Angle-based Localization and Rigidity Maintenance Control for Multi-Robot Networks

This letter proposes a novel distributed bearing-based pose estimator for time-varying multi-robot systems. The method uses angles computed from body-frame bearings to estimate the robots' positions in $\mathbb{R}^3$ without knowledge of their orientations. The orientations in $\mathrm{SO}(3)$ are recovered from the estimated positions, the bearings, and the bearing derivatives. The proposed observer only requires the (directed) sensing topology to be angle-rigid, a weaker condition than the commonly used ones like bearing rigidity. Local uniform exponential stability of the proposed observer is established under the assumption of persistently exciting motions for a subset of robots. Simulations are presented and discussed to evaluate the scheme's effectiveness and practicality.

Communication graph rigidity is a fundamental requirement in many multi robot formation control approaches. However, ensuring and maintaining a rigid communication topology becomes challenging in practice due to limited sensing ranges and dynamic operating conditions. This paper provides a method for achieving an inter robot collision free, rigid time varying communication graph, where communication links are established or broken according to limited sensing ranges, without assuming an initial rigid graph. In addition, the proposed approach guarantees the realization of a rigid graph for heterogeneous nonlinear multi robot systems. A computationally lean, distributed quadratic optimization-based controller is developed for a leader follower architecture, acquiring rigidity based on hierarchical second-order consensus among robots. Follower agents do not require global absolute positions of any agent, including their own. The proposed method is validated through both simulations and hardware experiments in a motion-capture environment, demonstrating reliable performance under the limited sensing capabilities of individual robots.

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. 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. 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. Firstly, it is common to formulate the MAP problem as an optimization problem, whose inherent non-convexity can result in local optima. 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, 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). Thirdly, 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.