Biological systems are collections of discrete molecular objects that move around and collide with each other. Cells carry out elaborate processes by precisely controlling these collisions, but developing artificial machines that can interface with and control such interactions remains a significant challenge. DNA is a natural substrate for computing and has been used to implement a diverse set of mathematical problems(1-3), logic circuits(4-6) and robotics(7-3). The molecule also interfaces naturally with living systems, and different forms of DNA-based biocomputing have already been demonstrated(10-13). Here, we show that DNA origami(14-16) can be used to fabricate nanoscale robots that are capable of dynamically interacting with each other(17,18) in a living animal. The interactions generate logical outputs, which are relayed to switch molecular payloads on or off. As a proof of principle, we use the system to create architectures that emulate various logic gates (AND, OR, XOR, NAND, NOT, CNOT and a half adder). Following an ex vivo prototyping phase, we successfully used the DNA origami robots in living cockroaches (Blaberus discoidalis) to control a molecule that targets their cells.