Robust optimal motion planning approach to cooperative grasping and transporting using multiple UAVs based on SDRE

Abstract

In this paper, we consider the problem of controlling a team of Quadrotors that cooperatively grasp and transport a common payload in three dimensions in the presence of external disturbances and parametric uncertainties such as wind field effects. The main contribution of this work is to propose a cooperative control algorithm based on a decentralized strategy. This algorithm consists of two main parts: first calculating the control vectors for each Quadrotor using Moore-Penrose theory and second combining these control vectors with individual control vectors, which are obtained from a closed-loop non-linear robust optimal controller. In this regard, a robust optimal sliding mode controller (ROSMC), which incorporates the statedependent Riccati equation (SDRE) method with sliding mode control (SMC) technique, is designed. It also has the capability of maximum dynamic load carrying capacity (DLCC) to increase the carrying capacity and the efficiency of the group of Quadrotors. The proposed method inherits the advantages of both approaches including robustness against model uncertainties and high flexibility in designing the control parameters to provide an optimal solution for the non-linear dynamic of the system. The control algorithm is based on the Lyapunov technique, which is able to provide the stability of the end-effecter during tracking of the desired trajectory with acceptable precision. Finally, the simulation results demonstrate the effectiveness of the control strategy for the cooperative Quadrotors to grasp and transport a common payload in various manoeuvres.

Self-tuning state-feedback control of a rotary pendulum system using adjustable degree-of-stability design

“…The State-Dependent-Riccati-Equation based control schemes offer to generate robust effort to regulate the performance of inherently unstable and nonlinear systems [22]. However, the accurate definition of state-dependent-coefficient matrices to fully realize the nonlinear characteristics of the system is difficult due to the system's complex dynamics [23].…”

Nonlinear sliding sector design for multi‐input systems with application to helicopter control

“…Optimal SMC approach was also applied in the control of spacecraft rendezvous process on elliptical orbits and from the comparative results with a SMC based on back‐stepping technique, both robust controllers enabled the chaser spacecraft to track the target effectively, even as some actuator faults occurred during the process . In another control problem, optimal SMC has been suggested as a remarkable solution to grasp and transport a payload by means of the cooperation of multiple unmanned aerial vehicle . However, optimal SMC has not lost its attraction yet since in a recent study, it was employed to control the trajectory tracking of a 2‐degrees of freedom (DoF) helicopter system …”

“…15 In another control problem, optimal SMC has been suggested as a remarkable solution to grasp and transport a payload by means of the cooperation of multiple unmanned aerial vehicle. 16 However, optimal SMC has not lost its attraction yet since in a recent study, it was employed to control the trajectory tracking of a 2-degrees of freedom (DoF) helicopter system. 17 The main problematic aspect of the conventional SMC is the chattering phenomena due to the finite switching frequency in the realization of SMC despite the theory's emphasis on switching at an infinitely high frequency.…”

Fully Coupled Six-DoF Nonlinear Suboptimal Control of a Quadrotor: Application to Variable-Pitch Rotor Design

“…Due to under-actuation, only Z direction was controlled. Babaie and Ehyaie proposed a robust SDRE, based on sliding mode design [4]. The position control was addressed through Lyapunov criteria for stabilization of sliding surfaces.…”