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.