Heung Wing Joseph Lee

Gangshan Jing, Guofeng Zhang, Heung Wing Joseph Lee et al.

This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between segments uniquely up to translations, rotations, scalings and reflections. The proposed angle rigidity theory is applied to the formation stabilization problem, where multiple single-integrator modeled agents cooperatively achieve an angle-constrained formation. During the formation process, the global coordinate system is unknown for each agent and wireless communications between agents are not required. Moreover, by utilizing the advantage of high degrees of freedom, we propose a distributed control law for agents to stabilize a target formation shape with desired orientation and scale. Simulation examples are performed for illustrating effectiveness of the proposed control strategies.

Gangshan Jing, Guofeng Zhang, Heung Wing Joseph Lee et al.

This paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of inter-agent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to determine a geometric shape in an arbitrarily dimensional space. A necessary and sufficient graphical condition for infinitesimal weak rigidity of planar frameworks is derived. As an application of the proposed weak rigidity theory, a gradient based control law and a non-gradient based control law are designed for a group of single-integrator modeled agents to stabilize a desired formation shape, respectively. Using the gradient control law, we prove that an infinitesimally weakly rigid formation is locally exponentially stable. In particular, if the number of agents is one greater than the dimension of the space, a minimally infinitesimally weakly rigid formation is almost globally asymptotically stable. In the literature of rigid formation, the sensing graph is always required to be rigid. Using the non-gradient control law based on weak rigidity theory, the sensing graph is unnecessary to be rigid for local exponential stability of the formation. A numerical simulation is performed for illustrating effectiveness of our main results.