Omnidirectional-Vision-Based Distributed Optimal Tracking Control

What is it about?

Although various methods of controlling mobile robots have been studied, the distributed tracking control problem for uncertain nonholonomic mobile multi-robot (NMMR) systems in an optimal manner with disturbance rejection for both kinematics and dynamics has not been thoroughly solved. This paper, therefore, devotes a novel method to solve the problem with application to real NMMR systems equipped with omnidirectional vision sensors of which parameters are unknown or uncalibrated. First, the distributed optimal tracking control problem of a separate system in the presence of kinematic and dynamic disturbances is transformed into the equivalent optimal regulation with disturbance rejection of an integrated system. Then, the theory of differential games is utilized to formulate the integrated system into coupled Hamilton-JacobiIsaac equations of which the solutions are approximated in real time by algorithms designed. By Lyapunov theory, it is proven that the algorithms converge, and the closedloop systems are stable. Finally, compared simulations and experiments for a group of three robots are provided to show the effectiveness of the proposed algorithms.

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Why is it important?

1. The distributed tracking control problem of NMMR systems in separation (strict-feedback form) under the influence of both kinematic and dynamic disturbances encountered when the robots use the OV sensors of which parameters are unknown or uncalibrated, is transformed into the equivalent distributed optimal regulation stabilization for an integrated system. Therefore, separate kinematic and dynamic control, as usual, is relaxed. 2. The new algorithms are proposed to approximate optimal control laws and disturbance policies while ensuring that tracking and function approximation errors are uniformly ultimately bounded. Compared with the existing ADP algorithms for optimal control subject to disturbance, our algorithms use only one NN for each robot and update control and disturbance inputs in only one iterative loop to reduce computational complexity and increase convergence speed. 3. In practice, ADP algorithms are applied to applications which require continuous improvements in performances, but knowledge to design optimal controllers is inadequate. Motivated by the existing ADP algorithms, our algorithms can be devoted to finding controllers for real NMMR systems in the presence of the kinematic and dynamic disturbances.