Zarzirbird1 project: Modeling RPAS dynamics for load stability

This paper presents a new mathematical modeling approach of flight behavior for a Remote Piloted Aircraft System (RPAS). The use of RPAS as an aircraft able to perform a commercial or personal service has been an incentive for many investigations, where we can pinpoint an example in how they behave with a load. The maximum altitude of RPAS, for example, is limited technically, with constrains related to the structural RPAS weight, and then subdivided on different categories as discussed in [5, 6] (see also Figure 1). For the flight operation there are definitions around the maximum flight level considering its embedded technologies characteristics [7, 8, 3]; there are considerations over the physical structure aspects that define each aircraft categories, and also it is important to understand the limit working capability of the RPAS, i.e. altitude [9]. In normal operation, selected information from RPAS motion is captured by physical onboard sensors and transmitted to the ground control, communicating its flight status. All the above mentioned data can be used to improve flight safety and to help in dealing with flight stability when carrying a load, thereby controlling motion from an RPAS aircraft and reducing the impact on the load, and vice versa. In this paper we focus on load stability adopting a new mathematical modeling approach to provide a safe flight behavior; this model considers the vibrational motion of the attached load to the center of mass of RPAS, and it considers the impact of possible external (wind and mechanical impacts) and internal agents (failures of engines). A common problem presented by a RPAS aircraft flight refers to the loss of motion referential, which occurs because Euler angles suffer from the Gimbal Lock, i.e, when the middle gimbal θ angle approaches ±90° degrees, and effectively occurs when |θ| > 90° - ε where ε is an angle which depends on the body rates and the system hardware [10]. The combined work of the gyroscope and accelerometer sensors to establish an orientation of flight could cause this effect of instability [11]. In this (w) core of physical control system (we named it Zarzirbird duo to its similarities with the homonymous bird flight patterns). A hexacopter is being considered as the RPAS throughout this paper to determine the aircraft model. The goal is to keep stability of a determined attached load on a RPAS aircraft for which a definition of mathematical modelling is presented. This mathematical approach explores the quaternions formulation in a spatial orientation, allowing a better motion control than the traditional modelling. It uses both Newton´s Law and Euler-Larange´s Equations, where the Lagrangian mechanics helps in solving the specific problem of calculus of variations. The proposed modelling has been validated in both normal and bad flight conditions, considering the occurrence of both internal and external events like wind variations, propeller damage limits and different environmental conditions.