Formation Control of Nonholonomic Multirobot Systems Over Robot Coordinate Frames and Its Application to LiDAR-Based Robots
Kazunori Sakurama, Chunlai Peng, Ryo Asai, Hirokazu Sakata, Mitsuhiro Yamazumi
Abstract
This article addresses a formation control problem for nonholonomic multirobot systems in robot coordinate frames. First, the nonholonomic constraint and measurement in robot coordinate frames are modeled with the Lie group theory on the special Euclidean group, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {SE}}_{d}$ </tex-math></inline-formula>. The control space under the nonholonomic constraint is defined as a subspace of the tangent space of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {SE}}_{d}$ </tex-math></inline-formula>, whereas the measurement in the robot coordinate frame is given as the group action of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {SE}}_{d}$ </tex-math></inline-formula>. Then, a gradient-based method is developed by using the projection of the gradient flow of an objective function onto the control space. By using the method with a clique-based objective function rather than edge-based ones, the designed formation controller is distributed and uses only measurement information in robot coordinate frames and has the best performance of the gradient-based distributed controllers. The proposed method is valid regardless of the dimension of the space, and therefore, it is applicable to not only automatic guided vehicles (AGVs) but also unmanned aerial vehicles (UAVs). Finally, the effectiveness of the method is demonstrated through simulations in 3-D space and an experiment by mobile indoor robots equipped with light detection and ranging (LiDAR).