Observer design for stable coordination of nonholonomic robotic systems under delayed measurements
Haonan Fan · 2019
In a multi-agent system implemented with multiple differential wheeled robots, the coordination control of these robots becomes an important topic. Considering the nonholonomic nature of differential wheeled robots, input/output linearization is an effective transformation technique that can help link between the robot states and multi-agent system states before applying multi-agent system theory to the physical system. However, when the system feedback suffers from relatively large delays, the linear condition might no longer hold, and the system with a linear controller could become unstable. In this thesis, a multi-agent consensus system subjected to delayed feedback is discussed in the context of coordinating differential wheeled robots. Starting with linear consensus dynamics, a delay margin can be found based on the eigenvalues of the system configuration matrix. Similar to the delay margin analysis, a strategy of choosing optimal coupling strengths ensuring fast consensus response for a known delay value is proposed. To deal with the non-linearity problem due to delayed orientation measurement in input/output linearization, observer-based controller frameworks with the optimal observer gain selection to compensate for the delay. Then, inspired by these results, a full-state observer framework with optimal observer gains selection is introduced to compensate for the delay effects on every state of the robots. The simulations indicate that this design gets faster dynamics compared to published work. Experiments on Georgia Tech Robotarium platform are provided to demonstrate the effectiveness of the full state observer, and further, the results are extended to robots with non-negligible inertia.