3-D relative localization for multi-robot systems with angle and self-displacement measurements

Inter-robot relative localization (including positions and orientations) is necessary for multi-robot systems to execute collaborative tasks. Realizing relative localization by leveraging inter-robot local measurements is a challenging problem, especially in the presence of measurement noise. Motivated by this challenge, in this paper we propose a novel and systematic 3-D relative localization framework based on inter-robot interior angle and self-displacement measurements, which are accessible from existing sensors. Initially, we propose a linear relative localization theory comprising a distributed linear relative localization algorithm and sufficient conditions for localizability. According to this theory, robots can determine their neighbors’ relative positions and orientations in a purely linear manner, relying solely on angle and self-displacement measurements. Subsequently, in order to deal with measurement noise, we present an advanced maximum a posterior (MAP) estimator by addressing three primary challenges existing in the MAP estimator. First, it is common to formulate the MAP problem as an optimization problem, whose inherent non-convexity can result in local optima when finding the optimal solution. To address this issue, we reformulate the linear computation process of the linear relative localization algorithm as a weighted total least squares (WTLS) optimization problem on manifolds. The optimal solution of the WTLS problem is more accurate and closer to the true values, which can then be used as initial values when solving the optimization problem associated with the MAP problem, thereby reducing the risk of falling into local optima. The second challenge is the lack of knowledge of the prior probability density of the robots’ relative positions and orientations at the initial time, which is required as an input for the MAP estimator. To deal with it, we combine the WTLS with a neural density estimator (NDE). Third, to prevent the increasing size of the relative positions and orientations to be estimated as the robots continuously move when solving the MAP problem, a marginalization mechanism is designed, which ensures that the computational cost remains constant. Indoor and outdoor experiments of multiple drones’ relative localization are performed to verify the effectiveness of the proposed framework.