal motion at the set angular accelerations from 0.5 (°)/s² to 20 (°)/s². The response accelerations for the basis of theodolite are 0.008-0.55 m/s² (Figs. 11 and 12). The maximum amplitude is 0.22 m/s² when the frequency is 21.7 Hz. There is no obvious resonance response that affects the tracking performance of the theodolite. The shaking amplitude of the platform is measured by an inclination sensor, with a maximum amount of 7.2″. The pointing error of vehicle-mounted optoelectronic theodolite is also measured, with an accuracy of 13.8″ at azimuth and 14.9″ at pitch. The supporting platform has a high support stability.

The stability of the vehicle-mounted supporting platform is an important factor enabling theodolite to achieve high measurement accuracy. In our paper, a novel supporting platform with the truss skinned structure is designed based on the discrete topology optimization method. The mass of the optimized platform is reduced by up to 26.5% to ensure the support stiffness and dynamic characteristics. The stability experiment of the supporting platform is carried out. The response accelerations for the basis of theodolite are 0.008-0.55 m/s² in the whole angle acceleration range from 0.5 (°)/s² to 20 (°)/s². The peak response acceleration appears from 20 Hz to 21 Hz. There is no obvious resonance response that affects the tracking performance of the theodolite. The shaking amplitude of the platform is measured by an inclination sensor. The maximum amount of platform shaking is 7.2″. The supporting platform has a high support stability and has been applied to a vehicle-mounted photoelectric theodolite. The real-time and non-landing pointing accuracy is better than 15″. It is suitable for vehicle-mounted optoelectronic theodolite to achieve high and non-landing measurement accuracy.