Distributed Adaptive and Resilient Control of Multi-Robot Systems with Limited Field of View Interactions using Q-Learning

In this paper, we consider the problem of dynamically tuning gains for multi-robot systems (MRS) under potential based control design framework where the MRS team coordinates to maintain a connected topology while equipped with limited field of view sensors. Applying the potential-based control framework and assuming robot interaction is encoded by a triangular geometry, we derive a distributed control law in order to achieve the topology control objective. A typical shortcoming of potential-based control in distributed networks is that the overall system behavior is highly sensitive to gain-tuning. To overcome this limitation, we propose a distributed and adaptive gain controller that preserves a designed pairwise interaction strength, independent of the network size. Over that, we implement a control scheme that enables the MRS to be resilient against exogenous attacks on on-board sensors or actuator of the robots in MRS. In this regard, we model additive sensor and actuator faults which are induced externally to render the MRS unstable. However, applying $H_{\infty}$ control protocols by employing a static output-feedback design technique guarantees bounded $L_2$ gains of the error induced by the sensor and actuator fault signals. Finally, we apply policy iteration based Q-Learning to solve for adaptive gains for the discrete-time MRS. Simulation results are provided to support the theoretical findings.