1. A method performed by a computing system, the method comprising: receiving, by one or more processors of the computing system, an instruction requesting that a robotic device perform, in an environment, a physical action involving a component of the robotic device; in response to receiving the instruction, the one or more processors determining multiple estimated trajectories of the component of the robotic device, wherein the multiple estimated trajectories are multiple trajectories along which the component is estimated to move in the environment as the robotic device performs the physical action; the one or more processors associating respective confidence scores to the robotic device moving along the multiple estimated trajectories; the one or more processors selecting, from the multiple estimated trajectories, a set of estimated trajectories having confidence scores that exceed a predetermined threshold; based on the selected set of estimated trajectories, the one or more processors determining a virtual safety cage representing a space that the robotic device is estimated to occupy in the environment while performing the physical action; and the one or more processors providing, into the environment, an indication of a location of the virtual safety cage.