Electrostatic actuators provide a promising approach to creating soft robotic sheets, due to their flexible form factor, modular integration, and fast response speed. However, their control requires kilo-Volt signals and understanding of complex dynamics resulting from force interactions by on-board and environmental effects. In this work, we demonstrate an untethered planar five-actuator piezoelectric robot powered by batteries and on-board high-voltage circuitry, and controlled through a wireless link. The scalable fabrication approach is based on bonding different functional layers on top of each other (steel foil substrate, actuators, flexible electronics). The robot exhibits a range of controllable motions, including bidirectional crawling (up to ~0.6 cm/s), turning, and in-place rotation (at ~1 degree/s). High-speed videos and control experiments show that the richness of the motion results from the interaction of an asymmetric mass distribution in the robot and the associated dependence of the dynamics on the driving frequency of the piezoelectrics. The robot's speed can reach 6 cm/s with specific payload distribution.