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 a physical action in a physical environment occupied by the robotic device; in response to receiving the instruction, determining, by the one or more processors, multiple estimated trajectories of one or more physical components of the robotic device, wherein the multiple estimated trajectories are multiple trajectories along which the one or more physical components are estimated to move as the robotic device performs the physical action, and wherein the multiple estimated trajectories are based on one or more parameters of the one or more physical components; associating, by the one or more processors, respective probabilities to the robotic device moving along the multiple estimated trajectories based on one or more parameters of the one or more physical components; determining, by the one or more processors, a virtual representation of a space that the robotic device is estimated to occupy in the physical environment while performing the physical action, wherein the space is determined based on the multiple estimated trajectories of the one or more physical components of the robotic device and further based on the respective probabilities associated to the robotic device moving along the multiple estimated trajectories; and causing, by the one or more processors, at least one projecting device communicatively linked to the computing system to project, into the physical environment, an indication of a location of the space in the physical environment, the indication visually depicting the determined multiple estimated trajectories. receiving, by one or more processors of the computing system, an instruction requesting that a robotic device perform a physical action in a physical environment occupied by the robotic device; in response to receiving the instruction, determining, by the one or more processors, multiple estimated trajectories of one or more physical components of the robotic device, wherein the multiple estimated trajectories are multiple trajectories along which the one or more physical components are estimated to move as the robotic device performs the physical action, and wherein the multiple estimated trajectories are based on one or more parameters of the one or more physical components; associating, by the one or more processors, respective probabilities to the robotic device moving along the multiple estimated trajectories based on one or more parameters of the one or more physical components; determining, by the one or more processors, a virtual representation of a space that the robotic device is estimated to occupy in the physical environment while performing the physical action, wherein the space is determined based on the multiple estimated trajectories of the one or more physical components of the robotic device and further based on the respective probabilities associated to the robotic device moving along the multiple estimated trajectories; and causing, by the one or more processors, at least one projecting device communicatively linked to the computing system to project, into the physical environment, an indication of a location of the space in the physical environment, the indication visually depicting the determined multiple estimated trajectories.