From Fourier topology representation to optimal robot: evolution of an ultrahigh performance XYθ_z nanopositioner

XYθ_z nanopositioners are robots that can deliver precise translations along the X- and Y-axes and rotations about the Z-axis via elastic deformation of their compliant bodies. Although the performance of these robots is critical across a vast range of microscopy technologies, biomedical research and industrial applications, existing XYθ_z nanopositioners are unable to optimize their workspace, disturbance rejection capabilities, speed and positioning resolutions. This is because their stiffness ratios are limited to 0.5-248 and their mechanical bandwidths are restricted to 70 Hz when they can deflect more than 2 mm. Here we use a unique combination of kinematic analyses and evolutionary algorithms to determine our robot's optimal geometry in which its structural topology is represented by Fourier basis functions. Our synthesis method has evolved an optimal XYθ_z nanopositioner that has stiffness ratios, mechanical bandwidth, workspace and positioning resolutions of 741-869, 123 Hz, 5.8 mm $\times$ 5.8 mm $\times$ 6° and 13 nm $\times$ 14 nm $\times$ 1.3 μrad, respectively. Our XYθ_z nanopositioner's workspace to positioning resolutions ratio is 4.9-2.31 $\times$ 10¹¹ folds higher than existing similar robots, while its disturbance rejection capability is 1142-2.10 $\times$ 10¹⁷ folds greater than those with a large workspace.