Distance + angle rigid formation control for multi-agent systems: nonholonomic kinematic realization and configuration preservation

Abstract

In multi-robot systems, relative-position measurements provide distance and angle information for characterizing formation geometry. Simultaneous distance + angle constraints can uniquely specify formation geometry for multi-agent systems (MAS) with single-integrator kinematics. However, extending the corresponding control methods to more realistic nonholonomic kinematic models may lead to control singularities or convergence failures due to the mismatch between task-space geometric gradients and admissible motion directions. To address this issue, this paper develops a distance + angle rigid formation controller for nonholonomic MAS. By employing a geometric offset mapping and a nonsingular decoupling transformation, the rigidity-based task-space command is mapped into kinematically admissible linear and angular velocities while preserving the original rigidity formulation. On this basis, the asymptotic convergence of the distance and angle errors and the boundedness of the relative adapted-point states are established through Lyapunov-based cascade analysis and forward-invariance arguments. The proposed controller is validated through simulations and multi-robot experiments, demonstrating its practical applicability to nonholonomic mobile robots. By incorporating global geometric constraints at the formation topology level, the proposed method helps prevent formation deformation and configuration instability often observed in path-tracking coordination methods, including APF-based approaches, thereby supporting complex multi-modal navigation scenarios. Moreover, the controller requires neither the pre-training associated with reinforcement learning nor the online optimization required by model predictive control, making it well suited to embedded robotic platforms with limited computational and memory resources.