Risk-aware Multi-robot Collaboration with Arrival Deadlines in Uncertain Environments

In this paper, we study the problem when a team of robots needs to reach a goal area subject to arrival deadlines, including the time-of-arrival (TOA) deadline and the time-difference-of-arrival (TDOA) deadline. The TOA deadline places an upper limit on the time that all robots arrive at the goal area while TDOA places an upper limit on the difference between the arrival time of any pair of robots. We first propose a formal definition of TOA risk and TDOA risk based on the probability that the TOA deadline and TDOA deadline are violated. Then we propose a new algorithm to derive the optimal communication strategy for the team of robots to minimize the TOA risk and the TDOA risk. In particular, the new algorithm first uses the Monte Carlo method to generate training datasets for a given communication strategy. Then two neural networks are trained to approximate the function that describes how the TOA risk and TDOA risk are related to the communication strategy and the TOA/TDOA deadlines. Obtaining the two neural network models allows the subsequent computation of gradient to optimize the communication topology for the minimization of the TOA risk and TDOA risk. Finally, simulation examples are presented to illustrate the effectiveness of the proposed approach in obtaining optimized communication topologies that are close to the ground truth.