This work proposes a quaternion-based sliding variable that describes exponentially convergent error dynamics for any forward complete desired attitude trajectory. The proposed sliding variable directly operates on the non-Euclidean space formed by quaternions and explicitly handles the double covering property to enable global attitude tracking when used in feedback. In-depth analysis of the sliding variable is provided and compared to others in the literature. Several feedback controllers including nonlinear PD, robust, and adaptive sliding control are then derived. Simulation results of a rigid body with uncertain dynamics demonstrate the effectiveness and superiority of the approach.
This paper studies an attitude control system design based on modified Rodrigues parameters feedback. It employs a linear continuous sliding mode controller. The sliding mode controller is able to bring the existence of the sliding motion asymptotically. Besides, the attitude control system equilibrium point is proved to have an asymptotic stability guarantee through further analysis. This stability analysis is conducted since the sliding mode existence on the designed sliding surface does not imply the stability guarantee of the system's equilibrium. This paper ends with some numerical exampl…
Decoupled Thrust-Axis Attitude Control Using Quaternions for Chandrayaan-3 Lunar Landing Mission
Controls and Digital Area, U R Rao Satellite Centre, Indian Space Research Organization (ISRO), Bangalore, India（控制与数字领域部，U R Rao卫星中心，印度空间研究组织（ISRO），班加罗尔，印度）
This work deals with error models for trident quaternion framework proposed in the companion paper (Part I) and further uses them to investigate the odometer-aided static/in-motion inertial navigation attitude alignment for land vehicles. By linearizing the trident quaternion kinematic equation, the left and right trident quaternion error models are obtained, which are found to be equivalent to those derived from profound group affine. The two error models are used to design their corresponding extended Kalman filters (EKF), namely, the left-quaternion EKF (LQEKF) and the right-quaternion EKF …
Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This paper proposes a compact and elegant representation of the body's attitude, velocity and position, with the aid of a devised trident quaternion tool in which the position is…
University of Cincinnati（辛辛那提大学）；Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）
In this paper, we present an autonomous flight controller for a quadcopter with thrust vectoring capabilities. This UAV falls in the category of multirotors with tilt-motion enabled rotors. Since the vehicle considered is over-actuated in nature, the dynamics and control allocation have to be analysed carefully. Moreover, the possibility of hovering at large attitude maneuvers of this novel vehicle requires singularity-free attitude control. Hence, quaternion state feedback is utilized to compute the control commands for the UAV motors while avoiding the gimbal lock condition experienced by Eu…
In this note, we have revisited the previously published paper "Particle Filtering for Attitude Estimation Using a Minimal Local-Error Representation". In the revisit, we point out that the quaternion particle filtering based on the local/global representation structure has not made full use of the advantage of the particle filtering in terms of accuracy and robustness. Moreover, a normalized quaternion determining procedure based on the minimum mean-square error approach has been investigated into the quaternion-based particle filtering to obtain the fiducial quaternion for the transformation…
Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots
Center for Robotics and Biosystems, Northwestern University（西北大学机器人与生物系统中心）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Department of Mechanical Engineering, Carnegie Mellon University（卡内基梅隆大学机械工程系）
A Lyapunov-Based Switching Scheme for Selecting the Stable Closed-Loop Fixed Attitude-Error Quaternion During Flight
Washington State University（华盛顿州立大学）；California Institute of Technology（加州理工学院）；School of Mechanical and Materials Engineering, Washington State University（华盛顿州立大学机械与材料工程学院）
Over the past few decades, continuous quaternion-based attitude control has been proven highly effective for driving rotational systems that can be modeled as rigid bodies, such as satellites and drones. However, methods rooted in this approach do not enforce the existence of a unique closed-loop (CL) equilibrium attitude-error quaternion (AEQ); and, for rotational errors about the attitude-error Euler axis larger than πrad, their proportional-control effect diminishes as the system state moves away from the stable equilibrium of the CL rotational dynamics. In this paper, we introduce a new ty…
RodFIter is a promising method of attitude reconstruction from inertial measurements based on the functional iterative integration of Rodrigues vector. The Rodrigues vector is used to encode the attitude in place of the popular rotation vector because it has a polynomial-like rate equation and could be cast into theoretically sound and exact integration. This paper further applies the approach of RodFIter to the unity-norm quaternion for attitude reconstruction, named QuatFIter, and shows that it is identical to the previous Picard-type quaternion method. The Chebyshev polynomial approximation…
With the characteristics of vertical take-off and landing and long endurance, tiltrotor has attracted considerable attention in recent decades for its potential applications in civil and scientific research. However, the problems of strong couplings, nonlinear characteristics and mismatched disturbances inevitably exist in the tiltrotor, which bring great challenges to the controller design in transition mode. In this paper, we combined a super-twisting extended state observer (STESO) with an adaptive recursive sliding mode control (ARSMC) together to design a tiltrotor aircraft attitude syste…
The conceptual design and flight controller of a novel kind of quadcopter are presented. This design is capable of morphing the shape of the UAV during flight to achieve position and attitude control. We consider a dynamic center of gravity (CoG) which causes continuous variation in a moment of inertia (MoI) parameters of the UAV in this design. These dynamic structural parameters play a vital role in the stability and control of the system. The length of quadcopter arms is a variable parameter, and it is actuated using attitude feedback-based control law. The MoI parameters are computed in re…
Nanjing Telecommunication Technology Research Institute（南京电信技术研究所）；National University of Defense Technology（国防科技大学）
The realization of motion description is a challenging work for fixed-wing Unmanned Aerial Vehicle (UAV) acrobatic flight, due to the inherent coupling problem in ranslational-rotational motion. This paper aims to develop a novel maneuver description method through the idea of imitation learning, and there are two main contributions of our work: 1) A dual quaternion based dynamic motion primitives (DQ-DMP) is proposed and the state equations of the position and attitude can be combined without loss of accuracy. 2) An online hardware-inthe-loop (HITL) training system is established. Based on th…
Eindhoven University of Technology（埃因霍温理工大学）；University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）
The control of a quadrotor is typically split into two subsequent problems: finding desired accelerations to control its position, and controlling its attitude and the total thrust to track these accelerations and to track a yaw angle reference. While the thrust vector, generating accelerations, and the angle of rotation about the thrust vector, determining the yaw angle, can be controlled independently, most attitude control strategies in the literature, relying on representations in terms of quaternions, rotation matrices or Euler angles, result in an unnecessary coupling between the control…
Aimed at solving the problem of Attitude and Heading Reference System(AHRS) in the complex and dynamic conditions for small-UAV, An intelligent Singular Value Decomposition Cubature Kalman Filter(SVDCKF) combined with the Variable Adaptive Methods(VAM) is proposed in this paper. Considering the nonlinearity of quaternion AHRS model and non-positive definite of the state covariance matrix, the SVDCKF algorithm is presented with both the SVD and CKF in order to better obtain the filter accuracy and reliability. Additionally, there are the different changes of the values in the accelerometer meas…
Dual-quaternion learning control for autonomous vehicle trajectory tracking with safety guarantees
Universidad Politécnica de Madrid（西班牙马德里理工大学）；School of Science and Technology, IE University（IE大学科学与技术学院）；Universidad de San Andrés (UdeSA) and CONICET（阿根廷圣安德烈斯大学（UdeSA）和CONICET）；Centre for Automation and Robotics (CSIC-UPM)（自动化与机器人中心（CSIC-UPM））
The problems of point-cloud registration and attitude estimation from vector observations (Wahba's problem) have widespread applications in computer vision and mobile robotics. This work introduces a simple approach for integrating sets of geometric feature observations (points, lines, and planes) in such a way that any solution to either point-cloud registration or to Wahba's problem can be used to find the SE(3) transformation between the two sets that minimizes the corresponding cost function. We compare the performance of three solutions: classic Horn's optimal quaternion method, Optimal L…
We discuss the problem of designing and implementing controllers for insect-scale flapping-wing micro air vehicles (FWMAVs), from a unifying perspective and employing two different experimental platforms; namely, a Harvard RoboBee-like two-winged robot and the four-winged USC Bee+. Through experiments, we demonstrate that a method that employs quaternion coordinates for attitude control, developed to control quadrotors, can be applied to drive both robotic insects considered in this work. The proposed notion that a generic strategy can be used to control several types of artificial insects wit…
organization= Advanced Research Lab for Control；Agricultural Robotics (Sharif AgRoLab) Department of Mechanical Engineering, Sharif University of Technology , city= Tehran , country= Iran；Robotics Research Group Saxion University of Applied Science , city= Enschede , country= Netherlands
