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Abstract

A method of solving the inverse kinematics problem for a humanoid robot modeled as a tree-shaped manipulator is presented. Robot trajectory consists of a set of trajectories of the characteristic points (the robot’s center of mass, origins of feet and hands frames) in the discrete time domain. The description of motion in the frame associated with the supporting foot allows one to represent the robot as a composite of several serial open-loop redundant manipulators. Stability during the motion is provided by the trajectory of the robot’s center of mass which ensures that the zero moment point criterion is fulfilled. Inverse kinematics solution is performed offline using the redundancy resolution at the velocity level. The proposed method utilizes robot’s redundancy to fulfill joint position limits and to reduce gravity-related joint torques. The method have been tested in simulations and experiments on a humanoid robot Melson, and results are presented.
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Authors and Affiliations

Kacper Mikołajczyk
1
Maksymilian Szumowski
1
Łukasz Woliński
1
ORCID: ORCID

  1. Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Warsaw, Poland
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Abstract

In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

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Authors and Affiliations

Jerzy Bałdyga
Grzegorz Tyl
Mounir Bouaifi

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