This paper is focused on tracking control for a rigid body payload that is connected to an arbitrary number of quadrotor unmanned aerial vehicles via rigid links. An intrinsic form of the equations ...of motion is derived on the nonlinear configuration manifold, and a geometric controller is constructed such that the payload asymptotically follows a given desired trajectory for its position and attitude in the presence of uncertainties. The unique feature is that the coupled dynamics between the rigid body payload, links, and quadrotors are explicitly incorporated into control system design and stability analysis. These are developed in a coordinate-free fashion to avoid singularities and complexities that are associated with local parameterizations. The desirable features of the proposed control system are illustrated by a numerical example.
Computational framework for optimal control of hybrid systems with a partitioned state space is presented. It is shown that necessary conditions for optimality for a discrete-time dynamic system can ...be solved concurrently for various boundary conditions, according to the recent development of discrete-time Hamilton–Jacobi theory. This unique property is utilized to construct computationally efficient numerical optimization of hybrid systems where discrete switching dynamics occurs at the boundary between partitions of the configuration space. A benchmark example shows that the proposed approach has substantial computational advantages compared with the existing ones.
This paper presents theoretical analysis and software implementation for real harmonics analysis on the special orthogonal group. Noncommutative harmonic analysis for complex-valued functions on the ...special orthogonal group has been studied extensively. However, it is customary to treat real harmonic analysis as a special case of complex harmonic analysis, and there have been limited results developed specifically for real-valued functions. Here, we develop a set of explicit formulas for real-valued irreducible unitary representations on the special orthogonal group, and provide several operational properties, such as derivatives, sampling, and Clebsch-Gordon coefficients. Furthermore, we implement both of complex and real harmonics analysis on the special orthogonal group into an open source software package that utilizes parallel processing through the OpenMP library. The efficacy of the presented results are illustrated by benchmark studies and an application to spherical shape matching.
This technical note presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to follow a given desired attitude ...trajectory, while guaranteeing almost semi-global exponential stability. It is generalized to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this technical note.
This paper studies a tracking control system for the attitude dynamics of a rigid body. By selecting an attitude error function carefully, we show that the proposed control system guarantees a ...desirable tracking performance uniformly for rotational maneuvers involving a large initial attitude error. A strict Lyapunov analysis is presented to show exponential stability, and a sufficient condition to avoid non-differentiable points of the attitude error function is also shown. The proposed control system is directly developed on the special orthogonal group to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. These are illustrated by numerical examples.
This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred ...to as the matrix Fisher distribution, is utilized to represent the uncertainties of attitude estimates and measurements in a global fashion. Various stochastic properties of the matrix Fisher distribution are derived on the special orthogonal group, and based on these, two types of intrinsic frameworks for Bayesian attitude estimation are constructed. These avoid complexities or singularities of the attitude estimators developed in terms of quaternions. The proposed approaches are particularly useful to deal with large estimation errors or large uncertainties for complex attitude maneuvers.
This brief describes robust adaptive tracking control systems for the attitude dynamics of a rigid body. Both the attitude dynamics and the proposed control system are globally expressed on the ...special orthogonal group, to avoid complexities and ambiguities associated with other attitude representations, such as Euler angles or quaternions. By designing an adaptive law for the inertia matrix of a rigid body, the proposed control system can asymptotically follow an attitude command without the knowledge of the inertia matrix, and it is extended to guarantee boundedness of tracking errors in the presence of unstructured disturbances. These are illustrated by the experimental results of the attitude dynamics of a quadrotor unmanned aerial vehicle.
The genomic structures of Vigna hirtella Ridl. and Vigna trinervia (B.Heyne ex Wight & Arn.) Tateishi & Maxted, key ancestral species of the allotetraploid Vigna reflexo-pilosa var. glabra (Roxb.) ...N.Tomooka & Maxted, remain poorly understood. This study presents a comprehensive genomic comparison of these species to deepen our knowledge of their evolutionary trajectories. By comparing the genomic profiles of V. hirtella and V. trinervia with those of V. reflexo-pilosa, we investigate the complex genomic mechanisms underlying allopolyploid evolution within the genus Vigna. Comparison of the chloroplast genome revealed that V. trinervia is closely related to V. reflexo-pilosa. De novo assembly of the whole genome, followed by synteny analysis and Ks value calculations, confirms that V. trinervia is closely related to the A genome of V. reflexo-pilosa, and V. hirtella to its B genome. Furthermore, the comparative analyses reveal that V. reflexo-pilosa retains residual signatures of a previous polyploidization event, particularly evident in higher gene family copy numbers. Our research provides genomic evidence for polyploidization within the genus Vigna and identifies potential donor species of allotetraploid species using de novo assembly techniques. Given the Southeast Asian distribution of both V. hirtella and V. trinervia, natural hybridization between these species, with V. trinervia as the maternal ancestor and V. hirtella as the paternal donor, seems plausible.
Adzuki bean (Vigna angularis var. angularis) is a dietary legume crop in East Asia. The presumed progenitor (Vigna angularis var. nipponensis) is widely found in East Asia, suggesting speciation and ...domestication in these temperate climate regions. Here, we report a draft genome sequence of adzuki bean. The genome assembly covers 75% of the estimated genome and was mapped to 11 pseudo-chromosomes. Gene prediction revealed 26,857 high confidence protein-coding genes evidenced by RNAseq of different tissues. Comparative gene expression analysis with V. radiata showed that the tissue specificity of orthologous genes was highly conserved. Additional re-sequencing of wild adzuki bean, V. angularis var. nipponensis, and V. nepalensis, was performed to analyze the variations between cultivated and wild adzuki bean. The determined divergence time of adzuki bean and the wild species predated archaeology-based domestication time. The present genome assembly will accelerate the genomics-assisted breeding of adzuki bean.
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