Microscopic robots exhibit efficient locomotion in liquids by leveraging fluid dynamics and chemical reactions to generate force asymmetry, thereby enabling critical applications in photonics and biomedicine. However, achieving controllable locomotion of such robots on terrestrial surfaces remains challenging because fluctuating adhesion on nonideal surfaces disrupts the necessary asymmetry for propulsion. Here, we present a microscopic robot composed of three-dimensional nanomembranes, which navigate diverse terrestrial surfaces with omnidirectional motion. We propose a general mechanism employing nonreciprocal shape morphing to generate stable asymmetric forces on surfaces. This nonreciprocal shape morphing is realized through a laser-actuated vanadium dioxide nanomembrane, leveraging the material's inherent hysteresis properties. We demonstrate that these robots can be fabricated in various shapes, ranging from simple square structures to bioinspired "bipedal" helical designs, enabling them to directionally navigate challenging surfaces such as paper, leaves, sand, and vertical walls. Furthermore, their omnidirectional motion facilitates applications in microassembly and microelectronic circuit integration. Additionally, we developed an artificial intelligence control algorithm based on reinforcement learning, enabling these robots to autonomously follow complex trajectories, such as tracing the phrase "hello world". Our study lays a theoretical and technological foundation for microscopic robots with terrestrial locomotion and paves a way for microscopic robots capable of operating on surfaces for advanced nanophotonic, microelectronic, and biomedical applications.