Simultaneous distributed localization and formation tracking control via matrix-weighted position constraints

This paper studies the problem of 3-D relative-measurement-based leader–follower simultaneous distributed localization and formation tracking control. The position information is only available to the leaders, and the followers have inter-agent relative measurements and communication with their neighbors. The key contribution is the development of a weight-matrix-based position constraint, which can make use of relative measurements such as bearing, ratio-of-distance, angle, distance, relative position and their mixture to describe the position relationship among each follower and its neighbors in 3-D space. A bearing-based distributed protocol is proposed for each follower to estimate its position and track its target position, which can drive the followers from their unlocalizable positions to localizable positions. The proposed algorithm is then extended to the case that both bearing and ratio-of-distance measurements are available, where the followers are localizable at all times if the followers and their neighbors are not collocated. In addition, the proposed method is also applicable to homogeneous or heterogeneous angle, distance, and relative position measurements as the ratio-of-distances or bearings can be obtained indirectly by these relative measurements. A remarkable advantage is that the proposed method can be implemented without persistently exciting motions. Some illustrative simulations are presented to verify the theoretical results.