Real-time nonlinear parameter estimation and tracking control of unmanned aerial vehicles in closed-loop

www.nature.com/scientificreports OPEN Real‑time nonlinear parameter estimation and tracking control of unmanned aerial vehicles in closed‑loop Imil Hamda Imran 1,2, Aydin Can 1, Rustam Stolkin 3 & Allahyar Montazeri 1* The real-time unknown parameter estimation and adaptive tracking control problems are investigated in this paper for a six degrees of freedom (6-DOF) of under-actuated quadrotor unmanned aerial vehicle (UAV). A virtual proportional derivative (PD) controller is designed to maintain the translational dynamics. Two adaptive schemes are developed to handle the attitude dynamics of the UAV with several unknown parameters. In the beginning, a classical adaptive scheme (CAS) using the certainty equivalence principle is proposed and designed. The idea is to design a controller for an ideal situation by assuming the unknown parameters were known. Then the unknown parameters are replaced by their estimation. A theoretical analysis is provided to ensure the trajectory tracking of the adaptive controller. However, an inherent drawback of this scheme is that there is no guarantee for the estimated parameters to converge to the actual values. To address this issue, a new adaptive scheme (NAS) is developed as the next step by adding a continuously differentiable function to the control structure. The proposed technique guarantees handling of the parametric uncertainties with an appropriate design manifold. A rigorous analytical proof, numerical simulation analyses, and experimental validation are presented to show the effectiveness of the proposed control design. Over the past decade, research and development on quadrotor UAV have drawn the attention of various researchers and industries. Quadrotor deployment has many potential benefits as compared to the traditional methods carried out by a human. Its deployment is specially useful for missions which are risky for humans. Further to improving the safety in executing tasks, it can also enhance the efficiency by saving the cost and time. Several UAV applications can be found in nuclear decommissioning, data collection, volcano monitoring, geographical photography, and creative industries1–3. From the control engineers’ perspective, one of the hottest research topics for autonomous operation and cognition of UAVs is to operate a single UAV or multiple UAVs interacting with other robots and sensors as a cyber-physical s ystem4,5. Many control approaches have been investigated under various settings5. The main objective in designing control systems for UAVs, is to make them more autonomous and less dependent to the operator while enabling the UAVs to have harsh maneuvers by compensating the nonlinearity and various sources of uncertainties the UAV might experience in realistic situations. UAV is an under-actuated nonlinear system, with four individual rotors to maintain a highly coupled six states as the system output. The rotors can be installed in a plus or cross configuration. The quadrotor has three states related to translational motion allowing UAV to move in the backward, forward, lateral, and vertical directions. The rest of the dynamics are related to the rotational or attitude motions, namely referred to as roll, pitch and yaw angles. The main concern in the trajectory tracking problem is to design the controller for the rotational dynamics. This is due to the natural behavior of UAV as an under-actuated system, where the position tracking control problem is maintained by controlling its attitude or rotational dynamics. Related works and main contributions The presence of nonlinearities in the system dynamics is one of the essential issues in designing the controller for the attitude dynamics. A proper and suitable nonlinear controller has an important role in maintaining the UAV motions with a full nonlinear behavior. Several studies have been presented to address the trajectory 1 Department of Engineering, Lancaster University, Bailrigg, Lancaster LA1 4YW, UK. 2Applied Research Center for Metrology, Standards and Testing, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. 3Extreme Robotics Lab (ERL), School of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK. *email: Scientific Reports | (2023) 13:3125 | https://doi.org/10.1038/s41598-023-29544-6 1 Vol.:(0123456789) www.nature.com/scientificreports/ tracking problem, especially for the attitude dynamics of UAVs. One of the common approaches is the feedback linearization method as developed in6,7. However, the parameters of the UAV are not always available or will change over time for the feedback control design in various practical situations. These unknown parameters may cause more complicated technical challenges in designing a proper controller. In general, there are two major research lines to tackle this issue. The first research direction is dealing with robust controllers. The idea behind this approach is to propose a feedback controller to dominate the uncertainties in the system dynamics. In this way, the controller guarantees to handle the uncertainties within a particular bound. This disadvantage of this approach is that the bound of the uncertainties should be available a priori to ensure the stability of the closed-loop control system. One of the popular methods in this research line is the sliding mode control (SMC). SMC is widely implemented in various practical situations as it is less sensitive to parametric uncertainties and disturbances as presented i n8–10. However, chattering is a common issue in designing SMC for the autonomous system. Several studies have been investigated to reduce the chattering as well as to compensate the effect of unmodelled dynamics as presented in11–13. The second major research line is adaptive control method. This approach is useful to handle the unknown constant parameters in the system dynamics. The traditional approach or CAS was initially proposed in the literature using the certainty equivalence principle. The idea behind this approach is to cancel the nonlinear terms containing unknown constant parameters. This scheme suggests a two-step control design procedure to handle the uncertainties. A controller under an ideal condition is designed in the first step, where all parameters are assumed to be known for feedback controller. In the second step, every unknown constant parameter is replaced by its estimation generated by an adaptive law along the gradient of Lyapunov function. The perfect cancellation of the nonlinear term is deemed to be achieved by driving the estimated parameter to converge to the actual value. This technique has a simple structure for practical implementation; however, it contains an inherent drawback. In this technique, there is no guarantee that the parameter estimation error converges to zero as it fully relies on the system dynamic states. The estimated parameters are updated constantly (even though they re (...truncated)