Geometric PID Control for Almost-Global Stabilization of a Quadrotor With Parameter Error and Constant Disturbances

2014 ◽  
Author(s):  
D. H. S. Maithripala ◽  
Jordan M. Berg
Keyword(s):  
Rigid Body ◽  
Pid Control ◽  
Parameter Uncertainty ◽  
Body Motion ◽  
Three Dimensions ◽  
Euler Angles ◽  
Time Varying ◽  
Global Stabilization ◽  
Quadrotor Uav ◽  
Integral Action

Intrinsic controllers are invariant under the coordinates used for their representation. In the case of rigid-body motion in two and three dimensions, the intrinsic approach eliminates problems with singularity or over-parametrization that may occur in specific choices such as Euler angles or quaternions. Intrinsic PD controllers that combine almost-global stabilization with a familiar and intuitive PD design framework have been known for several years. In this paper we show how intrinsic integral action may be added to intrinsic PD control. We apply the result to stabilize the attitude of a quadrotor UAV model, and demonstrate in simulation that performance is significantly improved in the presence of parameter uncertainty and constant disturbance forces. We also consider the effect of bounded, time-varying, disturbances.

Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in three dimensions

2011 ◽  
Vol 667 ◽  
pp. 474-519 ◽  
Author(s):  
HAMID ALEMI ARDAKANI ◽  
THOMAS J. BRIDGES
Keyword(s):  
Rigid Body ◽  
Shallow Water ◽  
Fluid Motion ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Three Dimensions ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Implicit Finite Difference Scheme ◽  
Shallow Water Models

New shallow-water equations (SWEs), for sloshing in three dimensions (two horizontal and one vertical) in a vessel which is undergoing rigid-body motion in 3-space, are derived. The rigid-body motion of the vessel (roll–pitch–yaw and/or surge–sway–heave) is modelled exactly and the only approximations are in the fluid motion. The flow is assumed to be inviscid but vortical, with approximations on the vertical velocity and acceleration at the surface. These equations improve previous shallow-water models. The model also extends to three dimensions the essence of the Penney–Price–Taylor theory for the highest standing wave. The surface SWEs are simulated using a split-step alternating direction implicit finite-difference scheme. Numerical experiments are reported, including comparisons with existing results in the literature, and simulations with vessels undergoing full 3-D rotations.

scholarly journals Time-varying Formation Dynamics Modeling and Constrained Trajectory Optimization of Multi-quadrotor UAVs

2021 ◽  
Author(s):  
Xi Li ◽  
Guoyuan Qi ◽  
Limin Zhang
Keyword(s):  
Rigid Body ◽  
Trajectory Optimization ◽  
Pseudospectral Method ◽  
Time Varying ◽  
Body Structure ◽  
Dynamics Modeling ◽  
Quadrotor Uav ◽  
Quadrotor Uavs ◽  
Turning Radius ◽  
Time Required

Abstract The formation of multiple quadrotor UAVs with long navigation will encounter many flight constraints, so it is necessary to change the formation to avoid these constraints. In this paper, Voronoi graph theory is used to treat UAVs formation as a rigid body. The rigid body structure can be changed by changing the formation before different constraints, after passing constraints the rigid body structure remains the formation unchanged or form into the prescribed formation. The time-varying model is established to facilitate the use of optimization. Based on Gauss pseudospectral method (GPM), the path optimization of a single quadrotor UAV is carried out. The followed UAVs in formation are treated as constraints. The constraints of maximum turning radius and formation transformation time of other UAVs are considered in the optimization process. The minimum time required for formation transformation is optimized to solve the transformation optimization, and the performance index of trajectory optimization is to minimize the energy consumed by the leader quadrotor UAV within the specified time. Finally, the simulation proves the method proposed in this paper.

scholarly journals Viscous Flow Around a Rigid Body Performing a Time-periodic Motion

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed
Keyword(s):  
Rigid Body ◽  
Sobolev Spaces ◽  
Periodic Motion ◽  
Viscous Incompressible Fluid ◽  
Body Motion ◽  
Translational Velocity ◽  
Ill Posed ◽  
Homogeneous Sobolev Spaces ◽  
The Mean ◽  
Time Periodic

AbstractThe equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

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