Manuscript Topics

Using attitude parameterization sets, such as Euler angles or quaternions, in dynamics analysis and control design for rotational and translational motions can result in singularities, nonuniqueness, and discontinuous control.  Treatment of dynamics and control in special orthogonal group SO(3) or special Euclidean group SE(3) and their tangent bundles mitigates the attitude parameterization sets issues.  Furthermore, formalism on SE(3) provides an alternative to the traditional strategy of separate analysis/control design for the translational and rotational motions of a rigid body by combining them into one formalism.  The group-theoretic formalism of SO(3) and SE(3) enables the use of additional mathematical tools and gives rise to deeper insight into rigid body motion.

While this special issue concentrates on leveraging geometric mechanic techniques in rigid body motion analysis, it considers original research and advancements relevant, but not limited to, any of the following topics:

• Variational integrators
• Discrete Euler-Poincaré and Lie-Poisson equations
• Dynamics analysis, stabilization, and geometric control
• Estimation and filtering in geometric mechanics framework
• Constrained motion analysis on Lie groups
• Static/dynamic rigid-body optimization on Riemannian manifolds
• Multibody dynamics on Lie groups
• Application of differential geometry in rigid body systems

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