Formulation of Fault-tolerant Control for Hyper-redundant Multi-copters

Fault-tolerant control (FTC) is known as a typical example of fail-safe systems applied to multi-copters. In particular, FTC, in which the control systems are reconfigured by linear virtual actuators, can clarify the relationship between the arrangement of rotational directions of the propellers and the reconfigurability by analyzing the structural controllability of the systems. In this study, the PNPN structure and the PPNN structure are introduced as the definitions of rotational directions of the propellers, where P and N are the propellers that generate positive and negative yaw rotations, respectively. In the former structure, propellers P and N are arranged alternately, while in the latter structure, propellers P and N are arranged in groups. In order to study the fault-tolerance of multi-copters with ten or more rotors, the structural controllability of the systems is expressed as general equations.In order for systems to be structurally controllable, they must satisfy the conditions for input-connectivity and for structural rank. Accordingly, these two conditions are formulated using the positions of the failed rotors as parameters. It is shown that the systems are always structurally controllable when the condition on the structural rank is satisfied. Analyzing the formulated structural controllability, the PNPN structure is proved to be superior in structure from the viewpoints of fault-tolerance.