Integral backstepping control for trajectory and yaw motion tracking of quadrotors

A common approach to control of underactuated vehicles is a prelude to cooperative control of heterogeneous networks. This article presents a novel nonlinear trajectory tracking control framework for general three-dimensional models of underactuated vehicles with twelve states and four control inputs, including underwater, air, and space vehicles. Given a desired reference trajectory for four of the six degrees of freedom, feasible state trajectories are generated using the second-order nonholonomic constraints in the vehicle equations of motion. A novel transformation is then introduced to formulate the error dynamics in a simplified form. The error dynamics is stabilized using a traditional nonlinear control approach. The control law is shown to uniformly asymptotically stabilize all six pose states assuming bounded unknown uncertainties and disturbances. Adaptation of the method to underwater vehicles is presented along with simulation under highly nonlinear conditions. The approach is also applied to quadrotors and both simulation and experimental results are presented. K E Y W O R D Sbackstepping control, trajectory tracking control, underactuated vehicles INTRODUCTIONAutonomous vehicles have become more practical and thus more prevalent as a consequence of sensors, computers, and power electronics becoming better, cheaper, and smaller. However, controlling the motion of such vehicles is complex, as they tend to be underactuated, that is, fewer actuators than degrees of freedom. These include cars, surface vessels, underwater vessels, and air vehicles. In one of our previous works 1 we considered developing a control algorithm that can be applied to any planar underactuated vehicle. We then extended that work to Spatial vehicle models but with only one degree of underactuation. 2 In this work, we attempt to develop a control algorithm applicable to a variety of spatial underactuated vehicles with two degrees of underactuation including underwater vessels and air vehicles.Considering underwater vehicles, a submarine's propeller produces a surge force along the axis of motion; this is the translational actuator. There are also rotational actuators. A rudder induces yaw motion and diving planes induce pitching motion. 3 Roll motion, however, is a bit more complicated. Many manned submarines are designed to be passively self-righting and therefore do not have active roll control, with some exceptions where roll motion is desired, such as the DeepFlight Super Falcon. 4 There are several works that ignore the roll motion or at least its coupling with the other degrees of freedom and use five degree-of-freedom (DOF) models. [5][6][7] These methods concentrate on uncertainty and disturbance rejection as well as other important topics such as actuation limits and velocity estimation. 8

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“…Next, consider the error dynamics along the thrust direction represented by (26) and define the Lyapunov function candidate…”

Section: Backstepping Control Law Designmentioning

confidence: 99%

Trajectory tracking control of spatial underactuated vehicles

Fetzer

Nersesov

Ashrafiuon

2021

Intl J Robust & Nonlinear

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“…Then the problems need to be addressed here are stated as: 1. Use the DE proposed in formula (7) to estimate the nonlinear term F a = [F a (1), F a (2), F a (3)] T for compensation such that the attitude system robustness against disturbances from the unknown payloads can be enhanced.…”

Section: B Problem Propositiomentioning

confidence: 99%

“…Recently, quad-rotors have been widely applied in many areas [1]- [3], due to their merits of high maneuverability, free hovering, and vertical take-off/landing. To meet the task requirements, many effective approaches were developed, such as proportional-integral-derivative (PID) [4], linear quadratic regulator (LQR) [5], model reference adaptive control (MRAC) [6], feedback linearization (FL) [7], sliding model control (SMC) [8], back-stepping (BS) [9], and disturbance observer-based control (DOBC) [10]- [20].…”

Section: Introductionmentioning

confidence: 99%

Disturbance Attenuation Predictive Optimal Control for Quad-Rotor Transporting Unknown Varying Payload

et al. 2020

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Quad-rotor is very suitable for payload transportation due to the merits of high maneuverability and free hovering. However, the unknown varying payloads can cause negative influences that act in forms of persistent disturbances and sudden changes, damaging flight performance especially the attitude stability seriously. Targeting the persistent disturbances, an entirely novel disturbance estimator (DE) which can estimate non-smooth disturbances in a highly accurate manner for feedback compensation is proposed in this paper. To deal with the sudden changes from prescribed references and the payloads that may induce too large overshoots and input surging, a type of predictive optimal controller, which considers tracking errors and their changing rates of a class of linear multiple-input-multiple-output systems, is developed. Simulation results show that the system enhanced by the DE has better control performance than the ones enhanced by the commonly used extended state observer or nonlinear disturbance observer. Compared with the typical control approaches, the proposed control scheme enables the quad-rotor attitude system more stable performance and more ideal inputs on both persistent disturbance and sudden change resisting during payload transportation. INDEX TERMS Quad-rotor, payload transportation, disturbance attenuation, predictive optimal control.

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“…Moreover, the trajectory generation for the presented adaptive backstepping control is stated so that the quadrotor system has a feasible desired trajectory. The contributions of this paper are summarized as follows: (1) a backstepping-based adaptive control is proposed for quadrotor systems to track time-varying trajectories when the system parameters, mass and inertia, are unknown; nevertheless, dynamic parameters are required in [9,28] for regulation and in [8,29,30] for trajectory tracking, respectively; (2) the proposed adaptive tracking control is transferred to velocity control input by taking the uncertainties of motor coefficients in lifting force and moment torque, and geometric parameter into consideration; (3) a trajectory generation for both the scenarios of torque input and velocity input scenarios is presented based on the proposed adaptive backstepping controller; (4) simulation and experimental results are presented, and the proposed control algorithms could be extended to quadrotor systems in cable-suspended load, aerial transportation, cooperative transportation, and aerial manipulation.…”

Section: Introductionmentioning

confidence: 99%

Non‐linear adaptive tracking control for quadrotor aerial robots under uncertain dynamics

Liu

2021

IET Control Theory & Appl

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This paper presents the design, analysis, and implementation of an adaptive backstepping controller for underactuated quadrotors to track time‐varying trajectories with parameter uncertainties. Quadrotor systems are subject to complicated non‐linearity and coupling dynamics, so the ignorance of parameter uncertainties may cause performance degradation and even instability. With the concept of nominal input, the uncertain mass and inertia are decoupled from the lifting force and moment torque. By utilizing the backstepping technique, the design procedure with adaptive laws for dynamic parameters is proposed to ensure stability and convergence of tracking errors to the origin asymptotically. The proposed control scheme is extended to control a quadrotor with velocity motor input while the motor coefficients and geometric parameters are handled by the adaptive laws. A trajectory generation for the proposed adaptive tracking controller is addressed subsequently. The proposed controller requires only the position and orientation of the quadrotor with the twice‐differentiable trajectories, while previous work demanded acceleration information. Simulation and experimental results are illustrated to show the efficacy of tracking performance for object transportation.

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Integral backstepping control for trajectory and yaw motion tracking of quadrotors

Cited by 31 publications

References 44 publications

Trajectory tracking control of spatial underactuated vehicles

Trajectory tracking control of spatial underactuated vehicles

Disturbance Attenuation Predictive Optimal Control for Quad-Rotor Transporting Unknown Varying Payload

Non‐linear adaptive tracking control for quadrotor aerial robots under uncertain dynamics

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