Motion Planning with Secrecy

In this paper, we introduce the problem of motion planning with secrecy guarantees. A robot is tracking a desired trajectory, which is transmitted on-line by a planner, e.g. a base station or a mobile station. The communication between the robot and the planner is organized in packets and takes place over a wireless channel, which is susceptible to eavesdropping attacks. Our goal is to design secure communication codes in order to encode the trajectory information and hide it from any eavesdroppers. Meanwhile, the robot should be able to recover the trajectory and the planner should be able to estimate the robot's motion. We introduce a novel coding scheme that creates secrets between the robot and the planner based on i) the randomness of the robot's motion and ii) the imperfection of the communication channel. We show that every time the planner receives the corresponding packet while the eavesdropper misses it, a new secret is created, which can be used as a key to encode the information about the motion intent. If the motion-planning is random enough, one occurrence of this event makes the eavesdropper lose track of the trajectory; even if the eavesdropper has unlimited computational power. We apply our framework to the problem of way-point tracking, where the robot should visit some target positions one after the other. We illustrate the theoretical results in simulations.