A Geometric Formulation of Multirotor Aerial Vehicle Dynamics

2021 ◽  
Author(s):  
Youngsuk Hong ◽  
Ramy Rashad ◽  
Soocheol Noh ◽  
Taeyoon Lee ◽  
Stefano Stramigioli ◽  
...  
Keyword(s):  
Lie Group ◽  
Trajectory Optimization ◽  
Screw Theory ◽  
The Body ◽  
Dynamic Equations ◽  
Modeling Framework ◽  
Inertial Parameters ◽  
Rotor Wing ◽  
Aerial Vehicle ◽  
Geometric Formulation

Abstract A geometric dynamic modeling framework for generic multirotor aerial vehicles (MAV), based on a modern Lie group formulation of classical screw theory, is presented. Our framework allows for a broad range of rotor-wing con gurations: any number of rotors can be attached in arbitrary con gurations to either the body or wings, with the rotors and wings also tiltable. Our framework takes into account all masses and inertias of the MAV body and rotors, and accounts for both rotor thrust forces and moments as well as external aerodynamic and other forces. Compared to existing methods, our Lie group framework possesses several practical advantages useful for applications ranging from design optimization to model identi cation and trajectory optimization: (i) the dynamic equations can be easily transformed to coordinates of any reference frame; (ii) kinematic and mass-inertial parameters can be easily factored from the dynamic equations; (iii) exact, closedform analytic derivatives of the dynamics with respect to the con guration variables are easily derived. We demonstrate our systematic modeling procedure on examples of xed-tilt, variable-tilt, and hybrid MAVs with wings.

scholarly journals Perception of the dynamic visual vertical during sinusoidal linear motion

2017 ◽  
Vol 118 (4) ◽  
pp. 2499-2506 ◽  
Author(s):  
A. Pomante ◽  
L. P. J. Selen ◽  
W. P. Medendorp
Keyword(s):  
Vestibular System ◽  
Spatial Orientation ◽  
Linear Acceleration ◽  
The Body ◽  
Body Motion ◽  
Whole Body ◽  
Linear Motion ◽  
Modeling Framework ◽  
Visual Vertical ◽  
The Brain

The vestibular system provides information for spatial orientation. However, this information is ambiguous: because the otoliths sense the gravitoinertial force, they cannot distinguish gravitational and inertial components. As a consequence, prolonged linear acceleration of the head can be interpreted as tilt, referred to as the somatogravic effect. Previous modeling work suggests that the brain disambiguates the otolith signal according to the rules of Bayesian inference, combining noisy canal cues with the a priori assumption that prolonged linear accelerations are unlikely. Within this modeling framework the noise of the vestibular signals affects the dynamic characteristics of the tilt percept during linear whole-body motion. To test this prediction, we devised a novel paradigm to psychometrically characterize the dynamic visual vertical—as a proxy for the tilt percept—during passive sinusoidal linear motion along the interaural axis (0.33 Hz motion frequency, 1.75 m/s2peak acceleration, 80 cm displacement). While subjects ( n=10) kept fixation on a central body-fixed light, a line was briefly flashed (5 ms) at different phases of the motion, the orientation of which had to be judged relative to gravity. Consistent with the model’s prediction, subjects showed a phase-dependent modulation of the dynamic visual vertical, with a subject-specific phase shift with respect to the imposed acceleration signal. The magnitude of this modulation was smaller than predicted, suggesting a contribution of nonvestibular signals to the dynamic visual vertical. Despite their dampening effect, our findings may point to a link between the noise components in the vestibular system and the characteristics of dynamic visual vertical.NEW & NOTEWORTHY A fundamental question in neuroscience is how the brain processes vestibular signals to infer the orientation of the body and objects in space. We show that, under sinusoidal linear motion, systematic error patterns appear in the disambiguation of linear acceleration and spatial orientation. We discuss the dynamics of these illusory percepts in terms of a dynamic Bayesian model that combines uncertainty in the vestibular signals with priors based on the natural statistics of head motion.

scholarly journals Pelvic Construct Prediction of Trabecular and Cortical Bone Structural Architecture

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Dan T. Zaharie ◽  
Andrew T. M. Phillips
Keyword(s):  
Cortical Bone ◽  
Structural Model ◽  
Thickness Distribution ◽  
Bone Adaptation ◽  
The Body ◽  
Lower Limbs ◽  
Fe Model ◽  
Adaptation Algorithm ◽  
Modeling Framework ◽  
Good Agreement

The pelvic construct is an important part of the body as it facilitates the transfer of upper body weight to the lower limbs and protects a number of organs and vessels in the lower abdomen. In addition, the importance of the pelvis is highlighted by the high mortality rates associated with pelvic trauma. This study presents a mesoscale structural model of the pelvic construct and the joints and ligaments associated with it. Shell elements were used to model cortical bone, while truss elements were used to model trabecular bone and the ligaments and joints. The finite element (FE) model was subjected to an iterative optimization process based on a strain-driven bone adaptation algorithm. The bone model was adapted to a number of common daily living activities (walking, stair ascent, stair descent, sit-to-stand, and stand-to-sit) by applying onto it joint and muscle loads derived using a musculoskeletal modeling framework. The cortical thickness distribution and the trabecular architecture of the adapted model were compared qualitatively with computed tomography (CT) scans and models developed in previous studies, showing good agreement. The sensitivity of the model to changes in material properties of the ligaments and joint cartilage and changes in parameters related to the adaptation algorithm was assessed. Changes to the target strain had the largest effect on predicted total bone volumes. The model showed low sensitivity to changes in all other parameters. The minimum and maximum principal strains predicted by the structural model compared to a continuum CT-derived model in response to a common test loading scenario showed good agreement with correlation coefficients of 0.813 and 0.809, respectively. The developed structural model enables a number of applications such as fracture modeling, design, and additive manufacturing of frangible surrogates.

Investigation on Kane dynamic equations based on screw theory for open-chain manipulators

2005 ◽  
Vol 26 (5) ◽  
pp. 627-635 ◽  
Author(s):  
Liu Wu-fa ◽  
Gong Zhen-bang ◽  
Wang Qin-que
Keyword(s):  
Screw Theory ◽  
Dynamic Equations ◽  
Open Chain

Dynamic Modeling of Robotic Fish Caudal Fin With Electrorheological Fluid-Enabled Tunable Stiffness

2015 ◽  
Author(s):  
Sanaz Bazaz Behbahani ◽  
Xiaobo Tan
Keyword(s):  
Equations Of Motion ◽  
Electrorheological Fluid ◽  
Robotic Fish ◽  
Dynamic Equations ◽  
The Finite Element Method ◽  
Modeling Framework ◽  
Caudal Fin ◽  
Body Theory ◽  
Tunable Stiffness ◽  
Er Fluid

In this study, we investigate the modeling framework for a robotic fish actuated by a flexible caudal fin, which is filled with electrorheological (ER) fluid and thus enables tunable stiffness. This feature can be used in optimizing the robotic fish speed or maneuverability in different operating regimes. The robotic fish is assumed to be anchored and the flexible tail undergoes undulation activated by a servomotor at the base. Lighthill’s large-amplitude elongated-body theory is used to calculate the hydrodynamic force on the caudal fin, and Hamilton’s principle is used to derive the dynamic equations of motion of the caudal fin. The dynamic equations are then discritized using the finite element method, to obtain an approximate numerical solution. In particular, simulation is conducted to understand the influence of the applied electric field on the stiffness and thrust performance of the caudal fin.

Elastic Formation Keeping Control of Unmanned Aerial Vehicle Adapting to Flight Speed

2013 ◽  
Vol 367 ◽  
pp. 411-416 ◽  
Author(s):  
Guang Yan Xu ◽  
Yi Bo Shi
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Relative Position ◽  
State Feedback ◽  
Feedback Controller ◽  
Flight Speed ◽  
Dynamic Equations ◽  
Aerial Vehicle ◽  
Distance Vector ◽  
Simulation Results ◽  
Formation Keeping

For an Unmanned Aerial Vehicle (UAV) formation in leader-follower mode, considering the relative position relationship between neighbor vehicles in the formation, an elastic distance vector is proposed. The dynamic equations of a flight speed adaptive UAV formation are established using the elastic distance vector we proposed. The state feedback controller is designed. Simulation results show that the controller can be used to control the follower vehicles to follow the leader vehicle maneuvering effectively and keep the desired formation well, most importantly, the relative distance between neighbor vehicles in the formation is adapted to the changes of flight speed.

The Robust Adaptive Control of Free-Floating Space Manipulator Systems

2001 ◽  
Author(s):  
Chen Li ◽  
Liu Yanzhu
Keyword(s):  
Adaptive Control ◽  
Jacobian Matrix ◽  
Robust Adaptive Control ◽  
Dynamic Equations ◽  
Generalized Jacobian ◽  
Space Manipulator ◽  
Floating Base ◽  
Inertial Parameters ◽  
Control Scheme ◽  
Robust Adaptive

Abstract In this paper, the kinematics and dynamics of free-floating space manipulator systems are analyzed, and it is shown that the Jacobian matrix and the dynamic equations of the system are nonlinearly dependent on inertial parameters. In order to overcome the above problems, the system is modeled as under-actuated robot system, and the idea of augmentation approach is adopted. It is demonstrate that the augmented generalized Jacobian matrix and the dynamic equations of the system can be linearly dependent on a group of inertial parameters. Based on the results, the robust adaptive control scheme for free-floating space manipulator with uncertain inertial parameters to track the desired trajectory in workspace is proposed, and a two-link planar space manipulator system is simulated to verify the proposed control scheme. The proposed control scheme is computationally simple, because we choose to make the controller robust to the uncertain inertial parameters rather than explicitly estimating them online. In particular, it require neither measuring the position, velocity and acceleration of the floating base with respect to the orbit nor controlling the position and attitude angle of the floating base.

scholarly journals UAV-Enabled Data Collection: Multiple Access, Trajectory Optimization, and Energy Trade-Off

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Lin Xiao ◽  
Yipeng Liang ◽  
Chenfan Weng ◽  
Dingcheng Yang ◽  
Qingmin Zhao
Keyword(s):  
Resource Allocation ◽  
Data Collection ◽  
Unmanned Aerial Vehicle ◽  
Trajectory Optimization ◽  
Minimum Energy ◽  
Trajectory Design ◽  
Energy Trade ◽  
Significant Performance ◽  
Aerial Vehicle ◽  
Resource Allocation Scheme

In this paper, we consider a ground terminal (GT) to an unmanned aerial vehicle (UAV) wireless communication system where data from GTs are collected by an unmanned aerial vehicle. We propose to use the ground terminal-UAV (G-U) region for the energy consumption model. In particular, to fulfill the data collection task with a minimum energy both of the GTs and UAV, an algorithm that combines optimal trajectory design and resource allocation scheme is proposed which is supposed to solve the optimization problem approximately. We initialize the UAV’s trajectory firstly. Then, the optimal UAV trajectory and GT’s resource allocation are obtained by using the successive convex optimization and Lagrange duality. Moreover, we come up with an efficient algorithm aimed to find an approximate solution by jointly optimizing trajectory and resource allocation. Numerical results show that the proposed solution is efficient. Compared with the benchmark scheme which did not adopt optimizing trajectory, the solution we propose engenders significant performance in energy efficiency.

The Geometry of Virtual Work Dynamics in Screw Space

1992 ◽  
Vol 59 (2) ◽  
pp. 411-417 ◽  
Author(s):  
Steven Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Virtual Work ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Coordinate Space ◽  
Dynamical Equations ◽  
Least Action ◽  
System Of Rigid Bodies ◽  
Configuration Manifold

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.

Application of Screw Theory to Rigid Body Dynamics

1992 ◽  
Vol 114 (2) ◽  
pp. 262-269 ◽  
Author(s):  
G. R. Pennock ◽  
B. A. Oncu
Keyword(s):  
Rigid Body ◽  
Euler Equation ◽  
Computer Aided Design ◽  
Graphical Representation ◽  
Screw Theory ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Dynamic State ◽  
Disk Rolling ◽  
Insight Into

This paper applies screw theory to the dynamic analysis of a rigid body in general spatial motion. Particular emphasis is placed upon the geometric interpretation of the velocity screw, the momentum screw, and the force screw which provide valuable physical insight into the dynamic behavior of the rigid body. The geometric relation between the velocity screw and the momentum screw is discussed in some detail. The paper shows that the dual angle between the two screws provides insight into the kinetics of the rigid body. The dynamic state of motion of the body is then described by a dual vector equation, referred to as the dual Euler equation. The paper shows that the geometric equivalent of the dual Euler equation is a spatial triangle which can be used as a graphical method of solution, or as a check, of the analytical formulation. The concepts introduced in this paper are illustrated by the well-known example of a thin, homogeneous, circular disk rolling without slipping on a flat horizontal surface. With the widespread use of computer graphics and computer-aided design, the geometric approach presented here will prove useful in the graphical representation of the dynamics of a rigid body.

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