Hybrid Controller based on Null Space and Consensus Algorithms for Mobile Robot Formation

This work presents a novel hybrid control approach based on null space and consensus algorithms to solve the scalability problems of mobile robot formation and improve leader control through multiple control objectives. In previous works, the training of robots based on the null space requires a rigid training structure based on a geometric shape, which increases the number of agents in the formation. The scheme of the control algorithm, which does not make formation scalability possible, must be changed; therefore, seeking the scalability of training based on null space is a challenge that could be solved with the inclusion of consensus algorithms, which allow the control structure to be maintained despite increasing or decreasing the number of robot followers. Another advantage of this proposal is that the formation of the followers does not depend on any geometric figure compared to previous works based on the null space; this new proposal does not present singularities as if the structure is based on geometric shape, the latter one is crucial since the formation of agents can take forms that cannot be achieved with a geometric structure, such as collinear locations, that can occur in many environments. The proposed hybrid control approach presents three tasks: i) leader position task, ii) leader shape task, and iii) follower formation task. The proposed algorithm is validated through simulations, performing tests that use the kinematic model of non-holonomic mobile robots. In addition, linear algebra and Lyapunov theory are used to analyze the stability of the method.